Archimedes in the Middle Ages, Vol. 4: A supplement on the Medieval Latin traditions of conic sections (1150-1566). Part ii 087169137X, 9780871691378 [PDF]

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ARCHIMEDES in the Middle Ages VOLUME FOUR Memoirs of the AMERICAN PHILOSOPHICAL SOCIETY held at Philadelphia

A SUPPLEMENT ON THE MEDIEVAL LATIN TRADITIONS OF CONIC SECTIONS ( 1150- 1566)

for Promoting Useful Knowledge Volume 137

Part B

P a r t II:

Bibliography, Diagrams, and Indexes

MARSHALL CLAGETT

THE AMERICAN PHILOSOPHICAL SOCIETY Independence Square Philadelphia 1980

PART II Copyright 1980 by the American Philosophical Society

Bibliography, Diagrams, and Indexes

Library of Congress Catalog Card Number 62-7218 International Standard Book Number 0-87169-137-X US ISSN 0065-9738

BIBLIOGRAPHY Alberti, L. B. Della prospettiva. Ed. of A. Bonucci in Opere volgari, Vol. 4, Florence, 1847. Albertus Magnus. Book o f M inerals. Trans, of D. Wyckof, Oxford, 1967. ---------------. Mineralium libri V . Ed. of A. Borgnet in Opera omnia, Vol. 5, Paris, 1890. Alhazen, see Ibn al-Haytham. Amodeo, F. “ II trattato delle coniche di Francesco Maurolico,’’ Bibliotheca mathematica, 3. Folge, Vol. 9 (1908-09), pp. 123-38. Anonymous. De duabus lineis semper approximantibus sibi invicem et nunquam concur­ rentibus. See my edition and English translation in Chap. 2 above. -------------- . De sectione optimi speculi: vocatur Mukefi. For MSS, see Chap. 5, η. 1. -------------- . Speculi almukefi compositio. See my edition and English translation in Chap. 4 above. Note my edition also of Regiomontanus’ version of this work in Chap. 5 above, where variant readings are given to A. H. Gogava’s edition of 1548 under the title De sectione conica orthogona quae parabola dicitur (see Ptolemy below). Anthemius of Tralles. See Huxley, G. L., below. Apollonius of Perga. Apollonii Pergaei Conicorum libri IV. Cum commentariis R. P. Claudii Richardi. Antwerp, 1655. -------------- .Apollonii Pergaei Conicorum libri octo et Sereni Antissensis De sectione cylindri et coni libri duo. Ed. of E. Halley. Oxford, 1710. ---------------. Apollonii Pergaei Conicorum libri quattuor, una cum Pappi Alexandrini lem­ matibus et commentariis Eutocii Ascalonitae, Sereni Antinsensis philosophi libri duo. Trans, and commentaries by F. Commandino. Bologna, 1566. ---------------. Apollonii Pergaei Conicorum sectionum libri V. VI. et VII. Trans, from the Arabie of Christianus Ravius. Kilonii, 1669. -------------- . Apollonii Pergei philosophi, mathematicique excellentissimi Opera. Trans, of G. B. Memmo. Venice, 1537. -------------- . Apollonii Pergaei Quae graece exstant cum commentariis antiquis. Ed. of J. L. Heiberg, 2 vols., Leipzig, 1891-93. Abbreviated as Gr 1 and Gr 2. ---------------. Apollonius o f Perga. The Treatise on Conic Sections. Paraphrase of T. L. Heath. Cambridge, 1896, repr. 1961. -------------- . Conics. Arabic translation by Hilal ibn Abi Hilal al-Himsi. Ms. Oxford, Bodl. Library, Marsh 667. -------------- . Conics (Books I—III). English transl. by R. C. Taliaferro in Great Books o f the Western World. Vol. 11, Chicago, 1952. -------------- . Elementa conica Apollonii Paergei (!) et Archimedis opera nova et breviori methodo demonstrata a Ioanne Alphonso Borellio. Rome, 1679. -------------- . Francisci Maurolyci Messanensis Emendatio et restitutio Conicorum Apollonii Pergaei. Messina, 1654. -------------- . Liber de pyramidibus. A fragment trans, into Latin by Gerard of Cremona, in Heiberg’s Apollonii Pergaei Quae graece exstant, Vol. 2, pp. L X X III-LX X X . See also MS Paris, BN lat. 9335, 85v-86r. -------------- . See also L. M. L. Nix. 'Arafat, W. See Ibn al-Haytham. Archimedes. Opera omnia. Ed. of J. L. Heiberg. 3 vols., Leipzig, 1910-15. -------------- . The Works o f Archimedes. English trans, and paraphrase by T. L. Heath. Cambridge, 1897; repr., New York, 1950. -------------- . See Dijksterhuis, E. J., below, and also the numerous entries in the Bibliog­ raphy appended to Vol. 3 of my Archimedes in the Middle Ages. Barozzi, F. Admirandum illud geometricum problema tredecim modis demonstratum: Quod docet duas lineas in eodem plano designare, quae nunquam invicem coincidant, etiam si in infinitum protrahantur: et quanto longius producuntur, tanto sibiinvicem propriores evadunt. Venice, 1586. See Chap. 7, Text B.

465

466

ARCHIMEDES IN THE MIDDLE AGES Bauch, G. Die Anfdnge des Humcmismus in Ingolstadt, in Historische Bibliothek, Vol. 13 (Munich/Leipzig, 1901). Boncompagni, B. “ Intorno alia vita ed ai lavori di Francesco Barozzi,” Bullettino di bibliografia e di storia delle scienze matematiche e fisiche, Vol. 17 (1884), pp. 795-848. -------------- . See Leonardo Fibonacci. Borelli, G. A. See Apollonius. Boyer, Μ. N. “ Barocius, Franciscus,” Dictionary o f Scientific Biography, Vol. 1, New York, 1970, p. 468. British Library. A Catalogue o f the Manuscripts o f the Cottonian Library Deposited in the British Museum. Vol. 1, London, 1802. Calcagnini, C. Opera aliquot. Basel, 1544. Camerarius, J., See Durer, A. Campanus. See Euclid. Cantor, M., Vorlesungen iiber Geschichte der Mathematik. Vol. 2, 2nd ed., Leipzig, 1913. Cardano, G. De subtilitate libri X XI. Nuremberg, 1550. Augmented ed., Basel, 1554. Cavalieri, B. Lo specchio ustorio. Bologna, 1632. Clagett, M. “ A Medieval Latin Translation of a Short Arabic Tract on the H yperbola,” Osiris, Vol. 11 (1954), pp. 359-85. -------------- . Archimedes in the Middle Ages. Vol. 1, Madison, Wise., 1964. Vols. 2 -3 , Philadelphia, 1976-78. -------------- . “ The Life and Works of Giovanni Fontana,” Annali dell’Istituto e Museo di Storia della Scienza di Firenze, Anno I (1976), pp. 5-28. -------------- . “ The Works of Francesco Maurolico,” Physis, Anno XVI (1974), pp. 149-98. Curtze, Μ. “ II. Der Briefwechsel Regiomontan’s mit Giovanni Bianchini, Jacob von Speier und Christian Roder,” Urkunden zur Geschichte der Mathematik im Mittelalter und der Renaissance, in Abhandlungen zur Geschichte der mathematischen Wissenschaften, XII. Heft (1902), pp. 185-336. Devreese, R. Le Fonds grec de la Bibliotheque Vaticane des origines a Paul V. Citta del Vaticano, 1965. Dijksterhuis, E. J. Archimedes. Copenhagen, 1956. Diodes. Burning Mirrors. The Arabic Translation o f the Lost Greek Original. Ed. and transl. of G. J. Toomer. Heidelberg / New York, 1976. Durer, A. Albertus Durerus Nurembergensis . . . versus e Germanica lingua in Latinam . . . Quatuor his suarum institutionum geometricarum libris, lineas, superficies et solida corpora tractavit, adhibitis designationibus ad eam rem accommodissimis. Latin trans, of Unterweysung der Messung by J. Camerarius. Paris, 1532. I have cited this under the title Institutiones geometricae. -------------- . Unterweysung der Messung. Nuremberg, 1525. Fasc. reprint, Zurich, 1966. Efodi. See Profiat Duran. Emden, A. B. A Biographical Register o f the University o f Oxford. Vol. 1, Oxford, 1957. Euclid. Euclidis Megarensis . . . Elementorum geometricorum libri λ:v. Basel, 1546. One of the standard editions that contains both the Campanus and Zamberti versions. -------------- . Elementorum geometricorum libri tredecim ex traditione doctissimi NasiriDini Tusini: nunc primum Arabice impressi. Rome, 1594. Eutocius. See Apollonius and Archimedes, where the various editions that contain these au­ thors and Eutocius’ commentaries are listed. Under Apollonius, see in particular the versions of Commandino, Halley, and Heiberg. Under Archimedes, see the edition of Heiberg. Also consult the Index of Names and Works under Eutocius. Fibonacci, Leonardo. See Leonardo. Fine, O. De speculo ustorio, ignem ad propositam distantiam generante, liber unicus. Ex quo duarum linearum semper approprinquantium et nunquam concurrentium colligi­ tur demonstratio. Paris, 1551. See corrected ed. in Chap. 7, Text A. Folkerts, M. “ Werner, Johann,” Dictionary o f Scientific Biography, Vol. 14, New York, 1976, pp. 272-77.

BIBLIOGRAPHY Fontana, Giovanni. Dicta atque notata. Notes on Alhazen’s De speculis comburentibus, which I have edited and translated as Text B of Chap. 5 above. France. Catalogue general des manuscrits des bibliotheques publiques de France. Departements. Vol. 5: Dijon. Paris, 1889. Fusoris, Jean. His version of Witelo’s Perspectiva. For the MS and extracts from it, see above, Chap. 5, n. 9. -------------- . Libellus de seccione mukefi. See my edition and English translation as Text A in Chap. 5 above. Gerard of Cremona. See Apollonius and Ibn al-Haytham. Ghetaldi, M. Nonnullae propositiones de parabola. Rome, 1603. Gogava, A. H. See Ptolemy and Anonymous, Speculi almukefi compositio. Heath, T. L. A History o f Greek Mathematics. Vol. 2, Oxford, 1921. ---------------. “ The fragment of Anthemius on burning mirrors and the 'Fragmentum mathe­ maticum Bobiense’,” Bibliotheca mathem atica, 3. Folge, Vol. 7 (1906-07), pp. 22533. -------------- . See Apollonius and Archimedes. Heiberg, J. L. “ Die Kenntnisse des Archimedes iiber die Kegelscnitte,” Zeitschrift fu r M athematik und Physik, XXV. Jahrg. (1880), Hist.-lit. Abtheilung, pp. 41-67. -------------- . See Apollonius and Archimedes. Heiberg, J. L. and E. Wiedemann, “ Eine arabische Schrift iiber die Parabel und parabolische Hohlspiegel,” Bibliotheca mathematica, 3. Folge, Vol. 11 (1910-11), pp. 193 — 208. Huillard-Breholles, J. L. A. Historia diplomatica Friderici Secundi. Vol. 2, Paris, 1852. Vol. 5, Paris, 1859. Huxley, G. L. Antemius o f Tralles: A Study in Later Greek Geometry. Cambridge, Mass., 1959. Ibn al-Haytham. De speculis comburentibus. Latin text, analysis and German trans, in J. L. Heiberg and E. Wiedemann, “ Ibn al Haitams Schrift iiber parabolische Hohlspiegel,” Bibliotheca mathematica, 3. Folge, Vol. 10 (1909-10), pp. 201-37. Cf. MS. Paris, BN lat. 9335, 86r-88v. See also English trans, in H. J. J. Winter and W. 'Arafat, “ Ibn al-Haitham on the Paraboloidal Focussing M irror,” Journal o f the Royal Asiatic Society o f Bengal. Science, Vol. 15 (1949), pp. 25-40. -------------- . Majamit' al-rasa’il . . . . ibn al-Haitham (Arabic), Hyderabad, 1357 A. H. -------------- . Perspectiva. Latin trans, published by F. Risner in Opticae thesaurus Alhazeni Arabis libri septem . . . Item Vitellonis Thuringopoloni opticae libri X. Basel, 1572. Separate pagination for each of the works. For Latin MSS of Alhazen, see Chap. 1 above, n. 41. -------------- . See Woepcke, F. Kepler, H. A d Vitellionem paralipomena quibus Astronomiae pars optica traditur. Frankfurt, 1604. -------------- . Nova stereometria doliorum . . . Accessit Stereometriae Archimedeae Sup­ plementum. Lincii, 1615. Knorr, W. R. “ Archimedes’ Neusis-Constructions in Spiral Lines,” Centaurus, Vol. 22 (1978), pp. 77-98. Krause, M. “ Stambuler Handschriften islamischer M athematiker,” Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abt. B: Studien, Vol. 3 (1936), pp. 437-532. La Hire, P. de. Sectiones conicae. Paris, 1685. Leonardo Fibonacci. Scritti di Leonardo Pisano. Ed of B. Boncompagni. Vol. 2, Rome, 1862. Lindberg, D. C. A Catalogue o f Medieval and Renaissance Optical M anuscripts. Toronto, 1975. -------------- . John Pecham and the Science o f Optics.Madison, 1970.

467

468 ARCHIMEDES IN THE MIDDLE AGES Madan, F. A Summary Catalogue o f Western Manuscripts in the Bodleian Library at Oxford. Vol. 4. Oxford, 1897. Maimonides, Moses. Dux seu Director dubitantium aut perplexorum. Paris, 1520. -------------- . The Guide o f the Perplexed. Trans, of S. Pines. Chicago, 1963. Margoliouth, G. Catalogue o f the Hebrew and Samaritan Manuscripts in the British Museum. Part III. London, 1915. Maurolico, F. Opuscula mathematica. Venice, 1575. -------------- . See Apollonius and Clagett, M. Memmo, G. B. See Apollonius. Mirot, L. “ La Proces de maitre Jean Fusoris,” Memoires de la Societe de I'Histoire de Paris et de TIle-de-France, Vol. 27 (1900), pp. 137-287. Moise Provenzale. Opera nova di giometria in dimostrare come possano uscire due linee sopra una superficie le quali proccedeno si accostino sempre ne poseno incontrarsi mai, cosa meravigliosa e prodotta per verace e certa damo Mose d ’Egitto Heb. nel suo Directio dubitantium a cap. 73 del primo composta per Magistro Moise Pro­ venzale Hebreo. Mantua, 1550. Motot, Simeon. See Sacerdote, G. Mugler, C. Dictionnaire historique de la terminologie geometrique des Grecs. Paris, 1958. Murdoch, J. E. “ Euclides Graeco-Latinus. A Hitherto Unknown Medieval Latin Translation of the Elements Made Directly from the G reek,” Harvard Studies in Classical Phi­ lology, Vol. 71 (1966), pp. 249-302. Nebbia, G. “ Ibn al-Haytham nel millesimo anniversario della nascita,” Physis, Anno 9 (1967), pp. 165-214. Nix, L. M. L., Das funfte Buch der Conica des Apollonius von Perga in der arabischen Vbersetzung des Thabit ibn Corrah. Leipzig, 1889. Pappus. Pappi Alexandrini Collectionis quae supersunt. Ed. of F. Hultsch. Vol. 2, Berlin, 1887; repr. Amsterdam, 1965. Para vicini Bagliani, A. “ Witelo et la science optique a la cour pontificale de Viterbe (1277),” Melanges de VEcole Erancaise de Rome: moyen age, temps modernes, Vol. 87 (1975), pp. 425-53. Paris. Catalogus codicum manuscriptorum Bibliothecae Regiae. Pars tertia, Vol. 4, Paris, 1794. Pecham, John. See Lindberg, D. C. Peletier, J. Commentarii tres: I. De dimensione circuli. II. De contactu linearum; et de duabus lineis in eodem plano neque parallelis, neque concurrentibus. III. De consti­ tutione horoscopi. Basel, 1563. Porta, G. B. della. Magiae naturalis sive de miraculis rerum naturalium libri Illi. Naples, 1558. Augmented ed. with title Magiae naturalis libri XX. Naples, 1589. Poulle, E. “ Fine, O ronce,” Dictionary o f Scientific Biography, Vol. 15, New York, 1978, pp. 153-57. -------------- . “ Fusoris, Jean,” Dictionary o f Scientific Biography, Vol. 15, New York, 1978, pp. 162-63. ---------------. Un Constructeur d ’instruments astronomiques au X V e siecle Jean Fusoris. Paris, 1963. Profiat Duran. Commentary on Chap. 73 of Bk. I of the Guide o f the Perplexed (Hebrew). Sabionetta, 1553. Latin Trans, by F. Barozzi, falsely ascribed by him to Rabbi Samtou. See above, Chap. 7, n. 41, and Text B, Extract VIII. Provenzale, Moise. See Moise. Ptolemy. Cl. Ptolemaei Pelusiensis mathematici operis quadripartiti in Latinum sermonem traductio: Adiectis libris posterioribus Antonio Gogava Graviens, interprete. . . . Item, De sectione conica orthogona, quae parabola dicitur; Deque speculo ustorio, libelli duo, hactenus desiderati, restituti ab Antonio Gogava Graviensi. Lovanii, 1548.

BIBLIOGRAPHY Ravius, C. See Apollonius. Regiomontanus. Additions to the Speculi almukefi compositio. See my ed. and English trans, in Chap. 5 above. Text D. -------------- . See Anonymous, Speculi almukefi compositio, for Regiomontanus' version of that work. Richard, C. See Apollonius. Risner, F. See Ibn al-Haytham and Witelo. Rose, P. L. “ A Venetian Patron and Mathematician of the Sixteenth Century: Francesco Barozzi, 1537-1604,” Studi Veneziani, N. S., Vol. 1 (1977), pp. 119-78. Sabra, A. I. “ Ibn al-Haytham,” Dictionary o f Scientific Biography, Vol. 6, New York, 1972, pp. 189-210. Sacerdote, G. “ Le livre de l'Algebre et la probleme des asymptotes de Simon M otot,” Revue des etudes juives, Vol. 27 (1893), pp. 91-105; Vol. 28 (1894), 228-46; Vol. 29 (1894), 111-26. Serenus. See Apollonius, eds. of Halley and Commandino. al-Sijzi. On the matter o f two lines— one o f which is a straight line and the other a perimeter o f a hyperbolic section— that always approach each other on being extended in­ definitely but without meeting. In Arabic, MS Leiden, Bibl. der Rijksuniversiteit, Cod. Or. 14(6), pp. 226-31. Spiazzi, G. “ Barozzi, Francesco,” Dizionario biografico degli Italiani, Vol. 6, Rome, 1964, pp. 495-99. Steinschneider, M. Catalogus librorum Hebraeorum in Bibliotheca Bodleiana. 2nd ed., Berlin, 1931. Tartaglia, N. La quinta parte del General trattato de’ numeri et misure. Venice, 1560. Toomer, G. J. See D iodes. al-Tusi. See Euclid. Unguru, S. “ A Very Early Acquaintance with Apollonius of Perga’s Treatise on Conic Sections in the Latin W est,” Centaurus, Vol. 20 (1976), pp. 112-28. -------------- . “ Pappus in the Thirteenth Century in the Latin W est,” Archive fo r the History o f Exact Sciences, Vol. 13 (1974), pp. 307-24. -------------- . See Ibn al-Haytham. Valla, G. De expetendis et fugiendis rebus opus. Venice, 1501. Vienna. Tabaluae codicum manu scriptorum praeter graecos et orientales in Bibliotheca Palatina Vindobonensi. Vol. 4, Vienna, 1870. Vogel, K. “ Fibonacci, Leonardo,” Dictionary o f Scientific Biography. Vol. 4, New York, 1971, pp. 604-13. Watson, A. G. “ A Merton College Manuscript Reconstructed: Harley 625, Digby 178, fols. 1-14, 88-115; Cotton Tiberius B.IX, fols. 1-4, 225-35,” Bodleian Library Record, Vol. 9 (1976), pp. 207-16. Werner, J. In hoc opere haec continentur: Libellus Ioannis Verneri Nurembergen. super vigintiduobus elementis conicis. Eiusdem commentarius seu paraphrastica enarratio in undecim modos conficiendi eius problematis quod cubi duplicatio dicitur. Eiusdem commentatio in Dionysidori problema, quo data sphaera plano sub data secatur ratione, alius modus idem problema conficiendi ab eodem Ioanne Vernero novissime compertus demonstratisque. Eiusdem Ioannis, de motu octavae sphaerae, tractatus duo. Eiusdem summaria enarratio theoricae motus octavae sphaerae. Nuremberg, 1522. See my ed. and English trans, of Libellus super vigintiduobus elementis conicis in Chap. 6 above, Text. Wickersheimer, E. Dictionnaire biographique des medecins en France au moyen age. Vol. 1, Paris, 1936. Wiedemann, E. See Heiberg, J. L., and E. Wiedemann, and Ibn al-Haytham. Winter, H. J. J. See Ibn al-Haytham. Witelo. Vitellionis mathematici . . . Περί οπτικής, id est de natura, ratione, et projec-

469

470

ARCHIMEDES IN THE MIDDLE AGES tione radiorum visus, luminum, colorum atque formarum, quam vulgo perspectivam vocant, libri x. Nuremberg, 1535; rep. 1551. For ed. of F. Risner in 1572, see Ibn al-Haytham. -------------- . Witelonis Perspectivae liber primus. Book I o f Witelo’s Perspectiva. Ed. of S. Unguru. Wroclaw, Krakow, 1977. A revision of Unguru’s doctoral dissertation, Uni­ versity of Wisconsin, 1970. ---------------. See Fusoris. Woepcke, F. L ’Algebre d ’Omar alkhayyami. Paris, 1851. Zamberti, B. See Euclid. Zeuthen, H. G. Die Lehre von den Kegelschnitten im Altertum. Copenhagen, 1886. Zinner, E. Leben und Wirken des Job. Muller von Konigsberg gennant Regiomontanus. 2nd ed., Osnabruck, 1968.

Diagrams

472

DIAGRAMS

ARCHIMEDES IN THE MIDDLE AGES Figures 1 .5 -1 .7

Figures 1.1-1.4

curves here and in Figs. 1.8 and 1.9 are circular arcs in the MSS. Fig. 1.5 c

Fig. 1.3

Fig. 1.4

Fig. 1.6

Fig. 1.7

473

474

ARCHIMEDES IN THE MIDDLE AGES

DIAGRAMS

Figure 1.8

As given in the edition

Figure 1.9

As in the Sloane MS

h

As in the Sloane MS. The same figure appears in the Royal College MS [with letters that differ given here in brackets]. In the Royal College MS letter n is m issing, as is the hyperbolic branch tp. T he latter MS adds a third line through point z that lies betw een kzl and ozr, a line designated as Izm, thus making two points l. No doubt this added line was mistakenly taken from Fig. 1.8. Fig. 1.8 Fig. 1.9

475

476

ARCHIMEDES IN THE MIDDLE AGES

DIAGRAMS

Figures 2.1-2.4

Figures 2.5-3.2

D

d

In MS P of Version B the letters z and h are interchanged, no doubt so that the figure m ight serve also for Proposition 2. In this and the rest of the figures I have drawn the base circles in perspective. In the manuscripts they are draw n as circles in the plane of triangle abg.

Only the base circle appears in MS P of Version B. In MS O the line dh was not draw n as a diam eter and diam eter beg (here ad d ed as a broken line) is missing. Fig. 2.3

Fig. 2.1

This and the succeeding diagrams through Fig. 3.8 have been reproduced from Clagett, A rchim edes in the M iddle A ges, Vol. 2, w here details concerning their appearance in the autograph of M oerbeke’s translations are given.

Fig. 2.5

Fig. 3.1

T

In MS O straight lines dh and he w ere not draw n parallel to lines zb and zg respectively, as they should have been. In MS P of Version B lines bzg and dhe are draw n as straight lines, i.e. as diam eters, and the figure serves for both Propositions 1 and 2. I have added the broken lines.

In MS O the letters m and n are falsely interchanged, as are letters s and o. In MS P of Version B the letters are correctly placed but the whole orientation is reversed. In MS O the base diam eter bg is m isdraw n as a b ent line. I have added the broken line that represents part of the hyperbolic curve.

Fig. 2.2

Fig. 2.4

K

M

Fig. 3.2

H

477

478

DIAGRAMS 479

ARCHIMEDES IN THE MIDDLE AGES Figures 3 .6 -3 .1 0

Figures 3.3-3.5

Λ

K

N

Fig. 3.4 z

9.

K

B

S2

As given by Risner; the MSS (as p resented by Unguru) do not include the base circle but only its diam eter. The letter D appears as E in the MSS. This letter is not m entioned in the text. Note that all of the letters in the diagrams and text, both in the MSS and R isner’s edition, are m inuscules but I have follow ed U nguru in using m ajuscules. Fig. 3.9

z

Fig. 3.7 A

Fig. 3.3

As taken from the m anuscript with all letters and lines rem oved except those referred to in note 6 above. A BG should be a parabola but appears as a sem icircle in the manuscript.

Fig. 3.5

Fig. 3.8

As given by Risner; again the MSS do not include the base circle.

Fig. 3.10

480

ARCHIMEDES IN THE MIDDLE AGES

DIAGRAMS

Figures 3.11-3.14

Figures 3.15-3.17 A A

As given in the MSS

As given by Risner; the base circles are m issing in the MSS. Fig. 3.11

As reconstructed by Risner. Fig. 3.12

As reconstructed by Risner.

Fig. 3.14

Fig. 3.17

A

A

481

482

DIAGRAMS 483

ARCHIMEDES IN THE MIDDLE AGES Figures 3.21-3.26

Figures 3.18-3.20

As given by Risner. Fig. 3.22 As given by U nguru according to the MSS. Fig. 3.21

As given by Unguru according to the MSS. Fig. 3.19

As given by Risner. Fig. 3.23

As given by U nguru according to the MSS. Fig. 3.20

Fig. 3.24

As given by Risner.

As given by Risner.

Fig. 3.25

Fig. 3.26

484

DIAGRAMS 485

ARCHIMEDES IN THE MIDDLE AGES Figures 4 .4 -4 .6

Figures 4.1-4.3

caput

None of the three figures is in FV. O nly the m iddle figure is in O, but all three figures are in R ed. Fig. 4.1

Not in FV. Fig. 4.2

As in R. Similar figures in ed. No figures in OFV. Fig. 4.3

Figure slightly m odified in accordance with the text. I have added the broken lines. None of the copies has a com pletely accurate diagram, but the diagram given by Regiom ontanus is the best.

Fig. 4.5

As given by Regiom ontanus. O ther copies do not have circles draw n in perspective.

Fig. 4.6

486

DIAGRAMS 487

ARCHIMEDES IN THE MIDDLE AGES Figures 4.7-4.8

Figures 4.9-4.11

Only the top half of the figure is in iMS C. T he additions rep resen ted by th e broken lines are in MS R, i.e. w ere added by Regiom ontanus, w ith lines m 'n' and xs apparently drawn in red ink (see R egiom ontanus’ marginal eom m ent toward the end of C onclusion 4, in Text C of C hapter 5).

T here is a small part of the right side of this figure in MS C. Fig. 4.10

Fig. 4.7

I have added the letter [c] and the broken line b[c].

Only the top of the figure is in MS C. I have added the broken lines, the letter [c'l and the prim e sign to c' in the texts of Conclusions 6 and 7.

Fig. 4.11

488

DIAGRAMS 489

ARCHIMEDES IN THE MIDDLE AGES Figure 4.13

Figure 4.12 4 i

8

j

a

1 2 1 16 j 20 i 24 i 28 i 32 i 36 i 40

£

h

left side of this figure is in MS C.

As in MS O.

As reconstructed from ed. T he latter, how ever, does not have the circles drawn and it erroneously places e on line ad.

As given correctly in R ed. It is possible that m and o w ere transposed in the original text.

Fig. 4.12

490

ARCHIMEDES IN THE MIDDLE AGES

DIAGRAMS 491

Figures 5.0(a)-5.1

Figures 5.2-5.3

As given in MS 3.

As reconstructed

T he text has h w here v is in the drawing. No doubt the author in ten d ed to have h w here v is and v w here h is. H ence my addition of the

Fig. 5.0(b)

Fig. 5.0(e)

Fig. 5.1

As redraw n by the editor. Fig. 5.3

492

DIAGRAMS 493

ARCHIMEDES IN THE MIDDLE AGES Figures 5.4-5.8

Below figure is w ritten “ pro 3a proprietate et etiam pro 4a.” Fig. 5.7

a I have added the prim e signs to distinguish these points from those on Fig. 5.7, which are also referred to in the text.

Fig. 5.8

Fig. 5.10

494

ARCHIMEDES IN THE MIDDLE AGES

DIAGRAMS 495

Figures 5.11-5.12

Figures 5.13-5.17

Quando ex est 100, erit xz. quoque centum

R econstructed from text— no separate diagram in the MS.

As given in the MS, w ith the parabola drawn as a circular arc. L ine f d should have been draw n parallel to ac. (b) Fig. 5.13

m quarta lateris erecti et sit 25

As given in m anuscript. Fig. 5.11

Fig. 5.15 Fig. 5.14 a

b

1

As draw n in the MS. (b)

Fig. 5.12

Fig. 5.16

As draw n in the MS, w ith the parabola draw n as a circular arc and w ithout any attem pt to make the line lengths conform to the data of the text. A few num bers have b een added to the lines, but they are not referred to in the text and I have deleted them. Fig. 5.17

496

ARCHIMEDES IN THE MIDDLE AGES

DIAGRAMS 497

Figures 6.1-6.5

Figures 6 .6-6.11 b

Basis

Fig. 6.6

Fig. 6.1

Fig. 6.3

Fig. 6.9 b

f

Fig. 6.5

Fig. 6.11 Fig. 6.10

498

DIAGRAMS 499

ARCHIMEDES IN THE MIDDLE AGES Figures 6.1 7 -6 .2 0

Figures 6.12-6.16

Fig. 6.13

Fig. 6.20 Fig. 6.15

Fig. 6.16

500

ARCHIMEDES IN THE MIDDLE AGES

DIAGRAMS

Figures 6.21-6.25

Figures 6.26-6.31

I

b

Fig. 6.27

d

K

■i

Fig. 6.22

h

Fig. 6.21

Fig. 6.25

Fig. 6.30

Fig. 6.31

501

500

502

DIAGRAMS 503

ARCHIMEDES IN THE MIDDLE AGES Figures 7 .1 -7 .5

Figure 6.32

As given in edition. L ine cl should be parallel to line dhe.

As given in edition. L ine m s should be parallel to line bhg. Fig. 7.2

Fig. 7.1

As given in the edition of 1525. T here is some carelessness in th e draw ing of the vertical lines.

L etters [t] and [k ] are found in M aurolico’s version b u t are m issing from M em m o’s version.

Fig. 7.3

Fig. 7.4

Fig. 6.32

Fig. 7.5

504

ARCHIMEDES IN THE MIDDLE AGES

DIAGRAMS 505

Figures 7.6-7.10

Figures 7.11-7.15

h

Fig. 7.12

Fig. 7.13

I

Fig. 7.14

Fig. 7.10

Fig. 7.15

506

DIAGRAMS

ARCHIMEDES IN THE MIDDLE AGES Figures 7.22-7.24

7.21

1

1

Fig. 7.22

Fig. 7.16

1

1 a

£/ b

/

o

_______ :

d

h

n

Fig. 7.20

η ?igura rectangulorum sub praefatis lineis rectis. m e ΐ_ £

1 Fig. 7.24

Fig. 7.17

Fig. 7.21

507

508

DIAGRAMS 509

ARCHIMEDES IN THE MIDDLE AGES Figures 7.29-7.34

Figures 7.25-7.28

^7 Fig. 7.30 Fig. 7.29

* / ✓

I have added broken lines to indicate the left side ot the right-angled cone that w ould be formed from the rotation of triangle dee around dc. Fig. 7.25

Fig. 7.33 Fig. 7.32 Fig. 7.31

(b)

(d) Fig. 7.26

Fig. 7.34

510

DIAGRAMS 511

ARCHIMEDES IN THE MIDDLE AGES Figures 7.39-7.40

Figures 7.35-7.38

H

Fig. 7.39

(B)

Fig. 7.37

In figure (C) the diagram in the text shows ER as a straight line. It in fact should be a curved line, as I have indicated by the broken line. Similarly in figure (B) E V ought to have been draw n as a curved line.

Fig. 7.39a

512

DIAGRAMS

ARCHIMEDES IN THE MIDDLE AGES Figures 7.46—7.46bis

Figures 7.41-7.45

Given thus in the edition. Of course, ri is not a chord of circle snl, and points m and n do not fall on line de as the diagram shows since circles rmi and snl are in planes perpendicular to the axial triangle cge. In the figure described but not given by P eletier (see Chap. 7, n. 63) the letter C becom es D and D C, w hile S and M are respectively designated by P eletier as G and H. Plane K is m erely called the plane on A C and plane H the plane on EF.

Fig. 7.41

Fig. 7.46

Fig. 7.46bis Fig. 7.45

513

514

DIAGRAMS 515

ARCHIMEDES IN THE MIDDLE AGES Figures 7.51-7.54

Figures 7.47-7.50 L

D

C

I

(a)

B D

C

L· H

£

B ~

l

L

[K] ~

G

E

F

M

(b) Fig. 7.49 Fig. 7.47

B

Fig. 7.53

Fig. 7.48

B

Fig. 7.54

516

DIAGRAMS 517

ARCHIMEDES IN THE MIDDLE AGES Figures 7.61-7.64

Figures 7.55-7.60 i

Fig. 7.56

Fig. 7.55

Fig. 7.57

D

C

A

B

Fig. 7.59

D A

C

4-

Fig. 7.58

Fig. 7.60

B

518

ARCHIMEDES IN THE MIDDLE AGES Figures 7.65-7.67

Index of Latin Mathematical Terms Fig. 7.66

Fig. 7.67

For the procedures and limits used in this index consult the introduc­ tion to the Index of Latin Scientific and Mathematical Terms in Volume Three. I note again here that not all instances of common terms and expressions have been included, though enough instances have been given to indicate their persistent usage. When et pass, is used with a page and line number it means that there are several other instances of the word on the same page and not merely in the same proposition or passage, as was occasionally the case in the index in Volume Three. Similarly, in multi­ page references to the long Extracts from Barozzi’s Admirandum prob­ lem a, the abbreviation for passim (pass.) has, for the most part, been used when there are many examples found on each page of the successive pages cited and not simply when there are many examples over the range of pages. In the latter case pass, is not often used. Though this index is largely devoted to Latin mathematical terms, some Latin terms with scientific implications have also been included. Italian terms have not been indexed (but see pp. 341-45, ns. 48-57).

abbrevio: 11 n. 28, 13 n. 32, 191 lines 20 and 22 abrado: 132 line 49, 187 line 17, 216 line 39 abscindo or abscido: 67, 79n, 80 n. 26, 96 n. 42, 97n bis, 133 line 77, 134 lines 31 and 33, 185 line 16, 217 line 64, 226 line 35, 317-18 n. 14, 331 n. 23 bis, 378, 402-03, 410, 412, 414, 434, 436 abscisio: 436 abscissio: 95 absimilis: 411 absurditas: 239 absurdus: 240n bis, 282 line 70, 394, 425 accedo: 351n, 453, 455 accendo: 97n accidentia: 332 n. 27, 365 accido: 65 n. 5, 79n, 82 n. 30, 97n acies: 59var., 132 line 49, 133 line 90 acuo: 217 line 76 acutangulus: 353 n. 65 acutiangulus: 264 n. 21 bis, 269lines 9 and 32; see piramis acutiangula acuties: 216 line 38, 217 line 76 acutus: 68 n. 8, 71n, 95 pass., 213 line 22 et pass., 237, 320n, 372 bis, 377, 399-400, 406, 455; see angulus acutus, trigonus acutus adamas: 136 line 81 additio: 4 n. 5 addo: 33 η. 1, 60 lines 46 and 56, 84, 96 n. 42, 125 line 34, 127 line 30, 129 lines 63 and 65, 211 line 32, 213 line 26, 214 lines 51 and 53, 282 line 90, 284 line 8 (El. XIX), 285 lines 15-16 (El. XIX), 287 line 37, 411; see mukefi, sectio addita, sectio mukefi ad d ita ;___ , pariter: 287 lines 24 and 26 adherens: 134 line 34, 188 line 57 adiaceo: 67, 278 line 6, 280 line 5 (El. XVI), 282 line 100, 283 line 9, 312 pass., 315-16 η. 11 pass., 317-18 n. 14pass. adiectio: 49 lines 53-54 adiicio: 48 line 45, 95, 96 n. 42, 277 lines 9 (El. XI) and 16, 286 line 38, 394, 444 adiungo: 226 line 10,277 line 13,315,391-92, 396, 415, 417, 444, 449, 451 admisceo: 134 lines 11 and 18 aeneus: 380, 454; cf. eneus aequalis: 20-21 ns. 42-43 pass., 29 n. 49, 78 n. 22, 91 n. 38, 93 n. 41, 94 - 96 n. 42 pass., 97n pass., 237-40n pass., 242n, 243-44 n. 5 pass., 260-61 n. 16 pass., 262 n. 18 bis, 263 n. 19 pass., 264 n. 21 pass., 265 ns. 22-23 pass., 267n bis, 271 line 78, 272 line 15 (El. II) et pass., 273 line 7 (El. IV) et pass., 274 line 30 (El. V) et pass., 275 line 9 (El. VII) et pass., 276 lines 10 and 20 and 26, 277 line 8 et pass., 278 lines 41 bis and 16, 279 lines 18 and 26, 280 lines 5 (El. XVI) and 11 (El. XVI), 281 line 40 et pass., 282 line 61 et pass.,

283 lines 28-29, 284 line 51 et pass., 285 lines 14 (El. XIX) and 19 (El. XIX), 286 line 33 et pass., 287 line 18 (El. XX) et pass., 288 line 42 et pass., 289 line 12 (El XXI) et pass., 314 n. 10, 315-16 n. 11, 317-18 n. 14, 320-21 n. 15pass., 332 n. 29, 333 n. 31 pass., 334 ns. 34-35, 335 n. 37, 346 n. 58pass., 347-48 n. 62pass., 363, 364 bis, 367-83 pass., 385 pass., 390-97 pass., 399-404 pass., 406-08 pass., 410-17pass., 420pass., 424bis, 426, 430, 434-35, 439, 442-44, 446, 4 4 8 -4 9 p ass., 451 p a ss., 455 bis, 456,457,461; cf. equalis aequalitas: 375, 417 bis] cf. equalitas aequedistans: 314-16 n. 11, 318n pass., 320n; cf. equedistans aequedistoor aeque disto: 315, 320-21 η. 15 pass. ] cf. equedisto aequiangulus: 279 line 17,282 line 63 et p a ss., 289 line 14 (El. XXII), 366-68pass., 385, 390 bis, 394, 400, 406; cf. equiangulus aequicrurius: 416 aequidistans: 21-23 n. 43 pass., 78 n. 22, 9 5 -% n. 42 pass., 264 ns. 21-22, 265 n. 23 pass., 266 n. 25, 316 n. 11, 317-18 n. 14 p a ss., 333 n. 31 p a ss., 346 n. 58 p a ss., 347-48 n. 62 pass., 377, 419-20, 423 bis] cf. equidistans aequidistanter: 95-96 n. 42 pass., 97n bis, 460; cf. equidistanter aequidisto: 95, 264 n. 21, 318n, 321 n. 15, 333 n. 31, 348n bis, 35In; cf. equidisto aequilaterus: 237, 281 line 43, 282 lines 63 and 94,385,416; see triangulus aequilaterus aequo: 20-22 ns. 42-43, 263 n. 19 bis, 275 line 10 (El. VII), 320n pass., 374, 382 aequus: 261 n. 16, 269 line 7, 320n pass., 332 n. 29, 367-70, 372-74, 378, 382, 403; cf. equus aggrego or agrego: 162, 224 lines 24 and 26 (Passage 1) and 25 (Passage 2), 284 line 3 (El. XIX) et pass., 285 line 16 (El. XIX) et pass., 391, 415-17 pass., 444, 449 ago (= to draw): 237-40n pass., 243-44 n. 5, 261 n. 16 pass., 262 n. 18, 263 n. 19, 265 n. 22, 269 line 18, 271 line 75 et pass., 272 line 9 (El. II) et pass., 273 line 12 (El. IV) et pass., 274 line 35 et pass., 275 lines 3 (El. VII) and 6 (El. VII) and 8 (El. VIII), 276 lines 10 and 12, 277 lines 23 and 25, 278 line 47 et pass., 279 line 2 (El XIIII) et pass., 280 line 14 (El. XIIII) et pass., 281 lines 22 and 54, 282 line 59 et pass., 283 lines 8 and 16, 285 lines 7 and 26, 286 lines 46-47, 287 lines 9 and 34, 289 line 11 (El. XXI) et pass.] see linea ordinatim acta, linea structim acta agregatio: 185 line 6 (Proem) albedo: 135 line 53, 136 line 73 albus: 134 line 24

521

522

ARCHIMEDES IN THE MIDDLE AGES allego: 114 line 4, 116 line 12, 118 line 54, 126 line 63 alterne: 21 altificans: 162 altitudo: 132 line 63, 216 line 50, 216var., 263 n. 19 pass., 275 line 13 (El. VII), 373, 377pass., 392, 449 altus: 188 line 56 ambio: 236 n. 3 ambitus: 385-86 ambligonius: 269 line 8; see sectio ambligonia amblygonius: 236 n. 3, 242n, 244 n. 6, 269 line 31, 331 n. 23; see conus amblygonius, sectio amblygonia ampligonia: 71n; see piramis ampligonia, pyramis ampligonia, sectio ampligonia analysis: 320n angulariter: 82 n. 30 angulosus: 332 n. 29 angulus: 13 n. 33 pass., 21-22 pass., 29 n. 49, 30 n. 55, 51var., 67pass., 68 n. 8 pass., 70 n. 11, 71n pass., 79n pass., 83-85n pass., 87n pass., 88n pass., 95 pass., 96n, 97n pass., 127 lines 11 and 23 bis, 185 line 8 (C. 1), 186 lines 23-24 (C.2), 189 lines 23-25, 191 line 76 bis et pass., 212 line 10, 213 line 21 et pass., 214 line 63 bis, 216 line 53 et pass., 217 lines 71-72, 226 line 37, 237-39 pass., 263 n. 19, 265 ns. 22-23, 272 lines 9 -1 0 (El. Ill), 275 line 10 (El. VIII), 276 lines 26-27, 279 line 15 et pass., 281 line 40 et pass., 282 line 61 bis et pass., 287 lines 18-20 (El. XXI) , 288 line 47, 289 lines 10 (El. XXII) and 21, 311-12n pass., 314 n. 11, 316 n. 11 bis, 317-18 n. 14pass., 320-21 n. 15 pass., 334 n. 34 bis, 346 n. 58, 348n pass., 35In bis, 364 pass., 366pass., 368 pass., 310bis, 372-79pass., 382-83, 385, 390, 395-96, 399-400pass., 402-03, 40506 pass .,411 p a ss., 420 p a ss., 427 p a ss., 430, 452, 456 bis; ___ acutus: 13-14 n. 33, 68 n. 8 pass., 80 n. 26, 95, 127 lines 24-25, 128 line 47, 213 lines 22 and 40, 226 lines 3 7 -3 8 ;____coalternus: 78 n. 22 bis; ___ expansus (=obtuse): 14, 15n, 1 6 n ;___ externus: 385 b i s ; ___ extrin­ secus: 78 n. 22 bis, 95, 128 line 4 4 ;___ incidentiae or incidentie: 130 line 8 (C.9), 133 line 97, 186 lines 23-24 (C.2), 189 lines 22-23, 191 line 78, 214 line 6 -7 , 364 bis, 375;___ , interior: 275 line 11 (El. VIII), 366; ___ intrinsecus: 78 n. 22 et pass., 95, 128 line 44; ___ obtusus: 80 n. 26, 95-96 n. 42 pass., 128 line 58, 129 line 81,452;___ rectilineus or vice versa: 275 line 6 (El. VIII), 360, 4 02;___ rectus or vice versa: 4 n. 5, 7n, 12 n. 31, 14, 35n, 44 lines 8 and 11, 45 line 12 (Prop. 1), 55 lines 8 and 11, 68 n. 8 pass., 78 n. 22, 95

pass., 104n, 116 line 3, 117 lines 19-20, 120 line 20 (C.4), 124 lines 22-23, 128 line 48, 132 line 66, 162, 185 lines 8 -9 (C .l), 188 lines 29 and 37, 191 line 12, 203 line 3 (Def.), 204 line 17, 207 line 18, 210 line 23, 212 line 51, 216 lines 52 and 56-57, 236-39 n. 3 pass., 243-44 n. 5 pass., 260n, 262 n. 18, 263 n. 19, 264 n. 21, 267n, 269 lines 5 and 7 and 28, 270 lines 36-37, 271 line 72 et pass., 272 line 15 (El. II) et pass., 273 line 6 (El. IIII) et pass., 274 line 26 (El. V) et pass., 275 lines 8 (El. VIII) and 7 (El. IX), 276 line 21 et pass., 277 lines 10 (El. XI) and 32, 278 lines 14-15, 281 line 15 et pass., 282 line 57 et pass., 283 line 31, 285 lines 9 and 12, 287 lines 2 -3 et pass., 288 lines 69-70 and 7, 289 line 10 (El. XXI), 315, 317-18 n. 14, 320n, 351n bis, 362-64, 367pass., 369-70pass., 373-74, 376-79, 382 bis, 389-90 pass., 393 pass., 395400, 402-03, 405-07, 410-13, 427-28, 434, 447, 453-54, 460; cf. rectus; ___ reflectionis or reflexionis; 130 line 8 (C.9), 133 line 98, 186 line 25 (C.2), 189 line 23, 191 line 78, 214 lines 6 -7 , 364 bis, 375 annularis: 187 line 41 annulus: 187 line 42 annuo: 429 anxioma (/), see axioma apertura: 134 lines 20 and 22 apex: 261 n. 16, 269 line 27, 363, 455 pass., 460 applicatio: 335 n. 37 applico: 131 line 41, 134 line 10, 215 line 32, 280 line 10 (El. XV), 317-18 n. 14pass., 376, 405, 450, 455 appono: 243n, 331 n. 23, 455-56 appositio: 135 lines 52 and 56 appropinquatio: 35 In, 418, 428-29, 445, 460 appropinquo: 44 lines 3 {Proem) and 19, 48 line 48, 55 lines 3 {Proem) and 14, 59 lines 4 -5 , 60 lines 35-36, 137 line 5, 218 line 4, 219 lines 21 and 25, 220 lines 47 and 54, 221 lines 73-74, 285 line 4, 286 lines 44 and 58, 346 n. 58, 384, 386, 396, 40809, 412, 416-17, 429-32, 445, 458 approximo: 334 n. 34, 347 n. 62, 428, 431; see linee approximantes archetypum: 331 η. 23 architectura: 388 arcuatio: lYlvar. arcus: 21 pass., 84, 88n, 138 lines 32-33, 219 lines 30-31, 226 line 23 (C.4), 267n, 382 pass., 455 bis, 459pass. area: 284 lines 7 (El. XVIII) and 13, 38586, 388, 433 arealis: 244 n. 6 arena: 134 line 25 areola: 243n bis, 261 n. 16, 275 lines 10 and

INDEX OF LATIN MATHEMATICAL TERMS 12 (El. VII), 283 line 34 bis, 287 line 13, 289 lines 2 and 24 (El. XXII) argenteus: 454 argentum: 134 line 17, 136 line 73, 454 argumentatio: 285 line 19 (El. XIX), 289 lines 20-21 (El. XXI), 413, 425 argumentum: 456 arguo: 122 line 62, 425 ascendo: 351η, 4 2 8 -2 9 pass. aspergo: 134 lines 11 and 18 asser: 381 assigno: 22 assumo: 13 η. 32, 57 line 32, 97n bis, 140 line 85, 277 lines 19 and 21, 278 line 50, 279 lines 5 (El. XIII) and 9 (El. XIII), 286 line 46 assumptum: 287 line 20 (El. XX), 289 line 25 (El. XXI), 326, 364 astrologia: 388 asymptota: 64, 66-67n pass., 247; cf. linea asymptota asymptotus: 318npass. attesto: 134 line 7 attingo; 66n, 68 n. 8, 90 n. 36, 223 line 3, 224 line 9 et pass., 240n, 243n pass., 427-28, 455 bis, 458 aufero or auffero: 21,84,131 line 16, 136 line 98, 239n, 272 line 8 (El. II), 111 line 25, 278 line 24, 287 line 12, 288 line 42, 289 line 19 (El. XXI), 426 augeo: 325; see sectio aucta aureus: 454 aurifabus: 136 line 89 aurum: 454 auster: 137 line 11, 218 line 9 axioma: 65 n. 5; anxioma (/): 3 n. 3, 160 n. 3 axis: 4 n. 5 pass., 12 n. 31, 40, 55var., 56 line 5 (Prop. 2), 66npass., 68 n . 8pass., 69-70 ns. 11 and 13 pass., 71n bis, 78-79 n. 23 pass., 80 n. 26 pass., 96-97 n. 43 pass., 116 line 6, 117 line 28, 118 lines 43 and 52, 119 line 6 (C.3) and 8, 120 line 10, 127 line 18, 132 lines 67-69, 162, 182n, 185 line 10 (C .l), 186 line 10, 188 line 32 et pass., 200 line 7 et pass., 201 line 37, 204 line 26, 205 lines 42 and 50, 206 line 5 (C.3) et pass., 209 line 23, 212 line 17, 216 lines 54-55, 225 lines 9 and 19, 226 lines 35-36, 227 line 3 (Passage 6), 237 pass., 239 pass., 243-44 n. 5 pass., 247, 249, 260-61 n. 16pass., 261 n. 11 bis, 263 ns. 19-20 , 264-65 ns. 21-23 pass., 266 n. 25, 269 lines 18 and 21 and 29, 270 line 36 et pass., 271 line 69 et pass., 273 lines 2 (El. V) and 7 (El. V), 274 line 33 (El. V) et pass., 275 line 3 (El. VII) et pass., 276 line 3 bis and 5 bis, 211 line 10 (El. X), 280 line 3 (El. XVI) et pass., 281 lines 14-15, 282 lines 98-100, 288 line

61, 311 —12n pass., 314-15 n. 11 pass., 317-18 n. 14 pass., 325, 331 n. 23 pass., 332 ns. 27 and 29, 333 n. 31, 335 n. 37 bis, 346 n. 58pass., 351 -52n, 354npass., 362-67, 374-77, 382, 398-99, 405-06, 455, 457 pass.; see triangulus ab axe, tri­ angulus ex axe, triangulus per axem; ____ communis: 69 n. 8; ____ erectus: 12; ___ mugenib: 12 n. 31; axes muzdaguageni or muzdeguege:4 n. 5, 12 n. 31 basis; 4 n. 5 pass., 40-41, 44 lines 10 and 5 (Prop. 1), 45 lines 2 (Prop. 2) and 5 (Prop. 2), 46 lines 13 (Prop. 3) and 6 and 24, 47 line 8,55 line 10,56line 1 (Prop. 2)etp a ss., 51 line 9 et pass., 58 lines 23 and 26, 59var., 64n pass., 67 bis, 68 n. 8 pass., 69-70 n. 11 pass., lln p a s s ., 78-79 n. 23 pass., 80 n. 26pass., 104n, 116 lines 7 and 15, 117 line 26, 118 line 43 et pass., 119 line 11 (C.2) et pass., 123 lines 10 (C.5) and 22, 124 line 23, 125 line 19, 127 lines 5 and 16, 131 line 19 et pass., 137 lines 9 and 11, 138 line 20, 162, 177n, 185 line 14, 186 lines 21 (C .l) and 11 and 13 (C.2), 187 lines 41 and 11, 190 line 74, 204 lines 9 and 13 and 23, 205 line 42 et pass., 206 line 10 (C.3) et pass., 207 lines 21 and 24, 208 line 53, 209 lines 9 (Prop. 5) and 20, 210 line 24, 211 lines 18 and 36, 212 lines 49 and 15, 214 line 63, 215 line 15 et pass., 216 lines 46 and 48, 217 lines 62 and 67 and 72, 219 line 18, 220 line 47 et pass., 226 line 27, 227 line 1 (Passage 5) et pass., 237-39 pass., 244 n. 6, 263 n. 19pass., 264 ns. 21-22, 266 n. 25, 267n, 269 lines 19 and 24 and 29, 270 line 36 et pass., 212 line 2 (El. Ill) et pass., 273 line 8 (El. IIII) et pass., 274 line 15, 276 line 27 et pass., 279 lines 2 (El. XIIII) and 4 -5 , 280 lines 14 (El. XIIII) and 4 (El. XV), 282 line 77, 283 line 3 et pass., 285 lines 5 and 8 and 14 (El. XX), 287 line 20, 288 line 47, 31112n pass., 314-15 n. 11 pass., 317-18 n. 14 pass., 331 n. 23 bis, 346 n. 58 pass., 347-48 n. 52, 351-52n pass., 362-78 pass., 381-82, 389-93, 395, 397-99, 40204, 406, 416, 419-20, 422, 427-29, 43640, 443-47, 449-53, 455-59 pass.; ___ recta: 117 lines 39-40, 205 line 38 baxis (=basis): 173, 200 line 7 et pass. bifariam: 239; see dirimo, dispesco, divido, seco bipartitus: 440-42 pass., 444 bipedalis: 182n boreus: 137 line 11, 218 line 9 brachium: 191 line 13 cado: 4 n. 5, 6 n. 12, 13 n. 32, 22, 57-58var., 78 n. 22, 80 n. 26, 85n, 88n, 91 n. 38, 95

523

524

ARCHIMEDES IN THE MIDDLE AGES pass., 127 line 26, 132 lines 60-61, 186 line 19 (C.2), 189 line 24, 190 line 36, 213 line 23, 216 lines 48-49, 225 lines 16-17, 226 line 35, 239-40n pass., 261 n. 17, 264 n. 21, 265 n. 22, 267n, 270 line 46, 272 line 19 (El. II), 273 line 3, 274 line 35 et pass., 278 line 45, 280 lines 2 (El. XVI) and 11 (El. XVI), 281 line 19,282 line 97, 285 lines 16 (El. XX) and 18 and 27, 346 n. 58, 347-48 n. 62, 36 5-67pass., 370, 372-73, 393-94 , 397-400, 403-04 , 419, 421-25, 421 pass., 429-30, 450-52 calefactio: 135 lines 66-68 calefio or calefacio: 135 lines 57 and 64 bis calibeus: 133 line 92, 188 line 21 bis et pass., 191 line 4 et pass., 217 line 78; cf. chaly­ beiis; see lamina calibs (= chalybs): 97n, 130 line 12 (C.9), 133 lines 1 and 3 bis, 134 line 8 et pass., 135 line 59 et pass., 162, 201 line 36, 214 line 1 (Prop. 10), 379-80 calor: 135 line 53 calx, see pulvis candens: 136 line 77 caput or capud (= vertex or apex): 4 n. 5 pass., In pass., 15n, 44 lines 16 and 2 (Prop. 1), 55 lines 17 and 2 (Prop. 1), 56 line 6 (Prop. 1), 60 line 24, 97npass., I l l , 116 lines 10 and 15, 117 line 30 bis., 118 line 4, 120 line 7 et pass., 122 line 3, 123 line 6 (C.6), 124 lines 14 and 4, 125 line 9, 137 line 10, 200 line 25, 204 line 9 et pass., 205 line 40 et p a ss., 207 lines 6 and 15 and 17, 209 line 2 (Prop. 5) et pass., 210 line 13 et pass., 212 line 11, 218 lines 7 and 8, 219 lines 15 and 17, 223 lines 2 and 4, 224 line 25 (Passage 1), 225 line 57 et pass., 226 line 36, 369, 455-56 pass., 459; see punctus cap itis;____piramidis: 4 n. 5, 7n bis., 8 n. 21 bis., 48 lines 21 and 23, 137 lines 8 -9 , 138 lines 1 7 -1 9 ;___ sectionis: 117 line 41, 118 lines 43 and 48, 123 lines 4 (C.5) and 7 (C.5), 125 line 8, 127 lines 12-13, 325 causo: 68 n. 8 pass., 70 n. 13, 127 lines 11-12 and 14, 132 line 68, 136 line 88, 212 lines 10-11 and 13, 217 line 70, 374 cavo: 130 line 3, 214 line 2 (Prop. 10), 217 line 77, 261 n. 17 celum: 135 line 54 census: 226 line 23 bis (Passage 3) centrum: 11 n. 26, 12 n. 28, 29 n. 49, 45 lines 3 (Prop. 2) and 7 and 18 (Prop. 2), 56 line 4 (Prop. 2) et pass., 57 line 10, 67, 68-69 n. 8 pass., 69 n. 11, 71n, 78-79 n. 23 pass., 80 n. 26, 116 line 15, 118 line 4, 119 lines 5 (C.3) and 7 and 11,120 line 20 (C.3), 123 lines 5 (C.5) and 8 (C.5), 131 line 46, 132 line 48, 182n, 186 line 21 (C .l), 200 lines 8 and 16-17, 204 line 13, 205 line 4,

206 line 4 (Prop. 3) et pass., 207 lines 21 (Prop. 3) and 17, 209 lines 4 -5 (Prop. 5) and 7 (Prop. 5), 216 line 36 et pass., 217 line 67, 218 line 7, 227 line 5 (Passage 6), 2 3 7 -4 0 n p ass., 262 n. 19, 265 n. 23, 267n, 269 line 18, 276 line 24, 277 lines 11 (El. XI) and 14, 278 line 55 et pass., 279 lines 3 -4 and 9 (El. XIII), 281 lines 19 and 26, 282 lines 59 and 73, 288 line 8, 289 line 16 (El. XXI), 334 n. 34 bis., 345-46 n. 58 pass., 363 pass., 365-67 pass., 369, 37475, 379, 382, 402-03 pass., 413-14, 429, 447 pa ss., 450 bis, 455 pa ss.; ___ gravi­ tatis: 388 bis cera: 321 n. 23 cerasa matura: 135 line 57 chalybeus: 217var., 331 n. 23 chorda: 377-79, 382 pass., 455-56 pass., 4 5 9 -6 0 pass.·, cf. corda cilex ( = silex): 136 line 82 cinis salicis: 381 circinus: 22, 88η, 90 η. 36, 189 line 32, 190 lines 54 and 62, 223 lines 16 and 20, 267n, 353-54 n. 65 pass., 377-78 circuitus: 385 circularis: 162, 182η, 362, 365-66, 381, 431 pass., 454-55; see linea circularis, portio circulus: 4 n. 5 pass., 8 n. 21, 20 n. 42 pass., 21 bis, 29 n. 49, 41, 44 lines 10 and 5 (Prop. 1), 45 line 10 (Prop. 1) et pass., 46 lines 14 (Prop. 3) and 16 (Prop. 3), 47 line 32 et pass., 55 line 10, 56 line 5 (Prop. 1) et pass., 57 line 9 et pass., 58 line 23 et p a ss., 64n bis, 68 n. 8 pa ss., 79n pa ss., 80 n. 26 pass., 83-84n pass., 88n pass., 90 ns. 3 6 -3 7 pa ss., 97n bis, 115 line 36, 116 line 7, 117 line 26, 119 lines 12 (C.2) and 10 (C.3), 121 line 22, 123 line 4 (C.5) et pass., 130 lines 8 (C.10) and 12, 137 line 13, 159-60 n. 2 pass., 162, 182n, 185 lines 10 (Proem) and 14, 186 line 21 (C .l), 190 lines 55 and 63 , 200 line 8, 204 line 24, 206 line 11 (C.2) et pass., 207 line 20, 208 lines 41 and 52, 209 line 3 (C.5) et pass., 214 line 5 (C.10), 215 lines 9 and 19 bis, 216 line 36 et pass., 218 lines 80 and 11, 219 lines 26-27 and 33, 220 lines 57 bis and 61, 226 line 22 (Pas­ sage 4), 227 lines 1 (Passage 5) and 1 (Pas­ sage 6), 2 3 7 -3 9 pass., 242η, 244 η. 6, 263 η. 20, 264 η. 22, 269 line 12 et pass., 270 line 57, 273 lines 13-15 (El. V), 274 line 18, 276 line 24 et pass., 278 line 55 et pass., 279 line 2 (El. XIII) et pass., 280 line 4 (El. XV), 281 line 18 et pass., 282 line 58 et pass., 283 lines 14 and 27, 285 line 5, 3Ϊ 1— 12n pass., 314-15 n. 11 pass., 31718 n. 14 pass., 333 ns. 31-32, 345-46 n. 58 pass., 347-48 n. 62 pass., 351-52n

INDEX OF LATIN MATHEMATICAL TERMS pass., 360bis, 362-69pass., 374bis, 376, 378-79 pass., 381-83 pass., 390, 393, 397-99 pass., 401-04 pass., 406 pass., 4 1 9 -3 0 pass., 434, 436-37, 439, 447-48, 450-52, 454-455 pass.·, ____ concen­ tricus: 447, 449-50 circumactio: 276 lines 31 and 33 and 41-42 circumago: 237, 261 n. 17, 269 line 12 circumduco or circunduco: 35n, 68 n. 8, 116 line 4, 118 line 9, 200 line 6, 204 lines 4 -5 , 205 line 11, 263 n. 20, 264 n. 21 bis, 269 lines 5 and 7 and 24-25, 276 line 29, 351-52 circumductus: 265 n. 23 circumferentia or circunferentia or circum­ ferenda: 20 n. 42, 45 line 10 (Prop. 1), 56 lines 9-10 (Prop. 1) and line 8 (Prop. 2), 64n, 79n, 83-85n pass., 88n pass., 104n, 119 lines 11 (C.2) and 10 (C.3), 123 lines 9 and 21-22, 159 n. 2 , 206 lines 10 (C.2) and 11 (C.3) and 14, 209 lines 8 -9 and 20, 237-39 pass., 264 n. 22, 266 n. 25, 267n, 269 lines 10 and 12-13, 270 line 40, 273 line 25, 274 lines 26-27 (El. VI), 278 lines 54-55, 279 line 5 (El. XIII) et pass., 280 lines 10 (El. XIV) and 14 and 9 (El. XV), 281 lines 15 and 17-18 and 48, 282 lines 57 and 66, 345-46 n. 58pass., 347-48 n. 62pass., 363, 365-67, 369, 382, 390, 397 , 401-04 pass., 406 pass., 419, 421-22 pass., 426 pass., 429-30, 434, 436 bis, 439, 447-48 pass., 450 bis, 452 bis, 455 circumferentialis: 135 line 61 circumvolvo or circunvolvo: 269 line 6, 353 n. 65, 363 circunductio: 352n, 380 circunsto: 450 circunvolutio: 366 cissoides: 242n citrinus: 136 line 82 claudo: 372, 453 clavus: 353 η. 65 coarcto: 331 η. 23, 362 coeo: 242η, 346, 409 coextendo: 383, 405 coincido: 237-38 pass., 240n pass., 242η, 243η, 264 η. 21 bis, 280 line 9 (El. XVI), 281 lines 49-50, 282 line 68, 285 lines 4 and 24-25 (El. XX), 286 line 41, 287 line 33, 288 lines 62-63 and 71, 312 pass., 315 pass., 331 n. 23, 333 n. 31, 334 n. 34, 346 n. 58, 363-64, 367, 369, 373, 375-76pass., 379, 386 bis, 393 - 98pass., 400, 405 bis, 407-09, 412, 424-25, 427, 429-31, 445, 455-56, 460; coincidentes, non ( = asymptotes): 243-44 n. 5 pass., 261 n. 16, 262 n. 18 bis, 263 n. 19 bis, 286 line 5, 289 line 2 et pass., 334 n. 34,

415-16, 441; see lineae non coincidentes, lineae nunquam coincidentes colcur: 136 line 91 collapsus: 315 collectio: 360 colligo: 335 η. 36, 362, 376, 382 collimo: 337 η. 40 colo: 136 line 83, 162 bis, 188 lines 47 and 57, 191 line 13 et pass., 192 line 34 color: 134 line 6, 135 line 54 et pass. columna (=axis): 455 bis columpna: 78-79 n. 23 pass., 80 n. 2 6 ;____ laterata: 7 9 n ;___ rotunda: 78-79 n. 23 pass., 80 n. 26 columpnaris or columnaris: 80 n. 26, 387 comburo: 115 line 35, 130 line 6 (C.10), 133 line 95, 159-60 n. 2 pass., 200 line 26, 201 line 38, 214 line 4 (C.10), 218 lines 81 and 83 and 88, 223 lines 2 -4 , 331 n. 23 pass., 388; see speculum comburens combustio: 13 η. 32, 159 η. 2 bis, 185 line 7 (Proem), 218 line 91, 223 line 5 et pass., 360, 365, 376; see punctus combustionis commoditas: 13 η. 32, 331 η. 23 communis: 97η, 263 η. 19; see axis com­ munis, diameter communis, differentia, sectio communis, superficies communis, utilitas compar: 4 η. 5 comparatio (= parabola): 243n pass., 244 η. 6 comparo: 61var., 386 complector: 242n, 334 n. 34 compleo: 79n, 82 n. 30, 260n, 263 n. 19, 315 pass. compono: 47 lines 38 and 42, 59 lines 42-43, 162, 185 line 2 (Proem), 186 lines 36 and 6 and 10, 188 line 28, 189 line 16, 243-44 n. 5, 282 line 91, 283 line 34 et pass., 288 line 6, 390 pass., 433 pass.·, ____, pariter: 289 line 22 (El. XXI) compositio (=synthesis): 14-15n p ass., 17; (= composition): 162, 189 line 8, 192 line 37; and in the title Speculi almukefi com­ positio edited in Chap. 4 comprehendo or compraehendo: 29 n. 49, 200 lines 15-16, 237, 242n, 260n, 263 n. 19, 279 line 10, 283 line 10 et pass., 287 line 5, 289 lines 3 and 17 (El. XXII) and 25, 35In, 362-64 pass., 366 bis, 369-70pass., 372-74p a ss.,377-79p a ss., 382 pass., 385 bis, 389-91 pass., 394 pass., 396-97, 406-07, 411-14 pass., 434-39 pass., 441, 443, 445, 449 bis comprimo: 244 n. 6, 450p ass., 453 comprobo: 364 computo: 201 line 40 concavatio: 111. 114-15var. concavitas: 96-97 n. 43 et pass., 129 line 2, 135 line 62, 214 line 1 (C.9), 261 n.

525

526

ARCHIMEDES IN THE MIDDLE AGES 17 pass., 353 n. 65, 374, 376; ___ mukefi: 130 line 12 (C .9 ):___ parabola: 130 lines 2 -3 (C.10), 214 line 2 (C.10) concavo: 129 line 2; see instrumentum, speculum concavatum concavus: 97η, 263 η. 20 pass., 265 η. 23 pass., 353 η. 65, 364-65 pass., 375-76 pass.·, see speculum concavum, super­ ficies concava, superficies specularis con­ cava conceptio, communis animi (=axiom): 125 lines 35-36 conchoides: 242n concido: 66-67n, 271 lines 68-69 concludo (= to include a figure): 282 lines 71-72 conclusio: 21, 57 line 29, 111, 114 lines 4 and 7, 118 lines 52 et pass., 122 lines 52 and 57, 123 lines 18 and 23, 124 lines 33 and 35, 125 lines 18 and 24, 129 line 80, 130 lines 10 (C.9) and 14, 133 line 95, 137 lines 107-08, 139 line 72, 203 line 7 et pass., 205 lines 52 and 13, 208 lines 46 and 50 and 67, 209 lines 70-72, 211 lines 17 and 23, 212 line 58, 218 lines 81 and 92, 219 line 39, 221 line 76, 224 line 1 concurro: 21n, 49 line 66, 55 line 14, 51var., 59 line 5, 60 line 35, 70 n. 13, 71n pass., 78 n. 22, 82 n. 30, 83npass., 91 n. 38,95, 1171ine 23, 118 lines 43 and 52, 120 line 10, 123 lines 6 -7 (C.6), 124 lines 20 and 4, 127 lines 10 and 18 and 27, 131 line 36, 137 lines 5 -6 , 204 line 21, 205 lines 42 and 50, 207 line 9, 209 line 5 (C.6), 210 lines 19 and 21 and 3, 212 lines 9 and 17, 213 line 24, 215 line 27, 216 line 54, 218 lines 4 -5 , 219 line 22 bis, 220 lines 47-48 and 53, 221 line 75, 224 line 3, 265 n. 22, 280 line 4 (El. XVI), 282 lines 98-99, 285 line 25 (El. XX), 336 n. 39, 347 n. 62, 351-52n pass., 383, 408, 425 bis\ concurrentes, non: 348n concursus: 20 n. 42, 21, 71n, 83n bis, 91 n. 38 bis, 95, 132 line 69, 209 line 22, 224 lines 14 and 36, 225 line 19, 226 lines 35-36, 265 n. 22, 280 line 5 (El. XVI), 282 lines 99-100, 352n, 370, 425; see locus, punctus concursus;___ , communis: 376; ----- radiorum: 186 line 13, 187 line 27, 190 line 49, 263 n. 20; see locus, punctus concursus radiorum ;___ radiorum, com­ munis: 360 conditio: 95n, 133 line 3, 190 line 46 et pass., 191 line 79, 429 conduco: 182n conficio: 237, 276 line 34, 331 n. 23 configuratio: 404 , 408 confluo: 240n conformitas: 87n confringo: 134 line 37, 135 line 45

congregatio radiorum: 186 line 14 congrego: 159 n. 2, 186 lines 3 -4 , 188 line 31, 331 n. 23 conicus: 66, 67n pass., 334 n. 34, 351 bis, 363-64, 366, 387-89pass., 391,427, 43638, 443, 451, 455, 457 bis; see corpus, elementum, sectio conica, superficies conica coniungo: 44 line 6 (Prop. 1), 48 lines 23 and 36-38, 55 line 3 (Proem) and line 3 (Prop. 1), 56 line 6 (Prop. 1), 82 n. 30 pass., 119 line 11 (C.2), 206 line 10 (C.2), 226 line 12, 237-40n pass., 269 line 11, 270 line 41, 276 line 25, 278 lines 13-14, 279 lines 6 (El. XIII) and 25, 281 line 54, 282 lines 73-74, 312 bis, 316 n. 11, 320n, 336 n. 39, 346 n. 58, 396, 400, 413, 429, 456 bis conmixtus: 136 line 85 connecto: 238-40n, 244 n. 6,270lines 45-46, 271 line 7, 275 line 9 (El. IX), 276 line 23, 278 line 10, 279 line 13 et pass., 281 lines 16 and 50-51, 282 lines 58 and 81,285 lines 15 (El. XX) and 22 (El. XX), 288 line 60, 289 line 8, 315 bis, 333 n. 31, 365-66, 370, 372, 374-76, 378-79, 382-83, 397, 411 connumero: 93 n. 41 consectio: 140 line 86 consimilis: 221 line 72 consisto: 363-64, 367, 373 bis, 318, 383, 436 consolidatio: 134 line 12 et pass. consolido: 134 lines 14 and 24 and 32 constituo: 69 n. 8, 78-79n, 132 line 55, 162, 216 line 44, 263 n. 19, 281 lines 38 and 53, 288 lines 59 and 65-66, 363, 375, 378, 382-83 pass. constitutio: 35 ln consto: 20 n. 42, 277 line 30, 279 line 28, 289 line 21 (El. XXI), 351n, 404 constructio: 262 n. 18, 263 n. 19, 271 line 12, 272 lines 11-12 (El. II), 273 lines 17 (El. V) and 22 (El. V), 274 lines 32 (El. V) and 28 and 30, 275 line 14 (EI. VII), 276 lines 11-12 and 21 and 35, 277 line 31, 281 lines 25 and 36 and 54-55, 282 lines 61 and 74, 286 line 2, 287 lines 16 and 22, 288 lines 54 and 59, 289 line 11 (EI. XXII), 335 n. 36, 371, 373-76, 378, 38283, 389-91, 393-96pass., 398-400pass., 402, 405-07, 410-14 pass., 416, 427 bis, 435-36, 444-45 construo: 278 line 46, 335 η. 36, 360. 36667, 369-70, 375-76, 382, 387-88, 390, 393, 404-06, 408, 411, 413, 416, 41920, 435, 454, 459 consumo: 134 lines 17 and 36-37 consurgo: 227 line 7 (Passage 5) contactus: 240np a ss., 278 lines 4 and 11,279 line 4 (El. XIII), 280 lines 22 and 6 (EI. XVI) and 10, 281 line 26, 282 line 101,

INDEX OF LATIN MATHEMATICAL TERMS 332 η. 27, 346 η. 58 bis, 351η, 370, 385, 397, 422, 423 bis, 428-29, 447; see locus, punctus contactus contango: 347-48 η. 62, 364, 374-75, 419 conterminalis: 389 pass., 437-38, 440-41, 442 pass. conterminus: 20 ns. 42-43, 274 line 9, 275 line 3 (El. VII) contineo: 4 n. 5, 7n, 8 n. 21, 13 ns. 32-33, 35n, 41, 44 line 7, 55 line 7, 51var., 58 line 15 et pass., 59 line 41 et pass., 6 6 -6 7 n pass., 68 n. 8 pass., 79n, 84, 93 n. 41, 95, 96 n. 43, 116 line 3 et pass., 121 line 24, 132 line 62, 160 n. 5, 182 n. 25, 200 line 19 et pass., 201 line 45, 203 line 3 (Def.), 204 lines 10 and 15 and 21, 212 line 51, 227 line 9 (Passage 6), 265 n. 22 pass., 267n, 283 line 22 et pass., 285 lines 20 (El. XX) and 30, 286 line 34, 287 lines 36 and 40, 288 lines 53 and 69-70 and 2, 289 line 23 (El. XXI), 311 —12n pass., 314-15 n. 11 pass., 317— 18 n. 14 pass., 320n, 346 n. 58 pass., 347 n. 62, 363 bis, 365, 369-70, 37374 pass., 379, 385, 389-91 pass., 39397pass., 401,403-04, 410-13pass., 43346 pass., 448-49 pass., 452, 460 bis; see linea continens circulum contingens: 13-15 η. 33 pass., 29 η. 49, 48 line 32, 57 line 5 et pass., 59 line 15, 66n, 84 bis, 87n, 91 n. 38 pass., 92 n. 39, 9596 n. 42 pass., 97n pass., 186 line 18 (C.2), 209 line 4 (C.6), 210 lines 21 and 2 (C.7), 212 lines 55 and 57, 224 line 13, 225 line 54, 265 ns. 22-23, 283 line 5, 285 line 11, 311 —12n pass., 315-16 n. 11 pass., 320-21 n. 15 pass., 345-46 n. 58 pass., 372 bis, 374-75, 379-80,429-30; see linea contingens, linea contingende, punctus contingendae contingo: 15n, 22n, 44 line 3 (Proem), 46 lines 17-18 (Prop. 3), 57 line 14, 88n bis, 90 n. 36, 91 n. 38 pass., 96 n. 42, 117 line 24, 124 line 19, 125 lines 13 and 16, 127 lines 8 -9 , 131 lines 27 and 43, 190 lines 66 and 72, 191 line 81, 210 lines 18 and 11 (C.7), 211 line 15, 212 lines 50 and 52 and 8, 213 line 20, 215 lines 22 and 33, 224 line 3, 225 lines 52-54, 227 line 10 (Passage 6), 240n, 265 n. 22, 287 lines 2 and 4 -5 , 288 line 69, 321 n. 15 bis, 332 n. 29, 346 n. 58, 347 n. 62, 399, 422 bis, 427, 445-46, 453 continue: 138 lines 22 and 26, 188 line 50, 191 line 8 et pass., 192 lines 30 and 36, 351-52n, 453; see proportionalis; ___ directeque: 408 continuo: 4 n. 5, 13 n. 33, 20 n. 43, 80 n. 26, 90 n. 36, 95, 210 line 12 (C.7), 212 lines 53 and 56, 213 line 24, 224 lines 3 and 14 and 36, 226 line 13, 315n, 413-14

continuum, in: 382-83, 408, 427; ____ et directum: 186 line 17 (C.2), 200 line 21, 394; cf. directum continuus: 453; see proportio, protractio, quantitas contrapositus: 334 n. 34 pass., 346 ns. 58-59; see tangens conus (=apex): 56var., 117 line 24, 119 line 10 (C.2), 190 lines 67 and 73, 191 line 81, 200 line 12, 204 lines 22 and 27, 206 line 4 (C.2) et pass., 216 lines 55-56, 217 lines 67 and 71, 220 line 56, 224 line 12, 225 line 8; ___ piramidis: 117 line 29, 119 lines 5 (C.2) and 9 and 13, 132 line 70, 139 line 62 conus ( = cone): 92 n. 39, 236-39 n. 3 pass., 244 n. 6 pass., 247, 264 ns. 21-22 pass., 269 line 4 et pass., 270 line 35 et pass., 271 line 69, 273 line 12 (El. V), 274 line 15 bis, 276 line 29 et pass., 279 line 2 (EI. XIIII) et pass., 280 line 11 (El. XIIII) et pass., 281 line 12 et pass., 283 line 2 bis et pass., 284 line 45 bis, 285 line 5 et pass., 311 —12n pass., 314-16 n. 11 pass., 317-18 n. 14pass., 324, 333 n. 31, 334 n. 34, 335 n. 36 p a ss., 346 n. 58 p a s s ., 347-48 n. 62 pass., 351-52n pass., 353 n. 65, 362-67 pass., 377, 382-83 pass., 388-91 pass., 393 pass., 395, 397-401 p ass., 404-08 pass., 415-16, 418-22 p ass., 424-26 pass., 428-31 p ass., 43642pass., 444-47p ass., 450-60pass.; see latus ( = side of cone), sectio coni, triangu­ lus ab axe coni, triangulus per axem coni; ____amblygonius or vice versa: 74 n. 17, 237;___ , orthogonius: 237,269 lines 8 and 31; ___ oxygonius: 74 n. 17; ____ rectangulus: 74 n. 17, 92 n. 39, 261 n. 16, 263 n. 20, 264-65 n. 22 pass., 269 lines 8 and 31, 276 lines 43-44, 363, 369-70, 374, 426; see sectio rectanguli c o n i;----- , rectangulus et erectus: 261 n. 17, 365; ____rectus: 237, 334 n. 34 bis, 4 57;____ , rectus atque rectangulus: 360-63, 365-68 pass., 370 bis, 376, 382; ___ rectus et rectangulus or vice-versa or rectus rectangulusque or rectus rectangulus: 273 lines 2 and 5, 274 lines 34-35 et pass., 275 line 2 (El. VII) et pass., 276 lines 29-30 and 42 and 2, 277 lines 11 (El. X) and 6, 278 line 45, 280 lines 2 (El. XVI) and 11-12, 281 lines 45-46, 282 lines 96-97, 335 n. 26; ___ rotundus or vice versa: 451-53 pass., 4 5 7 ;___scalenus: 237, 239, 247, 270 line 35 convenio: 262 n. 18, 318n pass., 347 n. 62, 370 bis, 372 pass., 376, 382-83 pass., 409, 427 conversa: 70 n. 11, 79n, 125 line 15, 211 line 14, 225 lines 50-51, 372, 402, 404; see demonstratio

527

528 ARCHIMEDES IN THE MIDDLE AGES conversio: 66n pass., 262 n. 18, 278 line 43, 288 line 61, 352n, 367-69, 371 bis conversus or conversum: 13 n. 33, 97n, 320-21 n. 15, 412 converto: 13 n. 32, 15n, 97n, 237, 269 line 13 convexus: 347 n. 62, 364 pass., 381, 418-19; see speculum sphaericum con­ vexum copulo: 66η, 95, 128 line 46, 240η pass. corda: 138 line 32 et pass., 219 lines 30-32; cf. chorda cordans (= latus cordans): 44 line 11, 45 line 12 (Prop. 1), 55 line 11 corelarium: 111, 121 lines 43 and 48 corolarium: 271 line 13, 272 lines 17 (EI. II) and 16 (El. III), 273 lines 19 (El. IV) and 20 (El. V), 274 lines 28 (El. V) and 21, 276 lines 16 and 21, 277 line 34, 279 lines 27 (El. XII) et pass., 280 line 14 (El. XV), 283 line 30, 284 line 53, 288 line 68, 289 lines 15-16 (El. XXII) corollarium: 315 bis, 322, 367-70 pass., 372-73, 375, 387, 390 bis, 396-97, 401, 404, 406-07, 413, 416, 426 corpus: 80 n. 26, 96-97 n. 43 pass., 131 line 18 et pass., 134 line 30, 215 lines 24 and 28, 216 lines 40 and 46 and 50, 455 bis; ___ conicum or vice versa: 414, 446, 4 57;____mukefi: 13 n. 32, 96-97 n. 43 pass., 173;------oblongum: 131 line 18 et pass., 215 lines 14-15 and 21 and 23, 216 line 40;------oblongum quadrangulum: 131 lines 1 8 -1 9 ;------rotundum: 96 n. 43; ----- solare: 9 7 n ;____ solis: 97npass. correlarie: 87n correlarium: 123 line 14, 190 line 45, 208 line 39 et pass., 209 lines 12-13 correlativa: 332 n. 29 correspondeo: 61 var. pass., 438 costa: 131 line 35, 271 line 21, 289 line 12 (El. XXII); ----- lateralis or vice versa: 132 line 49, 215 line 27, 216 line 39 cramponus: 188 lines 56 and 59 creber: 410-12 creo: 288 line 60, 352n bis, 411 cresco: 61var., 209 line 24, 446 creta: 331 n. 2 3 ;___ crocea: 381 cribro: 136 line 84 cribrum: 136 line 84 cristallarius: 136 line 91 crus: 353-54 n. 65 pass. culmen (=vertex): 270 line 48, 398, 406; see fastigium cultellus: 135 line 68 curtus: 205 line 45 curva (=linea curva or superficies curva): 71n, 200 line 16, 336 n. 39, 393 pass., 401, 446, 455-58 pass.·, cf. linea curva curvatura: 131 line 27 et pass., 215 lines 21 and 33-34, 216 lines 35 and 39-40 and 47, 221 line 27

curvilineus, see trigonum curvitas: 137 line 3, 218 lines 2 -3 , 220 line 61, 226 line 23 (Passage 4), 456 pass.·, ----- mukefi: 133 line 91, 217 line 77 curvo: 131 lines 29 and 43-44 curvum: 456 bis curvus: 138 line 37, 209 line 4 (C.6), 219 line 34; see latus ( = side), superficies curva cuspis: 162 pass., 185 line 12, 186 line 19 (C .l), 187 line 38, 188 line 33 e /p < m ., 191 line 4 et pass., 377-78 cylindrus: 431 cyssoides: 431

datus or datum: 20-23 n. 43 pass., 29 n. 49 pass., 61 line 2 et pass., 66-67n pass., 82 n. 30 pass., 83n pass., 87n bis., 88n pass., 97n, 114 line 2, 238 pass., 243-44 n. 5 pass., 260-61 n. 16pass., 262-63 ns. 18-19 pass., 264 n. 22 pass., 271 lines 2 (El. I) and 16 and 2 (El. II), 273 line 9 (El. V), 275 line 2 (El. VIII) bis et pass., 276 line 42 et pass., 277 line 9 (El. X) et pass., 278 line 45 et pass., 279 line 2 (El. XIII) et pass., 280 line 13 (El. XIV) et pass., 281 line 45, 282 lines 64 and 96, 283 line 2, 284 line 45 et pass., 287 line 2 (El. XXI) et pass., 288 lines 68 and 70, 3126(5,316n. 11 bis, 3\8npass., 331 n. 23, 332 n. 29, 337 n. 40, 364-65, 369-72p a ss., 374-77, 379, 383p a ss., 388-89p a ss., 402, 435-36 p a ss., 447 bis decido: 370 bis, 372 declaro: 13 η. 32, 1 4 -15η, 387, 409, 438 declivis: 4 η. 5, 5 decresco: 446 bis, 452-53 decretio: 453 deduco (= to draw): 243-44 n. 5 pass., 261 n. 16 pass., 262 n. 18, 271 lines 72 and 74-75, 273 line 9 (El. V), 274 line 34 et pass., 275 line 13 (El. VIII), 276 lines 2 and 4, 277 line 3, 278 line 4 et pass., 279 lines 3 -4 (El. XIII) and 8 (El. XIII) bis, 280 line 11 (El. XIIII) and 14 (El. XIIII), 281 lines 19 and 25, 346 n. 58, 347 n. 62, 363-67pass., 370-73 pass., 422, 438, 440 bis defectio ( = ellipse): 312 bis, 313, 315 bis, 345-46 ns. 58-59pass .\cf. sectio defectio defectus (=ellipse): 244 η. 6, 313 η. 1 deficientia: 67 deficio: 312 bis, 315 bis, 318n bis, 335 η. 37 defigo: 261 η. 17 definio: 236 η. 3, 242η, 403, 422, 436; cf. diffinio definitio: 264 n. 21, 265 n. 23, 269 line 29, 352n, 393-94, 397-400 pass., 402-05, 437-39, 445, 457 bis; cf. diffinitio delineatio: 332 ns. 27 and 29

INDEX OF LATIN MATHEMATICAL TERMS delineo or delinio: 267n, 332 n. 29 pass., 352n, 369-70, 377-79, 381 demitto: 365 demo: 271 line 6 (El. I), 272 line 9 (El. II), 277 line 26, 287 line 35, 289 line 7, 411 demonstratio or demonstracio: 13 n. 32 bis, 14-15np«55., 30 n. 55, 57 lines 25 and 32, 79n, 225 lines 5 -6 , 237, 261 n. 17, 26465 ns. 22-23 pass., 347 n. 62, 351n, 360, 364, 371 bis, 375, 382, 387 pass., 39798, 401 pass., 404 bis, 407-10 pass., 412-16,418-23p ass., 425-26p irn ., 42932, 434, 436, 439 ns. 47 and 49, 440, 44447, 451, 453-55, 457pass., 460-61 pass.·, ___ geometrica: 189 line 13; ------, indirecta: 419-21 pass.; ----- mathe­ matica: 65 n. 5 demonstratiuncula: 421-22 demonstro: 23n, 31n, 44 lines 1 and 12-13, 45 line 17 (Prop. 1) et pass., 46 line 19 (Prop. 3), 47 line 50 et pass., 49 line 64, 55 lines 1 and 13, 57 line 24, 59 lines 1-2, 61 lines 62 and 69, 65 n. 5, 79n, 82 n. 30bis, 87n, 92 n. 39, 93 n. 41, 95, 114 line 6, 115 line 19, 159 n. 2 bis, 189 line 5, 203 line 6, 237-39pa ss., 261 n. 16bis, 263 n. 20, 265 n. 22, 272 line 21, 273 line 24 (El. IIII), 274 line 36, 275 line 17, 276 line 45, 277 line 12 (El. X), 278 line 20, 279 line 23, 281 lines 46-47, 282 line 101, 284 line 46, 285 line 25 (El. XIX), 286 lines 56 and 58 and 15, 288 lines 44 and 73, 289 line 25 (El. XXII), 333 n. 31, 334 n. 34 pass., 335 ns. 36-37, 336 n. 39 bis, 337 n. 40, 347_48 n. 62pass., 360-61, 363, 365-66, 368-70, 372, 378, 381, 383-88pass., 39192, 394-96, 398-99, 401 pass., 404-05, 407-09 pass., 412-19 pass., 421, 42526 pass., 428-30 pass., 432-33, 435-38, 440-41, 443-47pass., 449-60pass.; con­ versa demonstrandi ratione: 328, 372 densus: 117 line 14 dentatus: 353 η. 65 denticulatus: 353 η. 65 depuratio: 134 lines 8 and 17 depuro: 136 line 72, 380 descendo: 118 line 42, 123 lines 7 -8 (C.6), 124 line 6 (C.7), 125 line 21, 127 line 5, 131 line 37, 132 line 60, 134 line 22, 188 line 48, 205 line 41, 209 line 6 (C.6), 210 lines 17 and 23 and 5,211 line 37,212 line 4 describo: 44 line 12, 45 line 12 (Prop. 1), 55 line 12, 66-61npass., 68 n. 8, 70 n. 11, 90 n. 36 bis, 117 line 36, 122 line 59, 122-23 lines 3 -4 , 185 line 10 (Proem)ei p im ., 186 line 9, 187 lines 5 and 7 and 9, 188 line 27 et pass., 189 line 11, 190 lines 55 and 63, 200 lines 8 and 11, 204 line 33, 208 line 52, 209 lines 3 (C.5) and 5 and 7 (C.5), 237-39, 243-44 n. 5 pass., 261 n. 17 pass., 262 n. 18 pass., 263 n. 20 bis, 264 n. 22, 269

lines 13-14 and 25, 271 line 15, 276 lines 42-43 and 45, 277 lines 2 -3 and 5 and 29, 278 line 48, 280 line 20, 284 line 12 (EI. XVIII), 286 line 5, 287 lines 3 and 7, 288 lines 62 and 71,312 pass., 316 n. 11 pa ss., 318n pass., 332 ns. 27 and 29, 351-52n, 353—54 n. 65, 360-64pass., 367-10pass., 372 -7 9 pass., 383 bis, 386, 394, 397, 399, 403, 406, 408-10 pass., 413-14, 416 bis, 421-22, 431 bis, 446, 449, 455-56 descriptio: 116 line 1 et pass., 117 line 38, 118 line 42 et pass., 120 lines 13 and 20 (C.4), 127 line 20, 132 line 71, 185 lines 8 -9 (Proem), 187 line 3, 188 line 25, 189 line 8, 191 line 4, 203 line 17, 204 lines 11 and 16, 205 lines 41 and 51 and 10, 207 lines 12 and 18, 213 line 18, 216 line 57, 237 bis, 269 lines 15-16, 278 line 57, 334 n. 34, 351-52 n. 63, 362, 364 bis, 373, 377, 379 bis, 404, 455 deseco: 244 n. 6 desero: 352n designo: 4 n. 5, 87n, 133 line 94, 134 line 7, 162, 351-52n pass., 353-54 n. 65 pass., 369-70, 386, 393, 396, 406, 413, 446-47, 450-54,458 diabeta: 244 n. 5 diagonalis: 67 diameter or diametrum (/): 4 n. 5 pass., 11 ns. 26 and 28, 12 n. 31, 14, 20 ns. 42-43 pass., 22-23n pass., 46 line 14 (Prop. 3), 47 lines 32 and 34-35, 57 lines 18-19, 58 lines 37 and 39, 59var., 66-67n pass., 91 n. 38 pass., 92 n. 39 bis, 93 n. 41 pass., 94-96 n. 42pass., 121 lines 23 and 26, 123 line 7 (C.5), 160 n. 2, 209 line 6 (C.5), 23740n pass., 244 n. 5, 262 ns. 18-19, 264 n. 22 bis, 271 line 71, 273 lines 15 (El. V) and 17 (El. V), 289 line 12 (El. XXII), 31112n pass., 314-16 n. 11 pass., 317-18 n. 14 pass., 331 n. 23, 332 n. 27, 333 ns. 31-3 2 pass., 334 n. 33, 345 n. 58 bis, 348n, 351-52n, 374, 381, 423, 456 pass., 459; cf. d y am eter;___ communis: 1 0 η ;------erectus: 4 n. 5 bis, 6 n. 15;----- mugenib: 4 n. 5 pass., 6 -7 , 12 n. 28; diametri muzdaguageni: 4 n. 5 bis, 6 - 7 ; ----- secunda: 12 n. 28 diametros: 332 n. 29 pass.; ----- , recta (=latus rectum): 332 ns. 28-29 differentia: 227 line 9 (Passage 5), 286 line 9, 362, 395; ____ communis or vice versa: 7n bis, 8 n. 21, 96 n. 43, 116 line 10, 117 lines 20 and 27, 118 lines 4 -5 , 133 line 78, 204 lines 9-10 and 18 and 25, 205 lines 4 -5 , 217 line 65, 227 lines 6 -8 (Passage 6), 264 n. 21, 363-64, 366 diffinio or difinio: 362—65; cf. definio diffinitio: 56 line 20, 57var., 68 n. 8 ,71n, 79n, 80 n. 26, 89 n. 34, 125 line 29, 126 line 49, 211 lines 28 and 43, 260-61 n. 16, 269 line

529

530

ARCHIMEDES IN THE MIDDLE AGES 31 et pass., 270 line 50, 271 line 70, 273 line 33, 138 line 25, 216 line 51, 217 line 61, lines 18-19, 274 line 26 (El. V) et pass., 219 line 23, 221 lines 63-64, 261 n. 17, 275 line 13 (El. VIII), 276 lines 19 and 30 278 line 54, 346 n. 58, 375, 383 bis, 395and 37, 277 line 4, 278 line 15, 280 line 14 96, 400-01, 417-18, 427-28 pass., 451 — (El. XV), 362 bis, 366, 369, 371 bis, 378 52, 455-56, 458 bis·, cf. definitio diversitas: 68 n. 8 dimensio: 351η diverso: 68 n. 8 dimetiens: 271 line 21, 281 lines 50 and 55, divido: 29 n. 49, 48 line 32, 60 lines 31 282 lines 58 and 67, 283 line 27, 325, 346 and 45, 70 n. 11 bis, 80 n. 26, 95-96 η. 58pass., 363-64, 367-69, 379, 389-90, n. 42 pass., 117 line 32, 121 lines 22-23, 397-98, 403-04pass., 407, 4 2 3 -2 5 pass., 127 lines 29-30, 133 line 82, 139 line 63, 427, 434 bis, 4 3 6 -3 9 pass. 163 n. 9, 186 line 15, 187 line 16, 190 lines dimidio: 20 ns. 42-43 53 and 62, 200 line 12, 204 line 30, 207 line dimidium: 115 line 36, 213var., 281 line 17, 20, 208 line 52, 213 lines 26-27, 214 lines 288 lines 55-56, 315-16 n. 11, 367 bis, 52-53, 217 line 68, 220 line 57, 228 line 29, 373-78 pass., 411, 455 bis 264 ns. 21-22, 271 lines 2 (El. I) and 8, dimidius: 216-17vw ., 244 n. 5, 262 n. 18, 332 n. 29, 345 n. 58, 365, 367, 372-73, 275 lines 7 (El. VIII) and 9-10 (El. VIII), 379 pass., 382, 394, 401, 403, 406, 410, 276 line 27, 282 line 77, 287 lines 18 and 412-13, 455pass.·,___ , bifariam: 286 line 20, 288 line 48, 289 line 11 (El. XXII), 369 37, 363-64, 367, 374-75, 377-78, 382 pass., 373, 377-79 pass., 4 3 1 ;___ per medium: 191 line 83, diminuo: 33 η. 1, 325, 363; see mukefi, 200 line 9, 397, 404, 413, 442 sectio diminuta, sectio mukefi diminuta, divisibiliter: 386 sectio parabola diminuta divisio: 30 n. 55, 267n bis, 269 line 32, diminutio: 452 270 lines 37-38, 379 bis, 442, 455; see dimoveo: 405 punctus divisionis;___ , media: 278 line 56 directe: 263 n. 20, 265 n. 23, 267n, 375, 383; dodecedrum: 64n see continue;___ et interminate: 405 ducibilis: 90 n. 36 directum, in: 277 lines 9 (El. XI) and 16, duco (= to draw): 20-23 ns. 42-43 pass., 284 lines 7 -9 (El. XIX), 287 line 14, 288 29 n. 49, 31n, 41, 46 line 12 (Prop. 4), line 5, 315, 317-18 n. 14, 365, 378, 56var., 58 line 7, 66-67n, 71n, 79n bis, 382, 389, 391 pass., 396, 399, 413, 41580 n. 26, 82 n. 30 bis, 83-84n pass., 17 pass., 437-38, 440, 449 bis\ directum 87n pass., 88-89 n. 34 pass., 91 n. 38, et continuum, in: 376; cf. continuum; 93 n. 41, 95-96 n. 42 pass., 127 line 25, directo, e or in: 97n, 345-46 n. 58, 455 189 line 33, 206 lines 14 (C.3) and 16 (C.3), dirimo: 276 line 7, 3 6 7 ;___ , bifariam: 363, 211 line 19, 212 lines 54-55, 213 line 47, 369 215 line 29, 224 lines 8 and 34, 225 lines dispergo: 360, 376 52 and 57, 226 line 3, 237-40n, 243-44 n. dispesco: 240n, 263 n. 19, 277 line 15, 402; 5 pass., 262 n. 18, 264-65 n. 22, 267n, ----- , bifariam: 237, 240n 271 lines 76-77, 277 lines 26 and 33, 283 dispono: 83n, 133 line 88, 217 line 74 lines 4 and 11, 288 line 59, 311 —12n p a ss., dispositio: 7n, 14npass, 314-16 n. 11 pass., 317-18 n. 14 pass., disseco: 239 320-21 n. 15, 332 n. 29, 333 n. 31 bis, dissimilis: 402-03 345-46 n. 38 pass., 347-48 n. 62 pass., distans: 83n, 97n, 131 line 24, 162, 215 line 352npass., 365,371,377-79,383, 389-90, 18, 217 line 61, 336 n. 39 393-95, 397-402 pass., 405-07, 410-16, distantia or distancia: 44 lines 2 -3 (Proem), 419, 421-25 pass., 427-28, 432, 437 bis, 55 lines 2 -3 (Proem), 114 line 2, 130 line 440, 445, 447 pass., 453-56 pass., 458 5 (C.10), 131 line 24, 162 pass., 185 line ductio: 82 n. 30 3 (Proem), 186 line 2 et pass., 187 lines 2 ductus ( = movement): 200 line 5 and 12, 188 line 31, 189 lines 64-66 and ductus ^m ultiplication; usually as quod fit 15-16, 190 line 70, 200 line 26, 201 line 38, ex ductu— ): 21-22 pass., 49 line 55 et 203 lines 3 (Praef.) and 16,214 line 4 (C. 10), pass., 84-85n pass., 93 n. 41, 95-96 217 line 79, 218 lines 83 and 88, 223 line n. 42 pass., 121 lines 29-30, 122 line 62, 11, 331 n. 23 bis, 336 n. 39, 360, 375-81 207 lines 25-26, 208 line 54, 210 line 26 pass., 395-96, 400, 402 bis, 404 bis, 417— bis, 213 lines 27-28 and 31 bis, 214 line 18 pass., 427-28 pass., 445-46 pass., 54 et pa ss., 227 lines 6 -7 (Passage 5), 320n 450 -5 6 pass., 458-60 pass. dulcarnon ( = Pythagorean theorem): 129 distello: 136var. line 74, 138 line 39, 178 distinctio communis: 48 line 29, 60 line 29 dupla ( = proportio dupla), see medietas disto: 80 n. 26, 83n, 126 line 42 bis, 131 duple

INDEX OF LATIN MATHEMATICAL TERMS duplico: 61 lines 13 and 17-18, 272 line 16 (El. II), 346 n. 58; see ratio duplo: 378 durities: 134 line 7 durus: 135 line 51 dyameter: 69-70 η. 11 pass., IXnpass., 79n, 80 n. 26pass., 8 3 -8 5 n pass., 87n bis, 88n pass., 118 lines 6 -7 , 123 lines 15 and 17-18, 133 line 85, 162 pass., 186 lines 21-22 (C. 1), 187 lines 28-29 and 11 (C.3), 190 line 74, 205 line 6, 207 lines 21 (C.4) and 24, 208 line 53, 209 line 13 et pass., 217 line 72, 227 line 5 (Passage 6); cf. diameter

eccentralis, see linea eccentralis educo: 58 line 10, 66-67n pass., 83-84n, 91 n. 38, 225 line 53, 240n, 242n, 35In, 363, 379, 382 efficio or eficio: 79n, 97n, 200 line 7, 218, 275 line 16 (El. VIII), 278 line 49, 280 lines 16 (El. XIIII) and 17 (El. XV), 284 line 17, 351n efformo: 331 n. 23 egredior: 4 n. 5, 30 n. 53, 33 η. 1, 96-97 n. 43 pass., 265 n. 23, 372 elementum: 261 n. 17, 272 line 18 (El. II), 273 lines 19-20 (El. IIII), 279 lines 12 and 16, 280 line 15 (El. XV), 281 line 12; ___ conicum: 65 n. 5, 66-67 n. 6 pass., 82 n. 30, 87 n. 33, 91 n. 38, 92 n. 39, 93 n. 41, 246n, 260-61 ns. 16-17 pass., 262 n. 18pa ss., 263 n. 19pa ss., 265 n. 22, 273 line 24 (El. V), 274 line 24, 275 lines 8 (El. VII) and 5 (El. IX), 276 line 6, 278 lines 43 and 46, 279 lines 19-20, 280 line 11 (El. XV), 281 line 22, 282 line 60, 286 lines 40 and 50-51, 288 lines 62 and 64 and 67-68, 289 line 16 (El. XXII), 388 elevo: 131 line 40, 188 line 60, 210 line 20, 215 line 31, 351n elicio: 121 line 32, 227 line 2 (Passage 6), 332 n. 29, 364, 369, 376, 390 ns. 5 and 7 ellipsis: 3, 64, 67pass., 71n, 72-73, 74 n. 17, 80 n. 26, 1llvar., 204var., 236-39 n. 3, 242n, 244 n. 6 , 247 , 264 n. 21, 266 n. 25, 267n, 270 line 63, 271 line 68, 315 bis, 331 n. 23, 333 ns. 31-32, 335 n. 37 bis, 35354 n. 65, 431; see sectio ellipsis; other terms for ellipse are defectio, defectus, sectio defectio, sectio diminuta, sectio oxigonia or oxygonii coni, thyraeos elongatio; 97n, 138 line 20, 219 line 19 elongo: 138 lines 20-21, 219 lines 18 and 20, 347 n. 62, 398 emerillus: 136 lines 80 and 87-88; cf. lapis emino: 237, 269 lines 17-18 emitto: 331 n. 23 eneus: 136 line 83, 188 lines 21 and 42 and 57, 215 line 6; cf. aeneus eo: 56 line 7 (Prop. 1), 206 line 15 (C.3),

220 line 41, 224 line 11, 244 n. 5, 262 n. 18, 276 line 24, 285 line 10, 456 equalis: 13 n. 33, 30 n. 55, 45 lines 14-15 (Prop. 2) and 17, 47 lines 36 bis and 47 bis, 56 line 17 bis (Prop. 2), 58 lines 39-40, 60 lines 43 and 45, 66-67n pass., 68 n. 8 pass., 69-70 n. 11 pass., 70 n. 13, 71n, 79n pass., 80 n. 26 pass., 82 n. 30, 83-85n p a ss., 87np a ss., 88np a ss ., 96 n. 43, 104 n. 8, 116 line 5, 117 line 33, 118 line 3, 121 line 27, 123 lines 10 (C.5) and 22, 125 lines 11 and 16, 127 line 11 et pass., 128 line 31 et pass., 130 line 9 (C.9), 132 line 65, 137 line 8, 162pass., 185 line 10 (C .l), 186 line 15 et pass., 188 line 30, 189 line 19 et pass., 190 line 50 et pass., 191 line 75 et pass., 192 line 30, 200 line 6, 204 lines 5 and 30, 205 line 3, 206 line 18, 207 lines 22 and 25, 208 line 40 et pass., 209 lines 10 (C.5) and 20, 210 lines 31 and 10, 211 line 14 et pass., 212 line 47 et pass., 213 line 21 et pass., 214 line 49 et pass., 216 lines 52 and 55, 217 lines 61 and 69, 218 lines 85 and 7, 219 lines 31 and 35, 220 line 58, 221 line 67, 224 line 24 (Passage 1) et pass., 225 line 48 et p a ss., 226 line 23 (Passage 3) et p a ss., 227 line 25, 311- 12npass.', cf. aequalis equalitas: 212 line 54; cf. aequalitas equedistans: 6 6 -6 7 n pass., I l l , 186 lines 24 (C .l) and 10, 189 line 25, 204 lines 9 and 29, 206 lines 2 (C.3) and 9 (C.3), 213 line 19, 215 line 15 bis et pass., 216 line 42, 217 lines 62-63 and 69 and 72, 219 lines 14 and 23, 220 lines 45 and 59, 225 lines 9-10, 227 line 7 (Passage 6); cf. aequedistans equedistanter: 66n, 186 line 19 (C.2), 189 line 21, 190 line 36, 207 line 21, 208 line 53, 212 lines 5 and 13-14, 214 line 3 (C.9), 219 lines 12-13 and 27, 220 lines 41 and 57, 221 line 69 equedisto or eque disto: 204 lines 19-20, 216 line 54, 217 line 73, 224 line 8; cf. aequedisto equiangulus: 60var., 84, 88n; cf. aequiangulus; see triangulus equiangulus, tri­ gonum equiangulum equidistans: 4 n. 5 pass., 5 n. 10, 13-15 n. 33 pass., 41, 45 line 2 (Prop. 2) et pass., 46 line 13 (Prop. 3), 47 line 31, 56 lines 2 (Prop. 2) and 6 -7 and 15, 58 line 33, 59var., 71n bis, 78-79 n. 23 pass., 80 n. 26, 8 3 -8 5 n pass., 88-89 n. 34pass., 97n, 111, 117 line 32, 119 lines 3 (C.3) and 8 (C.3), 121 lines 23 and 27 bis, 128 lines 43 and 46, 131 lines 19 bis and 28, 138 lines 16 and 35, 139 line 66, 200 line 14, 311I2 n pass., 331 n. 23; cf. aequidistans equidistanter: 41, 57 lines 16-17 and 31, 78-79 n. 23 pass., 80 n. 26 bis, 127 lines 6 and 21, 130 line 4 (C.9), 137 line 15, 139 lines 63 and 76, 162; cf. aequidistanter

531

532

ARCHIMEDES IN THE MIDDLE AGES equidisto: In bis, 8 n. 21 pass., 14pass., 71n bis, 79n, 80 n. 26 bis, 84, 117 line 22, 133 line 87; cf. aequidisto equo: 104n, 224 line 26 (Passage 1), 226 line 4; cf. aequo equus: 70 n. 13, 84, 88n, 226 line 5, 227 line 2 (Passage 6); cf. aequus erectus: 4 η. 5, 12 η. 31, 79η, 261 η. 17, 458; see axis, diameter, latus erectum, piramis rotunda erecta ereus: 130 line 9 (C.10) erigo: 4 n. 5, 69 n. 11, 71n, 187 line 26, 189 lines 19 and 31, 190 line 57, 191 lines 83 and 26, 207 line 24 , 264 n. 21, 267n, 270 line 64, 276 lines 34-35 and 37, 281 line 20 et pass., 285 lines 28-29, 331 n. 23, 375, 383, 389 pass., 393 bis, 397-98, 402-03, 410, 413 , 427 bis, 4 3 8 -4 0 pass., 447, 459 evacuo: 7n evado: 95, 346 n. 58, 382-83, 386, 393 bis, 396, 400, 407-08, 427, 446 evanesco: 453 evenio: 96 n. 43, 347 n. 62 eversim: 79n exaspero: 135 line 41 excavo: 331 n. 23, 360 bis, 365 bis, 37475, 376 bis, 379, 381 pass. excedo: 286 line 10, 312 pass., 315-16 n. 11 pass., 317-18n pass., 335 n. 37, 395, 442 excessus: 395, 435 pass., 441-44 pass.', (= hyperbola) 244 η. 6 excito: 263 η. 19, 211 line 10 (El. XI), 283 lines 6 and 19, 285 line 9, 288 line 7, 332 n. 29, 379 exeo: 120 lines 4 and 14, 123 line 10 (C.6), 124 line 21, 127 lines 7 and 21, 207 lines 3 and 13 and 32, 209 line 9 (C.6), 210 line 19, 211 line 13, 212 line 6, 213 line 19, 224 line 4, 336 n. 39, 404-05, 423, 432, 447, 450 existo: 7n, 41, 44 line 2 (Prop. 1), 45 line 1 (Prop. 3), 46 lines 10 (Prop. 4) and 14, 48 lines 24 and 33, 55 line 2 (Prop. 1), 56 line 1 (Prop. 3), 59 lines 13 and 19, 66n, 95, 119 line 3 (C.2), 127 line 7, 138 line 43, 205 line 2 (C.2), 212 line 6, 220 line 40, 311-12npas.s., 314-15 n. 11, 351npass., 366, 389 pass., 392-93, 396-97, 399, 402-03, 405-06, 411, 417, 422, 426-27, 430, 437-38, 441, 445, 456, 459 bis exitus: 44 line 2 (Proem), 55 line 2 (Proem) exordium: 264 n. 21, 269 line 6 experior: 136 line 71 expono: 13 n. 32, 44 lines 6 (Proem) and 11 and 14, 55 lines 6 and 11 and 16, 363 expositio: 13 n. 32, 64n exprimo: 136 lines 74 and 76 exsto: 377, 417 extendo: 138 line 45, 139 line 77, 189 line 33, 190 lines 55 and 63, 220 line 42, 221 line 70, 347 n. 62, 352n, 363, 389, 398, 408

bis, 419, 437-38, 440, 442 bis, 456 bis, 459 bis·, see linea ordinatim extensa extensio: 403 externus: 415 -1 6 ,4 4 3 -4 4 p ass.; see angulus externus extinguo: 134 line 36, 136 line 77 extractio: 4 n. 5, 135 line 63 extraho: 4 n. 5, 46 lines 7 -8 and 23-24, 56 line 2 (Prop. 3), 57 line 19, 58 line 6, 134 line 24, 136 line 75, 201 lines 35 and 39 extremitas: 4 n. 5 pass., 11 n. 28, 13 n. 33 bis, 59var., 94-95n, 96-97 n. 43, 191 line 18, 204 line 26, 209 line 4 (C.5), 210 line 30, 225 line 52, 264 n. 22,267n, 320n, 35 In, 369 bis, 377, 389, 400, 425 pass., 438, 440-42, 446-47, 452 extremum or extrema: 67, 117 line 29, 123 line 3, 124 line 29, 130 line 11 (C.10), 131 line 32, 209 line 2 (C.6), 210 line 11 (C.6), 215 lines 8 and 25-26, 237-39, 263 n. 19, 271 line 73, 332 n. 29, 334 n. 33, 346 n. 58, 370, 373-74, 377 extrinsecus: 177, 209 lines 3 -4 (C.6); see angulus extrinsecus, punctus extrinsecus extruo: 408 bis, 453-54 pass. exupero: 282 line 66 exurgo: 451

faber: 134 lines 12 and 31 fabrica: 134 lines 19 and 22, 380 fabricatio: 21 -2 2pass., 130line 11 (C.9), 134 line 15 fabrico: 130 line 13 (C.9), 203 line 16, 377 bis, 379-81 pass. fabrilis: 134 line 11 facio (= to make a geometrical construc­ tion): 45 lines 2 (Prop. 2) and 6 and 5 (Prop. 3), 46 line 9 (Prop. 3) et pass., 56 line 7 (Prop. 2), 57 line 5, 59 line 8, 78 n. 22, 119 line 9 (C.3), 237, 244 n. 6, 316 n. 11 (indexed sparingly) fastigium: 263 n. 19 pass., 270 line 45, 273 line 5, 274 line 5, 278 line 54, 288 line 61, 331 n. 23 bis, 397, 450; ____ cul­ men: 269 line 27 ferreus: 130 line 9 (C. 10), 134 line 8 et pass., 188 line 21 et pass., 191 lines 12 and 26, 215 line 7, 217 line 78, 331 n. 23, 377, 380, 454; see lamina, linea ferrea and linea ferrea recta ferrum: 134 line 14, 135 line 58, 162, 331 n. 23, 380pass.·,___ scindens: 135 line 41, 162 figo: 4 n. 5, 14, 96 n. 43, 162, 269 line 27, 362, 381 figura ( = proposition): 12 n. 28, 3 In figura (=geometrical form or diagram): 4 n. 5, 13 n. 32, 44 line 9, 55 line 9, 64n pass., 67 bis, 80 n. 26, 97n, 161-62 n. 9 pass., 173, 185 line 6, 186 lines 17 (C .l) and 29,

INDEX OF LATIN MATHEMATICAL TERMS 226 line 12, 237, 242npass., 244 n. 6, 264 n. 21, 265 n. 22, 269 lines 4 and 10, 317-18 n. 14 pass., 335 n. 37, 351-52n, 360-64, 366, 377-79 pass., 381-82, 385 bis, 455 pass., 457 pass.', ----- mukefi: 121 line 37, 126 lines 37-38 and 39, 208 lines 33-34, 211 line 35, 212 line 49; _ , rectilinea: 276 line 17; ----- rotunda solida piramidea ( = cone): 35, 44 line 7, 55 line 7 ; ____solida: 35n, 334 n. 34, 351n, 362;____triangularis: 7 In figuratio: 79n, 162 bis, 186 line 18 (C.2), 187 line 32, 190 line 71, 191 line 79, 279 line 11, 281 line 18, 351n figuro: 35In, 380 filum: 264 n. 22 finio: 369 finitus: 238 fio (= to be made geometrically): 2In, 7 In, 96 n. 42, 129 line 61, 131 line 45, 264 (indexed sparingly) fio ex (= to be produced by multiplying; with two lines given, the product is a rectangle; with one line, a square): 190 lines 51 and 59,207 line 22,213 lines 32 and 34, 226 line 5 et pass., 312 pass., 320n pa ss., 348np a ss., 367pass., 374pass., 399 bis\ see ductus ( = multiplication) fio sub (=the immediately preceding fio ex): 272 line 5 (El. Ill) et pass., 273 line 17 (El. IIII) bis et pass., 274 lines 30-32 et pass., 275 lines 9-10, 277 lines 38-40, 284 lines 49-52, 286 line 39 et pass., 287 lines 18-19 (El. XX) et pass., 288 line 43 et pass., 320n firmo: 14 fissura: 134 line 5, 135 line 49, 191 line 14 et pass., 192 lines 34-35 fixus: 35n, 44 lines 8 and 10, 55 line 8, 68 n. 8 pass., 116 line 3, 162, 200 lines 6 -7 , 203 line 3 (Def.), 204 line 4, 263 n. 20, 276 line 28, 331 n. 23, 362 bis; see punctus fixus flecto: 455, 459 flexus: 332 η. 27, 455, 460 fluxus: 332 η. 29 focus: 335 η. 37 bis forbio: 136 lines 94-95, 137 line 100 forbitor: 136 line 93 forma: 97n, 133 line 90, 162,173,200 lines 27 and 33, 201 lines 35 and 37 and 39, 217 lines 75-76, 243n, 360 bis, 365, 459 formo: 133 line 89, 136 line 73, 201 line 36, 217 line 75 fornix: 216var. fractio: 134 line 6, 380 fractura: 332 n. 29, 380 bis frangibilis: 135 lines 52 and 55 frango: 134 line 5, 238 bis, 380 frico: 381 pass. fuligo: 381

fundamentum: 261n pass. fundo: 114 line 5 fundus: 58var., 134 line 20 gemma: 136 line 78 geometres or geometra: 97n, 162n, 163, 187 lines 7 -8 , 237-39, 271 line 79, 274 line 10, 282 lines 71-72, 335 n. 37, 385 bis, 420 bis, 423 bis geometria: 33 η. 1, 351n, 385-86, 418-20, 429, 431-32, 438, 457 bis geometrice: 185 line 5 (Proem), 419,441,450, 460 geometricus: 235n, 237, 337 n. 40, 352n bis, 360, 364-66, 382, 385-86, 401, 418-20, 428, 430, 432pass., 441,446-47,459pass.; see demonstratio gibbositas: 10η, Sin pass., 131 line 17, 215 line 13 gibbosus: 381 gladius: 136 line 93 globus terrestris: 375 bis gnomon: 191 line 28, 375 gradatim: 35In, 428, 429 bis habeo, se: 61 lines 1 and 8, 70 n. 13, 78 n. 22, 120 line 5 et pass., 123 line 16, 124 line 25, 125 lines 30 and 32, 145n, 177, 207 lines 4 -5 and 13, 208 line 34 et pass., 209 lines 15 and 17-18, 210 line 22 bis, 211 line 29 et pass., 364, 371 pass., 375, 396 bis, 400, 414, 441 habitudo: 226 lines 19 and 22 and 24 helix: 431 bis hemiconus: 264 n. 22 bis hemisphaericus: 376 hiperbole: 263 n. 19, 331 n. 23, 399 horizon: 218var.; cf. orizon horoscopum: 35In, 385 humefactus: 136 line 86 hyperbola or hyperbole: 3, 64, 65 n. 4, 108, 117var., 137va/\, 218var., 236-38 n. 3, 242n, 243-44 ns. 5 -6 pass., 247, 260-61 n. 16, 262 n. 18, 263 n. 19 pass., 264 n. 21 bis, 266 n. 25, 270 lines 63 and 66, 285 lines 2 -3 , 286 lines 45 and 4, 287 lines 3 and 7 and 33, 288 line 60 et pass., 289 line 2 et pass., 312 pass., 315-16 n. 11 pass., 317-18 n. 14 pass., 334 n. 34 pass., 335 n. 37, 345-46 n. 58 pass., 347 n. 6 2 pass., 351-52npass., 353-54 n. 65, 397 bis, 404- 06 pass., 408 bis, 415-16 pass., 424, 427 bis, 4 2 9 -3 1 ,4 5 7 -5 8 pass., 460 bis; cf. yperbola; see latus (=latus hyperboles), linea inflexa hyperboles, sec­ tio hyperbole; other terms for hyperbola are excessus, sectio addita, sectio ambligonia or ampligonia or amplygonia, sec­ tio amblygonii coni. (See note at the end of the entry parabola.)

533

534

ARCHIMEDES IN THE MIDDLE AGES hyperbolica ( = linea hyperbolica): 396, 401, 407, 426, 445, 447; cf. linea hyper­ bolica, linea inflexa hyperbolica hyperbolicus: 428, 455, 458-59; see sectio hyperbolica hypothesis: 95, 263 n. 19, 272 line 13 (El. II), 273 line 18 (El. V), 274 line 30 (El. VI), 275 lines 14 (El. VII) and 9 (El. VIII), 276 line 36, 277 line 9 (El. X), 280 line 11 (El. XVI), 281 lines 27 and 54, 282 line 95, 284 line 9 (El. XVIII), 285 line 18 (El. XIX), 286 line 2, 287 lines 18 (El. XXI) and 41, 289 line 12 (El. XXI), 366, 373, 376; cf. ypotesis iaceo: 66-67n, 131 lines 18 and 22, 137 lines 10-12, 138 line 47, 215 lines 14 and 31, 216 line 46, 218 lines 8 and 10, 220 line 43, 221 line 67, 312, 315, 333 n. 31, 345 n. 58, 351-52n, 364, 385, 391 pass., 397-98, 403, 405, 407-08, 415-17, 42022, 426, 429-30, 440-47, 449-51 pass., 453, 457 icosedrum: 64n ignio: 134 lines 23 and 30 and 32, 135 line 40 bis and 42 ignis: 134 line 25 bis ei pass., 135 lines 42 and 48 ignitura: 135 line 53 imaginatio: 277, 322, 382, 386 pass., 429; imaginationem, per: 276 line 22, 277 line 33, 400, 429 imminuo: 237, 242n, 450 immitto: 239pass., 331 n. 23 immobilis: 352n, 354n implicatio: 177, 212 line 57 implico contradictionem: 177 inaequalis: 20 η. 42, 238,284 line 2 (El. XIX), 285 lines 15 (El. XIX) and 23-24 (El. XIX), 382 bis, 385 bis, 391-92, 394, 401-04 pass., 415-17pass., 424-26,451,459-60; cf. inequalis inaequalitas: 352n, 417-18, 425-26 pass., 445, 459-60 p a ss. inaequaliter: 382, 404; cf. inequaliter incendo: 135 line 53, 261 n. 17, 263 n. 20 incidentia, see angulus incidendae, punctus incidendae incido: 44 lines 14 and 4 (Prop. 1), 45 line 7 (Prop. 1) et pass., 48 lines 24 and 29, 95 pass., 97n bis, 104, 130 line 4 (C.9), 136 line 79, 188 line 36, 189 line 21, 214 line 3 (C.9), 261 n. 17, 263 n. 20 bis, 265 ns. 22-23 pass., 276 line 11, 277 line 6, 286 line 44, 287 line 9, 331 n. 23, 360, 364-65, 374-76; see linea incidens incisio, see locus inclino: 248, 270 lines 35-36, 337 n. 40, 354n, 378 incorporo: 135 line 41 incumbo: 408 bis

incurvatio: 408, 450 bis, 459-60 incurvo: 380, 382, 426 bis indefinite: 189 line 18 indefinitus: 82 n. 30, 189 line 32, 242 n. 4 indemonstro: 426, 447 indirecte: 334 n. 34 indirectus, see demonstratio indirecta indivisibiliter: 386 induco: 135 line 65, 331 n. 23 induratio: 135 line 66, 380 bis induro: 134 line 34, 135 lines 51 and 69, 380 inequalis: 80 n. 26 bis, 138 line 36, 212 lines 48 and 53, 219 line 33 inequaliter: 83n, 35ln inevanescentia: 452 inferior: 131 line 37, 132 line 47, 134 line 22, 215 line 28, 216 lines 36-37 and 47, 221 line 71 infigo: 446 infinitum, in: 47 lines 51 and 58, 48 line 13 et pass., 55 line 4 (Proem), 59 lines 5 -6 et pass., 117 line 23, 119 line 4 (C.2), 137 line 6, 138 lines 19 and 21-22, 204 line 21, 206 line 3 (C.2), 218 line 5, 219 lines 17-21, 237-38, 242npass., 244 n. 5, 269 lines 15-16, 277 lines 10 (El. XI) and 21 and 24, 285 lines 4 and 13 (El. XX) and 24, 286 line 56, 288 line 72, 334 n. 34, 336 n. 39, 337 n. 40, 346 n. 58, 347 n. 62 pass., 35ln, 382-84 pass., 386 bis, 393 — 94 pass., 396 bis, 398 bis, 400-01, 40509, 411-12, 416-17, 419, 424, 427, 429, 431 bis, 444-47, 451, 453, 455-56 infinitus: 4 n. 5, 44 line 12, 48 line 18, 55 line 12, 275 line 20, 346 n. 58, 35In pass., 395, 398, 416, 426, 429-30, 449 inflectio: 376 inflexa (= linea inflexa): 286 line 41, 394 bis, 396 bis, 398, 401, 407-08, 410, 412, 426,431,445-46, 453-54; cf. linea inflexa inflexus: 274 line 18, 278 line 51; see superficies inflexa ingredior: 119 line 9 (C.2), 206 line 8 (C.2) initium: 44 line 2 (Proem), 189 line 17 inmunditia: 134 lines 22 and 28-29 inscribo: 74 n. 17, 84, 88n, 348n, 384, 386 inscriptibilis: 88n insisto: 226 line 1 instructim: 2 39-40npass. instrumentaliter: 115 line 37 instrumentum: 130 lines 12-13 (C.9) and 2, 132 lines 48-49, 134 line 33, 135 line 68, 162, 214 line 1 (C.10), 216 line 38, 217 line 77, 353-54 n. 65 pass., 379-80; see v ia ;___ concavandi: 133 line 2 ;____ scin­ dens: 134 line 31, 135 lines 58-59 intercapedo: 215vw., 218var. intercedo: 4 5 5 -5 6 pass., 4 5 8 -6 0 pass. intercipio: 117 line 40, 118 line 47, 120 lines 6 -7 and 16 (C.4), 123 line 8 (C.5) et pass., 124 line 13 et pass., 125 lines

INDEX OF LATIN MATHEMATICAL TERMS 7 -8 , 138 lines 32-33, 205 lines 39 and 46, 207 lines 5 and 15, 208 lines 33-34, 209 lines 8 (C.5) and 13and 19,2101ines 11-12 (C.6) et pass., 219 lines 30-32, 227 line 5 (Passage 5), 368, 370 bis, 372 interiaceo: 2 2 -2 3 n pass., 30 n. 53, 82 n. 30 bis, 83-84n, 87n bis, 88n pass., 91 n. 38 pass., 93 n. 41 bis, 265 n. 22, 346 n. 58, 352n, 408 interficio: 317-18 n. 14pass., 458-59pass. intermedius: 66n, 409 interminate: 352n, 410, 412-13, 447; see directe interminatus: 413, 447 internus: 237, 385 pass., 415-16, 441-43 pass. interpono: 280 line 6 (El. XVI), 282 line 101 interseco: 70 n. 13 bis, 87n, 134 line 21, 408 intersectio: 162, 366 bis, 379, 383; -----pyramidalis: 97n interstitium: 407 intervallum: 238, 242n bis, 267η, 276 line 24, 277 line 14, 278 line 54, 288 line 8, 337 n. 40, 378, 400, 402, 413-14, 428 intinctio: 134 line 13 intingo: 135 line 61 intrinsecus: 177; see angulus intrinsecus, punctus intrinsecus intro: 188 line 33 invenio: 13 n. 32pass., 29 n. 49pass., 33 n. 1 pass., 61 line 1 et pass., 97n pass., 118 line 54, 134 lines 29-30, 236 n. 3, 238 bis, 243-44 n. 5, 260-61 n. 16 , 264- 65 n. 22, 274 line 11, 288 line 3, 346 n. 58, 347 n. 62, 361, 388pass., 415, 435-36, 450, 454 inventio: 97n bis inventor: 244 n. 5 isosceles: 237, 282 line 74,363; see triangulus isosceles, triangulus rectangulus et isos­ celes, triangulus rectangulus isosceles, trigonus isocheles iungo or iugo: 48 line 13 et pass., 59 lines 17 and 20, 218 line 90, 223 lines 9 and 18, 264 n. 22, 277 line 29, 278 line 51, 284 line 3 (El. XIX), 312,318npuss., 415-16pass., 434, 438; ____simul: 226 lines 4 and 9; ___ , pariter: 287 line 14 lamina: 97n pass., 133 line 89, 136 line 93, 162pass., 187 line 20, 188 line 21 et pass., 217 lines 75 and 78, 331 n. 23, 353 n. 65, 380-81 pass.; ____calibea: 133 line 92; ____ferrea, 133 line 92 lapis: 136 line 71 et pass.; ____emerillus: 380pass.; cf. emerillus lateralis, see costa lateratus, see columpna, pyramis latitudo: 80 n. 26, 130 lines 10 (C.10) and 11, 131 line 21, 134 line 9, 188 line 55,

215 line 8 bis, 243n, 261 n. 16, 267n, 284 lines 2 -3 (El. XIX) et pass., 285 lines 20-21 (El. XIX) and 24, 287 lines 14 and 24 and 26-27, 312 pass., 315-16 n. 11 pass., 317-18 n. 14 pass., 377 bis, 381, 398, 415-17 pass., 458 pass. lato: 162 latonum: 135 line 59 latus (adj): 188 line 56, 458 latus (=side): 7 n pass., 8 n. 21 pass., 30 n. 53, 35 n. 6, 44 lines 8 and 10-11, 45 line 12 (Prop. 1), 46 lines 4 and 24, 55 lines 8 and 10-11, 58 lines 4 and 25, 59 line 9, 61 line 4 et pass., 68 n. 8 pass., 70 ns. 11 and 13 pass., 71n, 79n, 80 n. 26 pass., 84, 89 n. 34, 104n, 116 lines 2 -3 , 117 lines 21 and 23 and 32,131 line 22 et pa ss., 138 lines 20 and 47, 186 line 10, 187 line 29, 188 lines 29-30 et pass., 189 line 26, 190 line 44bis, 191 lines 12-13,192 line 36, 200 lines 6 bis et pass., 204 line 4 bis et pass., 205line 12, 209line4 (C.6), 215 lines 16-17 et pass., 216 line 35 et pass., 217 lines 68-71, 218 line 10, 219 line 19, 220 lines 49 and 60, 225 lines 10 and 19, 226 lines 28-30, 227 lines 2 (Passage 6) and 7 and 24, 237-39pass., 261 n. 16, 263 n. 19, 264 ns. 21-22pass., 266 n. 25, 267npass., 269 line 5, 270 line 66, 271 line 69 et pass., 272 line 9 (El. II) et pass., 273 lines 6 (El. IIII) and 11 and 15 (El. IIII), 276 lines 18 and 28, 279 lines 15 and 18, 281 lines 42 and 44, 282 line 62 et pass., 283 line 2 et pass., 284 line 45 et pass., 285 line 13 (El. XIX) bis et pass., 289 line 22 (EI. XXII), 311-12 η. 1 pass., 314-16 n. 11 pass., 317-18 n. 14 pass., 346, 348n, 351-52n pass., 362-64 pass., 366 bis, 369-70, 372, 376, 378 pass., 382-83 p a ss., 385 pass., 388-94 pass., 396-98 pass., 402, 405-07, 412, 417, 420 pass., 424 bis, 432-33, 436-38, 440-42, 449 pass., 453, 455-60 p a s s . ; ____curvum or vice versa: 120 lines 5 and 15 (C.4), 123 line 5 (C.6), 127 lines 4 -7 and 20, 207 lines 4 and 13-14 and 32, 209 lines 4 and 6, 213 line 19, 216 line 44 latus (=side of cone): 324, 331 n. 23, 333 n. 31, 450; ____coni or vice-versa: 237 bis, 247, 270 line 42, 363 bis, 365-66, 450, 455, 457 bis latus (=latus hyperboles): 4 5 8 ;------hyper­ boles or hyperbolis: 346 n. 58 bis, 347 n. 62pass., 351-52npass., 393, 398,415-16, 428-31, 444, 457-58 latus erectum or erectum latus ^ p a r a m ­ eter): 97n bis, 118 lines 45 and 50, 120 lines 2 -3 and 12, 122 line 52 et pass., 123 lines 10-11 (C.5) et pass., 124 line 25, 127 lines 4 and 19, 128 lines 32-33 et pass., 129 line 70, 177, 182n, 205 lines

535

536 ARCHIMEDES IN THE MIDDLE AGES 43-44 and 48-49, 207 lines 1-2 and 11, 208 line 47 et pass., 209 line 2 (C.5) et pass., 210 line 22 et pass., 212 line 3, 213 line 18 et pass., 214 lines 56-57 et pass., 223 line 1 et pass., 224 line 25, 225 line 3 et pass., 226 line 25 (Passage 3) et p a ss., 227 line 3 (Passage 5) et pa ss., 228 line 29, 320n bis, 325-26, 363-64, 366-70^^55., 372-74p a ss., 376-77pass. latus rectum (=base of parabolic segment): 117 line 40, 205 line 39, 325-26, 363-64, 367, 381 bis latus rectum or rectum latus (=parameter): 13-14 n. 33 pass., 17-18, 38, 91 n. 38, 93 n. 41 pass., 94-96 n. 42 pass., 97n bis, 118 lines 44-45 and 49-50, 129 lines 71-73, 130 line 6 (C.9), 200 lines 25-26 and 29-30, 201 line 40, 226 line 17, 243n, 249, 260-61 ns. 16-17, 264-65 ns. 21-23 pass., 271 line 78, 273 line 3 et pass., 274 line 33 bis et pass., 275 line 7 (El. VII) et pass., 277 lines 4 and 31 and 35, 278 line 45 et pass., 315 bis, 326, 346 n. 58 lemma: 21 bis, 203var., 286 line 1, 287 line 19 (El. XX), 288 lines 61 and 64 and 1, 289 line 24 (El. XXI), 333 n. 32 bis, 406-07, 409-10, 447 pass., 450 bis lex geometrica: 352n ligneum: 188 line 28, 377 lignum: 136 line 92, 187 line 13, 377, 380-81, 454 lima: 131 line 16, 215 line 13 limo: 187 line 17 linea: 4 n. 5 pass., 11 n. 26 bis, 12 n. 31, 13 n. 33 pass., 20 n. 42, 21 pass., 29 n. 49, 3In, 41, 44 lines 1 (Proem) and 19 and 6 (Prop. 1), 45 line 7 (Prop. 1) et pass., 46 line 10 bis (Prop. 3) et pass., 47 line 30 bis et pass., 48 line 10 et pass., 49 lines 59-60 et pass., 55 lines 1 (Proem) and 20, 56 line 7 (Prop. 1) et pass., 57 line 11 et pass., 58 line 11 et pass., 59 line 48 et pass., 60 lines 22-23 et pass., 61 line 66 et pass., 64n bis, 68 n. 8 pass., 69-70 n. 11, 7 In pass., 78 n. 22 pass., 79n pass., 80 n. 26, 82 n. 30 pass., 83n pass., 87n pass., 88n pass., 95 pass., 97n pass., 117 lines 27 and 30 and 33, 119 line 5 (C.2) et pass., 120 line 15 (C.3) etpass., 121 lines 24-25 e tp a s s., 122 lines 55-56 et pass., 123 line 8 (C.6), 124 lines 20 and 22-23, 125 line 8 et pass., 126 line 40 et pass., 127 lines 14 and 21-22, 128 line 31 et pass., 129 lines 60-71 and 77, 131 line 19 et pass., 138 line 16 et pass., 160 n. 5, 162 pass., 185 lines 9 (C .l) and 12-13, 186 lines 23-24 (C.l) et pass., 187 line 26, 188 line 35 et pass., 189 line 66 et pass., 190 line 36 et pass., 191 line 75 bis et pass., 192 line 35, 200 lines 15 and 18 and 20, 204 lines 25 and 28 and 30, 205 line 38, 206line4 (C.2)etpass.,

INDEX OF LATIN MATHEMATICAL TERMS 207 line 12 et pass., 208 lines 33-34 et pass., 209 line 6 (C.6), 210 line 11 (C.7), 211 lines 13 and 15 and 37, 212 line 49 et pass., 213 lines 19-21 et pass., 214 lines 51-52 et pass., 215 line 17 et pass., 216 line 37 et pass., 217 line 60 et pass., 219 line 14 et pass., 220 line 40 et pass., 221 lines 63-64 and 68 and 74, 223 line 20, 224 line 3 et pass., 225 lines 39 and 14, 227 line 7 (Passage 6) et pass., 237-40n pass., 242n, 244 n. 6 , 264 - 65 ns. 2 2 -2 3 pa ss., 266 n. 25 bis, 267npass., 271 line 13, 285 line 11, 286 lines 43-44, 287 lines 16 and 31, 288 lines 55 and 70, 311-12 η. 1 pass., 314-16 n. 11 pass., 317-18 n. 14 pass., 320-21 n. 15 pass., 332 n. 29, 331 n. 31, 334 n. 34, 336 n. 39 pass., 337 n. 40, 345-46 n. 58pass., 34748 n. 62 pass., 351-52n pass., 361, 363, 366, 370 bis, 372, 374, 377-79, 382-83 pass., 385-86, 389-401 pass., 403, 40512 pass., 418-36 pass., 438-51 pass., 453-60 p a s s . ; ____asymptota: 82 n. 30; cf. asy m p to ta;____brevissima: 90 n. 36; ----- circularis: 82 n. 30; ____ coniunctiva: 44 line 3 (Prop. 1); ____ continens circulum: 4 η. 5, 29, 41, 56 lines 3 -4 (Prop. 2) and 19,57 lines 17-18, 58 lines 36 and 38, 119 line 5 (C.3), 120 line 20 (C.3), 206 line 4 (C.3), 207 line 21 (C.3); _ _ contingens: 13 n. 33, 91 n. 38, 95, 97n, 124 line 3, 127 lines 12 and 15 and 27, 210 line 2, 213 line 24, 265 ns. 22-23, 320-21 n. 15;----- contingende: 123 line 10 (C.6), 124 lines 15 and 31, 125 lines 9-10, 209 line 9 (C.6), 210 lines 14 and 8 -9 , 212 lines 11 and 1 4 ;___ curva or vice versa: 41, 44 line 18, 56 line 7 (Prop. 2), 119 lines 9-1 0 (C.3), 120 line 19 (C.3), 131 line 29, 137 lines 2 -3 , 138 lines 17-18 and 21 and 27, 162, 189 line 8 et pass., 190 lines 40 and 43 and 47, 201 line 34, 206 lines 10 (C.3) and 20, 215 lines 23 and 34, 217 line 77, 218 lines 1-2, 219 lines 16 and 20 and 25-26, 220 lines 46 and 51-52, 221 lines 65-66 and 72-73, 361, 393 pass., 395-96, 398-99, 403, 408 pass., 455-61 pass.; cf. c u rv a ;___ ducibilis: 90 n. 36; ----- eccentralis: 97n, 173 n. 19; ____ eccentrica: 173 n. 19, 200 line 16 et pass., 201 line 45; ___ ferrea (=iron ruler): 191 line 15;----- ferrea recta: 191 line 23; ___ horaria: 332 n. 27, 333 n. 30; ____ hyperbolica: 393, 398, 400, 408, 417, 446, 454, 459 bis; cf. hyperbolica; ____ in­ cidens: 265 n. 23; ___ inflexa or vice versa: 237pass., 247, 249, 270 line 61, 278 line 44, 280 lines 19-21 et pass., 285 lines 2 and 17 (El. XX) and 23 (El. XX), 286 line 57, 288 lines 60 and 66, 324, 361, 363 bis, 377-82, 395-96, 398-401, 40408, 411-12, 417, 427-29 pass., 444-45,

451; cf. inflexa; ___ inflexa et parabolica: 364; ___ inflexa hyperbolica: 4 5 9 ;___ , inflexa hyperboles: 4 1 2 ;-----intermedia: 139-40 lines 81-82; ----longitudinis: 68 n. 8 pass., 69 n. 11 bis, 70 n. 13pass., 71npass., 19npass., 80 n. 26; ___ mathematica: 364; ___ media: 131 line 34, 221 line 75, 377; cf. media; ___ minima: 22, 87n, 90 n. 36; -----m unanior muniani: 4 n. 5 pass., 5, 6 n. 12, 7, 8 n. 21, 102, 112, 116 lines 11 and 18, 117 lines 25 and 30-31, 160, 173, 200 line 17, 204 line 11 et pass., 205 line 47, 225 line 5, 227 line 9 (Passage 6), 247, 249, 324; cf. muniani; ____ obliqua or vice versa: 38, 42, 44 lines 4 -5 (Proem) et pass., 47 lines 2 -3 , 48 line 26, 55 line 5 et pass., 59 lines 2 -3 , 60 lines 27 and 48, 61 lines 67-68, 102, 249, 286 line 55, 396, 4 1 7 ;____orbicularis: 3 66;-------, or­ dinata: 368;____ordinate ducta: 397;-----ordinatim acta: 247 , 264 n. 21 bis, 265 n. 22, 271 line 7 5 ;____ordinatim extensa: 325, 363;____ordinis: 4 η. 5 bis, 6 η. 11, 12 η. 31, 117 lines 33 and 39-41, 118 lines 44 and 48 and 55, 120 lines 11-12, 123 lines 5 (C.5) and 9 (C.5) and 16, 200 line 24, 204 line 31, 205 lines 39 and 43 and 46-47, 207 lines 10-11, 208 line 68, 209 lines 1-2 (C.5) et pass., 223 lines 5 -7 et pass., 224 lines 25 (Passage 1) and 8 and 35, 225 line 52 et pass., 226 lines 2-3 and 11 and 19, 227 line 4 (Passage 5) et pass., 247, 249, 325, 363-65, 369 pass.; ____ perpendicularis: 46 line 10 (Prop. 3), 91 n. 38, 93 n. 41 bis, 95, 191 lines 6 -7 , 216 lines 45 and 48, 267n pass., 495 bis; cf. perpendicularis; ____ recta or vice versa: 4 n. 5 pass., In, 8 n. 21, 14, 20 ns. 42-43 pass., 29 n. 49, 44 lines 4 (Proem) and 17-18, 47 lines 2-3 and 7, 55 lines 19 and 3 (Prop. 1), 56 lines 6 (Prop. 1) and 8 (Prop. 1), 58 line 7, 59 lines 2 -3 , 60var., 70 n. 11, 71n, 78 n. 22, 82 n. 3 0 pass., 87n, 91 n. 38, 117 line 20, 119 line 3 (C.2) et pass., 123 line 4 (C.6), 124 lines 19 and 2, 127 lines 5 and 7, 131 line 38, 132 line 49, 137 line 2, 138 line 21 et pass., 162 bis., 190 line 65, 191 line 80, 200 lines 14 and 22, 204 line 18, 205 line 2 (C.2), 206 lines 9 (C.2) and 11 (C.2), 209 line 3 (C.6), 210 lines 18 and 1, 212 lines 4 and 6 -7 , 215 lines 24-25 and 29, 216 line 38, 218 line 1, 219 line 20 et pass., 220 line 45, 221 lines 65-66, 237-40n pass., 242npass., 243-44 n. 5, 260-61 n. 16 pass., 264-65 ns. 21-23 pass., 267n, 269 line 6 et pass., 270 lines 41-42 and 45, 271 lines 71-72 et pass., 272 lines 16-17 (El. II) and 18 (El. Ill), 273 line 21 (El. III1), 275 line 8 (El. IX), 276 line 37, 277 lines 2 -3 et pass., 278 line 41

et pass., 279 line 26 (El. XII) et pass., 280 lines 11-12 (El. XIIII) et pass., 281 lines 21 and 49 and 53, 282 line 68 et pass., 283 lines 4 -5 et pass., 284 line 2 (El. XVIII) et pass., 285 line 2 et pass., 286 lines 52 and 56, 287 lines 8 -9 , 288 line 60 et pass., 289 lines 2 and 4 and 24 (El. XXII), 315, 317-18 n. 14 pass., 333 n. 31 bis, 334 ns. 33-34, 346 n. 58 pass., 347 n. 62 pass., 351-52n pass., 363-66 pass., 369-70 pass., 372-79 pass., 382— 83, 385 bis, 388-91 pass., 393-408 pass., 410-19pass., 421-24, 426-40pass., 442, 444-47 pass., 449-61; cf. recta; -----reflexa: 265 n. 2 3 ;___ structim acta: 247, 249, 271 line 7 5 ;___ tangens: 333 n. 30; cf. tan g en s;____transversa: 267n pass.; cf. transversa;___ transversalis: 132 line 61, 215 lines 30-31, 216 lines 48-49, 267n; linee approximantes: 49 line 65; lineae, non coincidentes: 395, 398,409; cf. coincidentes, non; lineae nunquam coincidentes: 384 linealis: 366 lineo: 115 line 37, 125 line 14, 130 lines 8 (C. 10) and 12 (C.10), 131 line 14, 177-78, 215 line 6 et pass., 218 line 80, 223 line 13, 332 n. 29 lineola: 378, 413-14 linio: 136 line 95 locus: 4 n. 5, 35n, 44 line 9, 55 line 9, 68 n. 8, 90 n. 37, 96 n. 43, 116 line 3, 204 line 4, 346 n. 58 bis, 35In bis, 385 bis, 430, 452, 454; see proportionalis; ------ con­ cursus: 346 η. 58; __ _ concursus ra­ diorum: 162, 227 line 2 (Passage 5); ___ contactus: 348n, 422 pass.; -----fractionis: 134 line 6; ___ incisionum: 134 line 3 7 ;___ ustionis: 182n longitudo: 69 n. 11, 70 n. 13, 71 n. 14, 80 n. 26, 130 line 10 (C. 10), 131 lines 20-21, 162, 185 line 13, 186 line 19 (C .l), 188 lines 45 and 55 bis, 200 line 30, 201 lines 39 and 41 and 43, 215 lines 7 and 16, 217 line 63, 261 n. 16, 267n, 284 line 2 (EI. XIX) et pass., 285 lines 22-24 (El. XIX), 287 lines 13 and 23 and 25-26, 351n, 376-77, 381, 393, 415-18 pass., 429-30; see linea longitudinis longitudo (= side of cone): 324, 360, 363 bis longum, in: 60 line 46, 395, 400 longus: 204 line 5, 205 line 45, 219 line 36, 393-94 lumbricus terre: 136 line 75 luminaris: 133 line 97 machina: 388 magnitudo: 66η, 160 η. 2, 277 line 20, 286 line 32, 366 bis malleatio: 134 line 15, 135 lines 50 and 63 malleo: 134 lines 24 and 26, 135 lines 43 and 46

537

538

ARCHIMEDES IN THE MIDDLE AGES malleus: 134 line 37 marcassita alba: 381 marginalis: 182n margo: 182n massa: 134 line 11 et pass., 135 lines 39 and 45 and 4 7 ;____cerea: 185 line 15 materia: 9 7 n ;____solida: 130 line 3 mathematice: 362 mathematicus (adj.): 236 n. 3, 337 n. 40, 361, 365, 409; see demonstratio, linea mathematica mathematicus (noun): 236-37 η. 3, 269 line 16, 270 lines 42 and 61, 271 lines 75-77, 360, 387, 429 mechanica: 82 n. 30, 388 media (=linea media): 225 line 44; cf. linea media media ( = mean): 243n medietas: 14, 67, 70 n. 13, 95, 122 line 54, 123 line 16, 128 line 52, 132 lines 66 and 69, 138 lines 38-39, 178, 185 line 9 (C .l), 189 line 66, 200 lines 31-32, 208 lines 48-49, 209 line 14, 210 lines 30 and 32, 213 line 43 bis, 216 lines 53 and 55 bis, 217 lines 71-72 and 79, 218 lines 87 and 91, 223 lines 18-19, 224 line 24 (Passage 1), 226 lines 30 and 2 and 17, 227 line 25, 278 line 56, 320n; ____ duple ( = medietas duple proportionis): 208 lines 41-42; cf. proportio medium (= half): 4 n. 5 pass., 48 line 32, 60 line 31, 120 line 18 (C.4), 207 line 16, 218 line 10 medium ( = mean): 67, 370 medium ( = middle or midpoint): 59var., 71n, 127 lines 2 -3 , 132 line 75, 160 n. 5, 162, 187 line 41, 191 line 82, 207 line 10, 212 lines 2 -3 , 223 line 3, 331 n. 23, 40203, 413 bis, 434 bis, 440, 442; see divido medius (adj. = mean): 373-74, 413; see proportio, proportionalis medius (adj. = middle): 20 ns. 42-43, 162n pass., 215 line 26, 221 line 75, 239, 346 n. 58 bis, 352n, 377-78; see divisio, punctus medius medius (=punctus medius): 130 line 6, 213 line 18, 214 line 5 (C.9) mensura: 223 line 13 meo: 273 line 16 (El. V), 281 line 51, 288 line 63 meridianus: 137 line 13, 218 line 11 metallicus: 381 bis metallum: 134 lines 22 and 30, 135 line 60, 187 line 12, 192 line 34 minuo: 44 line 3 (Proem), 55 line 3 (Proem) misceo: 136 line 85 mobilis: 353 n. 65 modulus: 381 molitus: 136 line 89 mollifico: 135 line 48 mollis: 135 line 59 mortarium: 136 line 83, 380

motus: 68 n. 8 pass., 82 n. 30, 96 n. 43, 265 n. 23, 431 moveo: 4 n. 5, 35n, 116 line 4, 191 lines 7 -8 , 204 line 4, 265 n. 23 mugenib, see axis, diameter mukefi: 10, 71n, 72-73, 103, 109, 111-12, 122var., 123 line 20, 204 line 26, 264 n. 21, 320; see concavitas, corpus mukefi, curvi­ tas, figura, sectio mukefi, speculum mukefi annularis; ___ addita: 71n, 72-73, 103; ___ diminuta: 71n, 72-73, 103 multiangula: 385 multiplicatio: 14-15npass., 320npass., 399 multiplico: 223 line 8, 433 pass., 438 munani, see linea munani mundatus: 135 line 47 munditia: 134 line 6 mundus (adj.): 134 line 22 muniani, see linea munani muzdeguege or muzdaguageni, see axis, diameter

narro: 4 n. 5, 5 n. 11, 7n, 12 n. 28, 97n neusis: 20, 26-30, 31n, 85-86, 357 nigredo: 134 line 29 nomino: 4 n. 5 pass., 8 n. 21 pass., 10η, 11 ns. 26 and 28, 12 ns. 28 and 31, 74 n. 17 numerus: 33 η. 1, 121 line 31, 277 line 20, 432-33 pass., 441 bis; ____ cubus: 33 η. 1 ;____quadratus: 33 η. 1 pass.

oblique: 80 n. 26, 266 n. 25 obliquus: 205 line 9, 206 line 7 (C.3), 237, 239-40n, 248, 346 n. 58 bis, 366 bis; see linea obliqua, piramis obliqua, pyramis obliqua oblonga: 80 n. 26, 134 line 8, 366 obtineo: 118 line 49, 366 obtusangulus: 353 n. 65 obtusiangulus: 264 n. 21 bis, 269 lines 9 and 31-32; see piramis obtusiangula obtusus: 68 n. 8, 71n, 95, 213 lines 22 and 4 7 ,320n, 372-73,452; see angulus obtusus occurro: 8 n. 21, 30 n. 53, 56 line 17 (Prop. 1), 58 line 29, 115 lines 18 and 29, 119 line 16, 206 line 14 (C.2), 283 lines 6 -7 and 19-20, 286 line 47, 315 pass., 348n, 389 bis, 395, 398 bis, 400-01, 405 bis, 407 bis, 411, 423-25 pass., 427, 429, 432, 438-39,454 occursus: 315 octangulum: 385 oleum olivarum: 381 operatio: 134 line 19 oppono: 45 line 7 (Prop. 1), 48 line 20, 68 n. 8, 97n bis, 263 n. 20, 265 n. 23 oppositio or opposicio: 44 line 2 (Prop. 1), 48 line 23, 55 line 2 (Prop. 1), 56 line 6 (Prop. 1), 114-15 lines 13-14 oppositus: 4 n. 5, 23n, 78 n. 22, 87n, 88n,

INDEX OF LATIN MATHEMATICAL TERMS 90 η. 36, 97η, 131 line 41, 215 line 31, 216 line 35, 239-40npass., 346 n. 58, 367, 377-78 pass., 383, 385, 406, 424; see sectio opposita orbicularis: 381; see linea orbicularis, specu­ lum orbiculare orbita: 366 ordinate: 312 pass., 315-16 n. 11, 397, 399 ordinatim: 261 n. 16, 265 n. 22, 271 lines 75 and 77, 273 lines 2 -3 and 5 and 10, 274 line 30 (El. VI), 275 line 8 (El. VIII), 277 lines 11 (El. X) and 3, 281 line 18, 317-18 n. 14, 363; see linea ordinatim acta, linea ordinatim extensa ordinatus or ordinata: 311η, 332 η. 29 bis, 333 ns. 31-32, 346 η. 58, 347 η. 60; see linea ordinata ordo: 97n, 238, 368 pass.; see linea ordinis; ordinem, secundum: 12 n. 31, 14 pass., 249, 271 line 76, 320-21 n. 15pass. orison: 218 line 8 orizon: 59var., 131 line 18, 137 line 10, 215 line 14, 218 line 10; cf. horizon orthius: 240n bis orthogonalis: 207 line 10, 225 line 9, 227 lines 3 -4 (Passage 6) et pass., 383; see piramis rotunda orthogonalis orthogonaliter: 4 n. 5, 57 lines 28-29 and 31 and 3 (Prop. 4), 58 line 25, 68 n. 8, 69 n. 11, 80 n. 26, 117 line 31, 120 line 11, 121 line 26, 134 line 21, 138 line 46, 186 line 22 (C .l), 200 line 23, 204 line 28, 207 line 24, 212 line 54, 220 lines 42-43, 226 line 1, 383 orthogonius or orthogonus: 71n, 111, 236 n. 3, 269 line 31, 377; see conus ortho­ gonius, piramis orthogonia, piramis ro­ tunda orthogonia, pyramis orthogonia, tri­ angulus orthogonius, trigonus orthogonius and orthogonus ortogonaliter: 200 line 14 ortogonius: 111, 160 n. 3; see pyramis ortogonia, sectio ortogonia, triangulus ortogonius ostendo: 12 n. 31, 14, 67, 84, 88n, 97n pass., 114 line 8, 118 line 55, 122 line 67, 126 line 58, 278 line 42, 279 line 26, 282 lines 60 and 83 and 86, 286 line 41, 288 line 68, 289 lines 13 (El. XXI) and 19 (El. XXII) oxigonius: 71n, 331 n. 23; see piramis oxigonia, pyramis oxigonia, sectio oxigonia oxygonius: 236-37 n. 3, 244 n. 6, 269 lines 9 and 32; see conus oxygonius, sectio oxygonia pannum lineum: 136 lines 83-84 par: 263 n. 19 bis parabola or parabole: 3, 64, 65 n. 4, 66-67n pass., 71n, 72-73,74 n. 17, 97npass., 112,

Wlvar., 207var., 209-12var., 214var., 236-38 n. 3, 243-44 ns. 5 -6 pass., 247, 260-61 ns. 16-17 pass., 262 n. 18, 263 ns. 19-20, 264-65 ns. 21-23, 266 n. 25, 267n bis, 270 lines 63-64, 273-78 pass., 280-82 pass., 320, 324, 331 η. 23 pass., 332 η. 29 pass., 333 η. 31 pass., 335 ns. 36-37, 346 n. 58 pass., 351n bis, 353 n. 65 bis, 360 bis, 362-63, 368, 374 bis, 381, 388, 431; cf. concavitas, sectio parabola, sectio parabole. Other terms for parabola are comparatio, sectio mukefi, sectio orthogonii coni, sectio ortogonia, sectio parabola or parabole or parabolea or parabolica, sectio rectangula. (Note the confusion with parabola and parabole. Ordinarily when parabola is used for the nominative case the genitive and accusa­ tive cases appear as parabolae and para­ bolam and similarly for other cases, and when parabole is the nominative the in­ flected cases are paraboles, or occasionally parabolis, and parabolen. But with some authors a mixture of forms occurs: the inflected cases of parabole are used when the nominative is parabola. The same situation pertains, to a lesser extent, with hyperbola and hyperbole.) parabolea: 331 n. 23 parabolice: 265 ns. 22-23 parabolicus: 261 n. 17, 331 n. 23, 380-81; see linea inflexa parabolica, portio, sectio parabolica, speculum parabolicum, super­ ficies concava et parabolica, superficies parabolica parallelepipedum: 263 n. 19pass. parallelogrammum or parallelogramum: 67, 89 n. 34, 260 n. 16, 263 n. 19 pass., 287 line 13 et pass., 288 line 45, 289 line 23 (El. XXII), 334 n. 35, 367, 370, 378 bis, 383 bis, 390, 392 bis, 407, 424 bis; ____rectangulum or vice versa: 261 n. 16 bis, 277 lines 38-39, 283 line 33, 287 lines 25 and 35-36, 373, 388-92, 397, 399, 406, 410-13, 415, 435 parallelus: 21, 212-13var., 216-17va/\, 220var., 237-40n pass., 243-44 ns. 5 -6 , 261 ns. 16-17, 262 n. 18, 266 n. 25, 267n, 270 lines 56 and 60 and 66, 271 lines 8 and 16 and 4 (El. II), 272 line 6 (El. II) et pass., 273 lines 7 -8 et pass., 274 lines 15-17, 276 line 10, 281 line 27 et pass., 282 lines 77-78, 283 lines 23 and 25, 287 line 15 et pass., 288 lines 58 and 63, 289 line 6, 316 n. 11, 320npass., 351-52n, 354n, 363 pass., 365-68, 372-75 pass., 377-79 pass., 382-83 pass., 390 pass., 394-95, 397-401 pass., 404-08 pass., 410-12 pass., 414-18 pass., 422, 424-25 pass., 427 pass., 429-30, 432, 436-45 pass., 447-48, 450-51 pass., 453 pass., 458 pass., 460 bis

539

540

ARCHIMEDES IN THE MIDDLE AGES paralogismus: 348n, 417-18, 422-23, 445, 451-52 pararius: 136 line 91 pars: 12 n. 31, 22 bis, 41, 46 line 12 (Prop. 4), 67, 71n, 82 n. 30, 83n pass., 87n pass., 88npass., 91 n. 3 8 pass., 94n, 120 lines 6 and 16 (C.4), 123 line 8 (C.5) et pass., 124 line 13 et pass., 125 line 7 et pass., 160 n. 5, 162, 182n, 187 lines 29 and 19, 188 line 23, 200 line 30, 201 line 39, 205 lines 46-47, 207 lines 5 and 14, 209 lines 7 (C.5) and 16 and 19, 210 line 12 (C.6) et pass., 211 lines 29-30, 223 lines 1 and 3 and 10, 225 lines 55-58 and 4 and 12, 226 line 32, 227 line 5 (Passage 5), 237-38, 244 n. 6, 263 n. 20, 265 ns. 22-23, 266 n. 25, 267n, 269 line 16, 271 line 2 (El. II), 272 line 4 (El. IIII), 273 lines 13 (El. IIII) and 16 (El. IIII) bis, 275 line 9 (El. IX), 276 line 11, 277 line 8 et pass., 278 line 49, 280 lines 4 (El. XVI) bis and 9 (El. XVI), 281 line 50, 282 lines 67-68 and 99, 283 line 15, 285 line 6, 287 lines 11 and 29, 288 lines 65-67 and 72, 289 line 15 (El. XXI) et pass., 318n, 332 n. 29, 345-46 n. 58 pass., 347-48 n. 62 pass., 363 bis, 368-70p a ss., 372-74 p a ss., 37679 pass., 381 bis, 383 pass., 385 bis, 389bis, 393-95, 398-400,402-04,406bis, 410-12, 414, 425, 427 bis, 434, 437-38 pass., 441-44 pass., 447, 450, 455-56, 458-59 particula: 272 line 7 (El. Ill), 273 line 8 (El. IIII), 274 line 9, 278 lines 52 and 6, 283 line 11, 377 partior: 267n passio: 65 n. 5 pedalis: 130 lines 6 (C.10) and 8 (C.10), 215 lines 12 and 18, 216 lines 50-51 penetro: 451 pentagonus: 64n perago: 44 line 12, 287 line 31, 411 perdo: 115 line 33 perduco: 429 perficio: 115 line 38, 130 line 2, 263 n. 19 periferia: 79n, 80 n. 26, 83-84n, 90 n. 36, 185 line 10 (Proem), 281 line 17, 332 n. 29 bis, 333 n. 31 pass., 332 n. 29, 334 ns. 34-35, 346 n. 58 bis, 347 n. 62 bis periphaeria or peripheria: 20 ns. 42-43, 22 bis, 29 n. 49, 91 n. 38 pass., 93 n. 41 bis, 94-95 n. 42, 315, 351n, 361, 365, 378, 419pass., 421 pass. permisceo: 136 lines 74-75, 380 permutatim or permutantim: 79n, 89 n. 34, 206 line 17, 368 perpendicularis: 13 n. 33, 41, 45 lines 2 (Prop. 3) and 4 (Prop. 3), 46 line 15 (Prop. 3) et pass., 47 line 35 et pass., 48 lines

9-11 et pass., 49 lines 50 and 60-61, 56 line 2 (Prop. 3), 57 line 4 et pass., 58 line 9 et pass., 59 lines 10-11 and 14, 60 line 28 et pass., 66-67n, 91 n. 38, 93 n. 41 pass., 95-96 n. 42 pass., 120 line 4 et pass., 123 line 15 et pass., 124 line 13 et pass., 125 lines 7 -8 , 127 line 25, 128 line 39, 132 lines 48 and 56, 138 lines 25 and 34, 187 line 26, 189 lines 19-20 and 32, 190 lines 57-58 and 68, 191 lines 83-84, 207 lines 3 -6 et pass., 208 line 33 et pass., 209 lines 14-15 et pass., 210 lines 11-13 (C.6) et pass., 211 lines 13 and 15, 213 lines 23 and 41 and 47, 216 line 37, 219 lines 24 and 32, 224 line 4, 238-39, 243-44 n. 5, 262 n. 18, 263 n. 19, 264 n. 22, 267n pass., 277 line 12 (El. XI) et pass., 278 line 42 et pass., 279 lines 4 and 7 (El. XIII) and 10 (El. XIII), 283 line 6 et pass., 285 line 18 (El. XX) et pass., 286 line 46, 287 line 10, 288 line 9, 289 lines 10-11 (El. XXI) and 17 (El. XXI), 317-18 n. 14 pass., 320n, 345-46 n. 58 pass., 347-48 n. 62, 36774 pass., 378, 383, 393-95, 400 pass., 406-07, 413, 417-18, 422, 427-28 pass., 434 bis, 445, 447, 450-53, 455-56, 45860; see linea perpendicularis perpendiculariter: 48 line 11, 57 line 19, 59 line 15, 91 n. 38, 120 line 21 (C.4), 123 lines 9 -1 0 (C.6), 125 line 21, 126 lines 40-41, 132 line 60, 186 line 23, 188 line 36, 191 line 26, 192 line 35, 200 line 8, 207 line 19, 209 line 8 (C.6), 211 lines 19 and 37, 264 n. 21, 331 n. 23, 375, 394, 459 perpendiculum: 347-48 n. 6 2 pass., 351n perpendo: 114 line 3, 203 line 4 perpetuo: 346 n. 58 perspectiva: 114 lines 5 and 9, 203var., 214 line 6, 387-88; and see the tracts Perspectiva of Alhazen and Witelo in the Index of Names perspectivus: 133 line 96, 185 line 5 (Proem), 187 line 8 persumo: 189 line 19 pertica: 130 line 7 (C.10), 214 lines 4 -5 (C.10) pertranseo: 11-12 n. 28, 69-70 n. 11, 138 lines 27-28, 190 line 42 peruro: 331 n. 23 pervenio: 4 n. 5, 11 n. 28, 13 n. 33, 46 line 9 (Prop. 4), 97n, 115 line 16, 348n bis, 365, 441-42 pes: 131 lines 21-22, 160 n. 2, 182n, 214 lines 4 -5 (C.10), 215 line 17, 218 line 88 petia: 134 line 15 et pass., 162 petitio or peticio: 51var., 389-90, 397pass., 399pass., 410, 424, 439 bis, 451 piramis: 4 n. 5 pass., 5 ns. 7 -8 , 7n pass., 8 n. 21, 40-41, 44 line 10 et pass., 45 line 7 (Prop. 1) et pass., 46 line 9 (Prop.

INDEX OF LATIN MATHEMATICAL TERMS 3) et pass., 47 lines 31-33 and 5, 48 line 10 et pass., 55 line 10 et pass., 56 line 5 (Prop. 1) et pass., 57 line 4 et pass., 58 line 5 et pass., 59 lines 7 -8 et pass., 60 lines 24-26 and 30-31, 111, 116 lines 6 -7 and 11, 117 lines 29 and 35, 118 lines 43 and 52, 119 lines 5 -7 (C.2) et pass., 120 lines 9-10 and 18, 121 lines 23 and 26 and 46, 122 line 60, 123 line 10 (C.5), 127 line 18, 132 lines 54 and 67 and 70, 137 line 7 et pass., 160 ns. 3 and 5, 162, 185 line 13, 186 lines 26 and 6, 187 line 16, 190 line 74, 204 lines 9-10 et pa ss., 205 line 42 et pass., 206 lines 4 -8 (C.2) et pass., 207 lines 8 -9 et pass., 208 lines 52-53, 209 lines 9 (C.5) and 20 and 23, 212 line 17, 216 lines 43 and 54, 217 lines 67-68 and 72, 218 lines 6 -8 , 219 line 12 et pass., 220 line 42 et pass., 221 lines 67-68 and 70 and 72, 224 lines 1213, 225 line 8; cf. pyramis; see conus (=apex), superficies piramidis, ypotenusa; ____ acutiangula: 116 lines 5 -6 , 204 lines 5 -6 , 225 lines 2 -3 and 16; -----ampligonia: 226 line 29 et pass.·, ----declivis: 226 lines 27-28; ___ obliqua: 226 line 28; ____obtusiangula: 116 lines 5 -6 , 204 lines 5 -6 , 225 lines 2 -3 ; ___ orthogonia: 4 n. 5; ----- ortho­ gonia rectangula: 225 line 2 ;------oxigonia: 226 line 21; ___ recta: 44 line 15; ____ rectangula: 116 line 5, 132 lines 52 and 72, 204 line 5, 216 lines 41 and 45-46 and 57, 217 lines 58-59, 225 line 6, 226 line 21; ___ rotunda: 40, 44 lines 5 -6 (Proem) and 1-2 (Prop. 1), 45 lines 1 (Prop. 2) and 2 (Prop. 3), 46 line 1, 55 lines 6 and 1-2 (Prop. 1), 57 line 9, 104n, 116 line 2, 119 lines 2 -3 (C.2), 186 line 28, 203 line 2 (Def.), 205 lines 8 and 1-2 (C.2), 206 lines 6 (C.3) and 8 (C.3), 224 line 11; ____ rotunda erecta: 116 line 4 0 ;___ rotunda orthogonalis: 137 line 7, 218 line 6 ; ____ rotunda orthogonia: 116 lines 40 and 9 and 14, 118 line 2, 119 line 2 (C.3), 204 lines 8 and 12, 205 line 2 (C .l), 206 line 1;____rotunda rectangula: 116 line 14, 185 lines 4 -5 (C .l) and 11 (C .l), 187 lines 10-11, 204 line 12 planities or planicies: 13 n. 32, 97n, 351n planum: 237-39pass., 242n, 244 n. 5, 264 n. 21 pass., 269 line 11, 270 lines 48-49 et pass., 271 line 69, 273 lines 11-12 (El. V), 274 lines 15-17, 275 line 8 (El. IX), 276 lines 34-38 and 40, 277 lines 3 and 19, 278 line 48, 279 lines 2 (El. XIIII) and 8 (El. XIIII), 280 line 10 (El. XIIII) et pass., 281 line 14 et pass., 283 lines 6 and 18 and 24, 285 line 8 et pass., 311- Mnpass., 314-15 η. 11 pass., 317-18 n. 14 pass., 333 n. 31 pass., 334 n. 34

bis, 336 n. 39, 337 n. 40, 347 n. 62 pass., 351-52n, 353-54 n. 65, 360, 362-67, 375 bis, 377-78, 382-84, 386 bis, 38990, 393-94 pass., 396-401 pass., 404JO pass., 412, 414, 418-25 pass., 42631 pass., 436, 438-41, 444-47 pass., 450-54 pass., 457-58 pass. planus: 162, 187 line 20, 188 line 41 et pass., 215 line 6, 331 n. 23, 381, 431 bis, 45253 pass., 457 bis’, see regula, superficies plana plastrum: 187 line 13 plumbum: 134 line 18, 136 lines 79 and 86 bis pochea: 136 lines 89 and 91, 380 polio: 133 line 92, 135 line 65, 136 lines 80 and 87, 217 line 78, 379-81 pass. polus: 68 n. 8 bis pono: 13 n. 33, 41, 45 line 13 (Prop. 1) et pass., 46 line 25, 47 lines 50 and 57, 48 line 19 et pass., 60 lines 27 and 32, 67, 90 n. 36 pass., 116 line 41, 125 line 22, 132 line 63, 134 lines 18 and 25, 137 line 10, 208 line 68, 211 line 38, 215 line 20, 223 lines 1 and 16, 224 line 24 (Passage 2), 225 lines 50 bis and 55, 226 line 12, 237, 239 pass., 243-44 n. 5, 262 n. 18 (not indexed hereafter) porrigo: 237, 269 line 12 portio or porcio: 30 n. 53, 48 line 30, 60 line 30, 67, 92 n. 39, 115 line 36, 130 lines 8 (C.10) and 12-13 (C.10), 131 line 46, 132 line 52 et pass., 138 lines 37-38, 159— 60 n. 2, 178, 185 line 15, 187 lines 3840, 215 line 6 et pass., 216 line 35 et pass., 218 line 80, 219 lines 34-35, 220 lines 59-61, 221 lines 62 bis and 64, 264 n. 21, 265 n. 22, 271 line 78, 272 line 5 (El. II), 274 line 4, 275 line 4 (El. VII), 278 line 53, 280 line 5 (El. XVI), 282 line 100, 283 line 8, 331 n. 23, 346 n. 58, 366, 378 bis·, ____ circularis: 138 lines 32-33, 219 lines 30-31; ------parabolica: 182n positio: 66n pass., 70 n. 13 bis, 243n; positionem, per: 13 n. 33, 320n possum (“ to be squared” ): 66-67n, 24344 n. 5 bis, 261 n. 16 pass., 271 line 79, 111 lines 2 and 7, 278 line 48, 31112n, 315-16 n. 11 pass., 317-18 n. 14 pass., 332 n. 29; see potens postulatum: 270 line 39 et pass., 273 line 12 (El. V), 274 line 19, 279 line 6 (El. XIIII), 283 line 25, 285 line 16 (El. XX), 364-66, 375 potens ( = squared): 284 line 7 (El. XVIII), 287 line 35, 288 line 3, 289 line 23 (El. XXI) bis, 412, 414 potentia, see ratio potentia dupla praeceptio: 236 η. 3 praeceptum: 237, 244 η. 5, 262 η. 18

541

542

ARCHIMEDES IN THE MIDDLE AGES praemissa: 93 n. 41 praemissum: 286 line 2 premissa: 130 line 7 (C.9); premissam, per: 41, 57 line 18, 69 n. 11, 80 n. 26, 83n, 88n pass., 95 pass., 119 line 9 (C.3), 127 lines 28-29; ex premissa: 130 line 7 premissio: 7n premitto: 3 n. 3, 70 n. 11, 88n pass., 114 line 6, 116 line 18, 122 lines 77-78, 123 line 18, 124 line 25, 130 line 10 (C.9), 133 line 99 preparo or praeparo: 134 line 19, 381 principio: 70 n. 13 pass. principium (=principle): 12 n. 28, 200 line 4, 214 line 6, 387, 401, 418-22, 425 bis, 457 probabilis: 429 bis, 460 probabiliter: 429 probatio or probacio: 115 line 14 et pass., 119 line 7 (C.2), 122 lines 75-76, 123 line 12 (C.5), 124 lines 18 and 35, 125 line 18, 126 line 61, 127 lines 65 and 24, 132 line 57, 139 line 53 and var. (line 60), 187 line 34, 203 lines 12-13, 209 line 71, 211 lines 22-23 and 40, 424-25, 434, 455, 4 59;____, indirecta: 420 problema: 385pass., 393, 396-98, 401, 40709pass., 412, 414-16, 425-28pass., 43132, 446 bis, 457 problematice: 387, 409 problematicus: 409 probo: 21 pass., 44 line 17, 45 lines 8 (Prop. 1) and 8 (Prop. 2), 46 line 12 (Prop. 3), 47 line 29, 48 line 36, 56 line 18 (Prop. 2), 57 line 15, 89 n. 34, 114 line 10, 115 lines 17 and 29, 116 line 16, 118 lines 52-53, 119 line 7 (C.3), 120 lines 18 (C.4) and 21 (C.4), 122 line 74, 123 line 23, 124 line 32, 128 line 57, 132 line 72, 137 line 9, 138 line 27 et pass., 139 lines 53 and 5960, 189 lines 5 and 23, 190 lines 37-38, 200 line 3, 205 line 51, 206 line 19, 207 lines 22 (C.3) and 31, 208 lines 50 and 67, 210 line 31, 212 line 53, 216 line 46, 217 line 59, 219 lines 25 and 37 and 39, 221 line 65, 227 line 14, 277 line 40, 279 line 20, 285 line 20 (El. XIX), 289 line 13 (El. XXII), 399-400, 418-30 pass., 434, 437-38, 442 bis, 455, 459-60 procedo: 206 line 6 (C.2), 212 line 8, 265 n. 23, 432 procido: 239 prodeo: 64η, 70 η. 13, 378 producens ( = multiplier): 121 line 30, 207 line 27 producibilis: 88n produco (= to draw): 7n, 13 n. 33, 20 n. 42, 21 pass., 30 n. 53, 58 line 27, 66-67n, 70 ns. 11 and 13 pass., 80 n. 26, 83n, 85n, 87n, 89 n. 34, 90 n. 36, 91 n. 38, 95, 97n, 226 line 4, 237-40n, 242n, 244 n. 5 pass.,

261 n. 16, 262 n. 18, 263 n. 19, 264 n. 21, 265 ns. 22-23, 267n, 269 line 16, 270 line 67, 272 line 4 (El. IIII), 273 line 6 (El. IIII) et pass., 275 line 9 (El. IX), 276 line 11, 277 lines 11 and 24, 278 line 43, 280 line 8 (El. XV) et pass., 281 line 50, 282 lines 67-68 and 98-99, 283 lines 2 - 3 and 15-16, 284 line 45, 285 lines 3 - 4 et pass., 286 lines 42-43 et pass., 287 line 8 et pass., 288 lines 67 and 73, 289 line 8, n i p a s s . , 315-16 n. 11, 317-18 n. 14pass., 320n, 332 n. 29, 333 n. 31, 34546 n. 58, 365 bis, 370 bis, 372, 376, 382-83 pass., 386 bis, 389, 391, 393403 pass., 405-06, 408-10pa™ ., 412-13, 416-17, 422, 424-25, 427 bis, 429, 431 pass., 433, 437-38, 440-42, 444-45, 44748, 451, 454-56 productio: 395 productum: 121 line 30, 207 line 27, 223 lines 9 and 11 profunditas: 182n, 227 line 2 (Passage 5) prohicio (=projicio): 14 prolongo: 48 line 47, 60 line 35 prominens: 378 propinquitas: 352η propinquo: 285 line 25 (El. XX) propono: 33 η. 1, 68 η. 8, 70 η. 11, 79η pass., 82 η. 30, 85η bis, 87η pass., 89 η. 34, 90 η. 36 pass., 95, 120 line 8, 140 line 84, 277 line 30, 278 line 50, 280 line 7 (El. XVI), 289 line 24 (El. XXI), 391 proportio or proporcio: 21 pass., 45 line 14 (Prop. 2) bis, 46 lines 10 (Prop. 4) and 14 (Prop. 4) and 27, 48 lines 33-34 and 40-43, 56 line 16 (Prop. 2), 58 line 10 et pass., 61 line 2 et pass., 67, 68 n. 8, 19npass., 83-85npass., 88-89 n. 34pass., 93 n. 41, 111, 120 line 16 (C.3), 121 lines 31-34 and 50, 123 line 11 (C.6), 124 lines 24 and 28, 126 line 48, 206 line 17, 207 lines 27-28 and 30, 208 line 56 et pass., 209 lines 9-1 0 (C.6), 211 line 23 bis et pass., 224 line 15 et pass., 225 lines 40-46, 227 lines 16 and 18, 247, 264 n. 22, 277 line 9 (El. X), 286 line 15, 317-18 n. 14, 345-46 n. 58 pass., 348 n ;____, con­ tinua: 346 n. 58; ___ media: 346 n. 58; proportionis, dupla: 126 lines 45-46 and 48-49; proportionis, in medietate duple: 121 lines 44 and 46-47, 145n, 208 line 40; cf. medietas duple; proportionis, me­ dietas: 224 lines 20-21 et pass., 225 lines 42-44, 227 lines 19-21 proportionabilis: 284 line 12 (El. XVIII) proportionalis or proporcionale: 61 lines 11-12, 67, 84, 238, 243n, 271 lines 13-14 and 20-21, 272 line 18 (El. Ill), 273 line 21 (El. IIII), 279 lines 15 and 18, 282 line 83, 284 line 11 (El. XVIII), 345 n. 58, 366, 368-71, 394 bis, 432-34, 438 bis:

INDEX OF LATIN MATHEMATICAL TERMS 60 line 27 et pass., 66-67n pass., 83n, 97n ___ , continue: 261 n. 16 pass., 271 line pass., 117 lines 30 and 33, 119 line 4 16, 272 line 17 (El. II), 278 lines 6 -7 (C.2) et pass., 120 lines 15 (C.3) and 19 et pass., 279 line 26 (El. XII), 282 lines (C.3), 122 line 2, 123 line 12 (C.5) et pass., 80-81, 373; ____, media: 238 pass., 124 lines 21 and 3, 125 line 10, 127 lines 243-44 n. 5, 260-61 n. 16, 262 n. 18, 271 14 and 22 and 27, 131 lines 17-18 et pass., lines 3 -4 (El. I) and 8 -9 , 272 lines 5 137 lines 4 -5 , 138 line 19 et pass., 162 (El. II) and 3 -4 (El. Ill) and 12 (El. Ill), pass., 188 line 36, 189 line 66, 200 line 273 lines 8 -9 (El. IIII) et pass., 274 lines 21, 204 lines 21 and 28 and 31, 206 lines 28 (El. V) and 23-24, 276 line 20, 277 lines 3 (C.2) and 9 (C.2) and 20, 209 line 1 34-35 and 37, 289 lines 11 (El. XXI) and (C.5) et pass., 210 lines 19 and 2 and 9, 13 (El. XXI), 315 bis, 367-68, 370, 374, 212 line 13, 213 lines 20-21, 215 line 17 390, 413;____, medio loco: 162, 190 lines et pass., 216 line 37, 217 lines 60 and 62 51-52 and 60, 208 lines 64-65, 211 line and 70, 218 lines 3 bis and 5, 219 lines 27, 226 line 25 (Passage 3), 227 lines 13 17 and 21 and 24, 223 line 14, 264-65 ns. and 28; proportionale, medium: 227 lines 22-23, 266 n. 25, 267n, 283 line 22, 285 21-22 line 23 (El. XX), 286 line 44, 289 line 9, proportionalitas: 64n, 84, 88 320-21 n. 15, 336 n. 39, 347 n. 62 pass., proportionaliter: 191 line 8, 264 n. 22 351-52n, 353 n. 65, 384, 386, 393-94, 396, propositio: 21,44 line 12, 55 line 12, 91 n. 38, 398, 400pass., 403, 405-08, 411, 419, 429 111, 161-62 n. 9, 186 lines 27-28 and 31, bis, 444-45, 447, 453-54, 456 187 lines 32 and 15, 189 lines 3 -4 , 190 lines 38-39 and 41, 206 line 6 (C.3), 223 proveho: 337 n. 40, 400 line 18, 224 line 1 et pass., 225 lines provenio: 96 n. 43, 320n proximo: 401, 407-08, 445 bis 50 and 1, 227 line 14, 261 n. 16 pass., proximus: 401, 407 262 n. 18, 263 n. 19, 264-65 ns. 22-23 pass., 271 lines 10 and 13 and 17-18, pulverico: 136 line 83 272 line 12 (El. II) and 14 (El. II) and pulveriso: 380 17 (El. Ill), 273 lines 20 (El. IV) and 19- pulvis: 136 line 83 et pass.: ------ calcis: 137 line 99 20 (El. V), 274 line 27 (El. V) et pass., 275 line 11 (El. VII) et pass., 276 line punctum or punctus: 4 n. 5 pass., 11 n. 26, 12 n. 28, 13 ns. 32-33, 20 n. 42, 21, 29 12 et pass., 277 lines 32 and 34 and n. 49, 30 n. 53, 31 n. 55, 41, 44 lines 16 37-38, 278 lines 14 and 23, 279 lines 17 and 1 (Prop. 1), 45 line 7 (Prop. 1)etpass., and 27-28, 280 line 13 (El. XIV), 281 line 46 line 9 (Prop. 3) et pass., 47 line 30 21 et pass., 282 line 63 et pass., 283 et pass., 48 lines 21-22 et pass., 49 lines lines 30-32, 284 lines 6 -7 (El. XVIII) 61-63, 55 lines 17 and 1 (Prop. 1), 56 and 10 (El. XVIII), 285 lines 17-18 (El. line 5 (Prop. 1) et pass., 57 line 3 (Prop. XIX), 286 line 32 et pass., 287 line 8 3) et pass., 58 lines 5 -6 et pass., 59 et pass., 288 line 46 et pass., 289 line 10 bis, 60 lines 31-32 et pass., 68 n. line 14 (El. XXI) et pass., 311 —12n, 322, 8 pass., 79n pass., 80 n. 26 pass., 82 n. 360-61, 365-68, 370-75, 378-79, 381, 3 0 pass., 8 3 -8 5 n pass., 87npass., 88-89 383, 386-89, 391-92, 394, 396, 402-04, n. 34 pass., 90 n. 36, 91 n. 38, 93 n. 41 406, 409-11, 414, 427, 429, 432-46pass., bis, 95-96 n. 42pass., 97npass., 119 line 4 4 9 ;___ lateralis: 190 line 46 2 (C.2) et pass., 120 line 15 (C.3) et pass., proprietas: 13 n. 32, \90\me Abet pass., 191 121 lines 22 and 36, 122 line 60, 123 line 12 lines 79 and 2, 332 n. 27 (C.5), 124 lines 19 and 21-22, 125 line 13 protendo: 119 lines 4 (C.2) and 7 -8 (C.2), bis et pass., 126 lines 40 and 59-60, 125 line 13, 127 lines 8 -9 and 13 and 17, 127 lines 2 -4 et pass., 128 line 59 bis, 129 139var., 205 lines 49-50, 206 line 3 (C.2), line 64, 130 line 5 bis (C.9), 131 line 28 209 line 24, 210 lines 4 and 12 (C.7), 212 et pass., 138 line 17 et pass., 159 n. 2, 160 lines 7 and 12 and 16, 224 line 3, 337 n. n. 5, 162-63 n. 9 pass., 186 lines 40, 455 bis 22-23 (C .l) et pass., 187 line 27, 188 protractio: 187 line 3, 191 line 4, 192 line lines 33 and 38, 189 line 17 et pass., 190 3 7 ;____continua: 185 line 9 (Proem) line 35 et pass., 191 line 82 et pass., 192 protraho: 4 n. 5 pass., In, 8 n. 21, 11 n. 28, lines 32-35, 200 lines 7 and 21,201 line 40, 12 n. 31, 13-14 n. 33 pass., 20 n. 43, 44 205 line 1 (C.2), 206 line 3 (C.2) et pass., lines 1-2 (Proem) et pass., 45 line 9 (Prop. 207 line 21 (C.3) et pass., 208 line 52, 1) et pass., 46 line 9 (Prop. 3) et pass., 209 lines 11 and 3 (C.6), 210 lines 1947 line 51 et pass., 48 line 9 et pass., 55 20 and 11-12 (C.7), 211 lines 15-16, 212 lines 1-2 (Proem) et pass., 56 line 12 line 50 et pass., 213 lines 19-20 et pass., et pass., 57 line 6 et pass., 58 lines 214 lines 53 and 4 bis, 215 line 33, 216 25-26 and 28 and 33, 59 line 2 et pass.,

543

544

ARCHIMEDES IN THE MIDDLE AGES lines 47 and 49, 217 lines 60 and 63, 219 lines 15 and 26 and 28, 220 lines 55-56 and 58 and 60, 221 lines 62 and 64, 223 line 10, 224 lines 2 and 4 and 10, 225 lines 53-54 and 18, 226 line 2, 237-40n pass., 243n, 261 n. 17, 264-65 ns. 20-23, 267n pass., 269 lines 11-12 and 18 and 27, 270 line 45, 271 lines 73 and 2 -3 (El. II), 272 line 7 et pass., 273 lines 12 (El. IIII) and 23 (El. IIII), 275 line 7 (El. VIII), 276 lines 32-33, 277 lines 18 bis and 28, 278 line 42 et pass., 279 line 2 (El. XIII) et pass., 280 line 2 (El. XV) et pass., 281-82 lines 56-57 and 64 and 69, 283 line 18, 285 lines 7 and 17 (El. XX) and 26, 286 lines 45 and 54, 287 lines 5 and 11 and 35, 288 lines 63 and 69, 289 line 5, 311-12ηρα.?ί., 315-16 n. 11 pass., 317-18 n. 14 pass., 320-21 n. 15, 332 n. 29 pass., 333 n. 31 pass., 335 n. 37, 345-46 n. 58 pass., 347-48 n. 62, 351-52n pass., 360, 362-67, 370-79 pass., 382-83 pass., 385, 395-400 pass., 403 bis, 406-07 pass., 414 bis, 417, 419, 421, 423-25 pass., 427-30, 434, 437-40, 445-47, 450-51, 453-55, 458 bis·, ____ capitis: 4 n. 5, 7 n ;___ combustionis: 223 line 17, 224 line 26 (Passage 1), 226 line 1 1 ;___ communis: 200 line 22, 376; ____ con­ cursus or vice versa: 21, 83n, 124 lines 14-15 and 30-31, 125 line 9, 210 lines 1 3 - 14 and 8 (C.7), 265 n. 22, 352n; ----- concursus radiorum: 162-63 η. 9, 186 line 16, 189 lines 16-17, 191 lines 84-85, 201 line 4 1 ;____contactus: 91 n. 38, 190 line 68, 265 n. 22, 346 n. 58, 347 n. 62, 372, 419, 421 pass.·, ____ contingendae or contingende: 91 n. 38, 123 line 7 (C.6), 124 lines 5 -6 , 209 line 6 (C.6), 210 line 4 (C.7), 225 line 56; ____divisionis: 271 line 3 (El. I), 288 line 58; ____ extrin­ secus: 46 lines 15 (Prop. 4) and 19 (Prop. 4) and 21, 123 lines 4 -5 (C.6); ____ fixus: 4 n. 5 ; ___ incidendae: 97n, 265 n. 23, 364, 375;___ intermedius: 190 line 41; ----- intrinsecus: 123 lines 4 -5 (C .6);____ medius: 71n, 118 line 44, 120 line 11, 121 line 42, 127 lines 18-19, 131 lines 2627 and 33 and 42, 162 bis, 186 lines 1 4 - 15 and 21, 187 lines 26 and 28, 191 lines 83 and 25-26, 200 line 24, 205 line 43, 212 line 17, 215 lines 20-21 and 32, 225 line 18, 226 line 36, 352n, 363-64, 367, 372 pass., 374-75; ___ reflexionis: 29 n. 49, 376; ___ supremus: 71n, 363; ___ tactus: 29 n. 49, 333 n. 31 purgatio: 134 line 7 purpureus: 135 lines 58 and 67 purus: 134 line 17 pyramidalis: 80 n. 26; see intersectio, sectio pyramidalis

pyramis: 68 η. 8 pass., 69-70 ns. 11 and 13 pass., 71n pass., 78-79 n. 23 pass., 80 n. 26 pass., 162 pass., 173, 186 lines 29 and 4, 188 line 24, 200 line 7 bis et pass., 201 line 44, 226 line 27, 227 line 3 (Passage 6) and 6 (Passage 6) and 8 (Pas­ sage 6), 264 n. 21, 266 n. 25, 267n pass., 331 n. 23; cf. piramis; see sectio pyramidis, ypotenusa;___ ampligonia: 68 n. 8 ; ----- declivis: 247;____ laterata: 6 9 70 ns. 11 and 13, 7 9 n ;____obliqua: 247; ----- orthogonia: 227 line 2 3 ;____ ortho­ gonia rotunda: 200 line 5 ; ____ortogonia: 201 line 3 5 ;___ oxigonia: 68 n. 8 pass. ·, ----- rectangula: 68 n. 8, 186 lines 2 and 8, 187 lines 29-30, 200 lines 27-28; ____ rectangula rotunda: 331 n. 23: ____ ro­ tunda: 35 n. 6, 68 n. 8 pass., 69-70 ns. 11 and 13, 71n, 78-79 n. 23 et pass., 205 line 8, 227 line 1 (Passage 6), 247, 324, 331 n. 23 bis, 362; ___ rotunda orthogona: 185 lines 6 -7 (C .l); ____ rotunda rectangula: 185 lines 6 -7 (C .l) and 16, 186 line 18 (C.l) Pythagoricus: 385

quadrangularis: 215 lines 6 and 15, 380 quadrangulum: 84, 207 line 22, 284 lines 13-14; see corpus oblongum quadrangulum quadrans: 281 lines 17 and 48, 282 line 66, 316 n. 11 quadratum or quadratus: 13-14 n. 33 pass., 21 pass., 46 lines 13 (Prop. 4) and 17, 48 line 34 bis et pass., 58 line 14 et pass., 60 line 33 bis et pass., 61 line 1 et pass., 8 4 -8 5 n p a sj., 93 n. 41, 95-96 n. 42pass., 121 line 24 et pass., 124 line 26, 127— 28 lines 30-31, 128 line 32 et pass., 129 lines 63 - 64 et pass., 146 n. 2, 187 line 29 bis, 190 lines 50 and 59, 207 line 21 et pass., 208 line 35 et pass., 210 line 25, 213 line 27 et pass., 214 lines 51-52 et pass., 223 line 9 bis, 224 line 15 bis et pass., 225 lines 38-39 et pass., 226 lines 31-33 et pass., 227 lines 7 -9 (Passage 5) et pass., 228 line 29, 261 n. 16, 263 n. 19 pass., 265 n. 22, 271 lines 10-11 and 21, 272 lines 14-15 (El. II), 273 lines 3 and 10 (El. V), 274 line 2 et pass., 275 line 3 (El. VII) et pass., 276 lines 1416 and 6 -8 , 277 line 39, 278 line 41, 283 line 9 et pass., 284 lines 50-52 et pass., 285 lines 13-14 (El. XIX) et pass., 286 lines 34-36 et pass., 287 line 18 (El. XX) et pass., 289 line 12 (El. XXII), 311- 12n, 315-16 n. 11 pass., 317-18 n. 14 pass., 320-21 n. 15 pass., 346 n. 58 bis, 348n pass., 367-70 pass., 372-74 pass., 385, 388-97 pass., 399 bis, 407, 410-13, 41517pass., 432,434-36pass., 438-49pass.

INDEX OF LATIN MATHEMATICAL TERMS 71 and 5, 289 line 9, 311 —12n pass., 314-16 n. 11 pass., 317-18 n. 14, 332 n. 29, 333 n. 31, 346 n. 58, 347-48 n. 62, 352n bis, 365 pass., 367-79 pa ss., 38283, 388-89, 391, 393-94, 396-408 pass., 412-15, 418, 426-31 pass., 445 bis, 450, 452-58, 460; cf. linea recta rectangula quadrangula: 5Svar. rectangulum: 21, 84, 93 n. 41, 131 line 20, 215 line 16, 244 n. 6, 261 ns. 16-17, 263 n. 19pass., 265 n. 22, 272 line 6 (El. Ill) bis et pass., 273 lines 6 -7 (El. Ill) et pass., 274 lines 30-32 (El. V) et pass., radians, sol: 375 275 line 9 (El. VII) et pass., I l l line 40, radio: 136 line 78 283 line 10 et pass., 284 lines 49-50 et radius (=ray of light): 13 n. 32, 97n, 159— pass., 285 line 13 (El. XIX) et pass., 286 60 n. 2, 162, 185 line 6 (Proem), 186 lines 33-34 et pass., 287 line 13, 288 line lines 3 -4 and 19, 187 line 12, 188 lines 31 45 et pass., 289 lines 23-24 (El. XXI) and 52, 189 lines 16 and 21-22, 190 lines et pass., 315-16 n. 11 pass., 317-18 n. 36 and 38, 261 n. 17, 264 n. 20, 265 ns. 14 pass., 332 n. 29, 335 n. 37, 346 n. 58 22-23, 331 n. 23 pass., 360, 364 bis, pass., 347 n. 62, 363, 369-70, 372-74 375-76; see concursus, locus, punctus pass., 383, 388-97 pass., 399, 410-17 concursus radiorum, unio radiorum ;-----pass., 4 3 3 -4 6 pass., 448 -4 9 pass. solaris: 129 line 3, 133 line 97, 162 bis, 214 line 2 (C.9), 263 n. 20, 265 n. 23, rectangulus: 244 n. 6, 261 n. 16, 275 lines 10 (El. VII) and 12 (El. VII), 289 lines 2 360 bis, 364-65, 375-77, 380-81; ____ and 24 (El. XXII), 363, 377, 381; see conus solis: 261 n. 17, 263 n. 20, 364, 388 rectangulus, piramis orthogonia rectangula, radius ( = streak): 136 line 88 piramis rectangula, piramis rotunda rec­ radix: 33 η. 1, 218 line 91, 223 lines 9 tangula, pyramis rectangula, pyramis ro­ and 11; ____ quadrata: 218 lines 85 and tunda rectangula, quadrilaterum, sectio 89-90 rectangula, superficies rectangula, tri­ rafani, succus: 136 lines 74-75 angulus rectangulus, trigonus rectangulus rapa: 348n, 453-54 rectifico: 159 n. 2 raphanus: 352n, 380 rectilineus: 284 line 12 (El. XVIII), 385, ratio (= proportio): 262-63 ns. 1 8 -1 9 p im ., 402; see angulus rectilineus, figura, tri­ 271 line 21, 272 lines 15-16 (El. II) and angulus rectilineus, trigonum rectilineum 15 (El. III), 273 line 18 (EI. IIII) bis, 275 lines 3 (El. VII) bis and 6 (El. VII) and rectitudo: 7n, 8 n. 21, 46 line 4, 58 line 6, 456 12 (El. VII), 276 lines 15 and 6, 278 line 23, 279 line 27 (El. XII) et pass., 282 rectogonus: 124var. line 85, 283 line 7 et pass., 284 line 3 rectum (= at right angles to): 237pass., 244 n. 5, 262 n. 18, 276 lines 38 and 40, 405 (El. XVIII) et pass., 285 lines 20-21 (EI. bis (indexed sparingly) XX) and 29 and 31, 286 line 33 et pass., rectum, in: 47 line 7, 286 line 37, 287 lines 289 lines 12-13 (El. XXII) and 21 (EI. 24 and 37, 289 line 22 (El. XXI), 315 XXII), 311 —12n, 314-15 n. 11, 346 n. bis, 394, 411 58, 366-71 pass., 373, 388-96pass., 399400 pass., 406 bis, 423, 433 pass., 435- rectus (= angulus rectus): 21,84, 88n, 95 bis, 185 line 9 (C .l), 216 lines 53 and 56, 217 43 pass., 4 4 5 -4 6 ;____, dupla: 276 line 18 lines 71 and 73, 243n, 275 line 6 (El. VIII) bis, 369;____, duplicata: 276 line 19;-----et pass., 276 line 27, 282 line 77, 287 lines potentia dupla: 271 line 22, 272 line 17 18 (El. XXI) and 20 (El. XXI), 288 line 48, (El. Ill), 273 line 20 (El. IV); ____ , 289 line 11 (El. XXII), 311- 12n pass., subdupla: 369 314-15 n. 11 pass., 332 n. 29, 346 n. 58, reciprocus: 263 n. 19, 289 line 22 (El. XXII); 348 bis, 378, 382, 385 bis, 395, 405, 411, reciproce: 370 416-17, 427; cf. angulus rectus recta (= linea recta): 67 bis, 82 n. 30, 87n, 91 n. 38, 200 line 17, 201 line 34, 269 line rectus (adj.): 205 line 8, 206 line 7 (C.3), 213 lines 22 and 41, 236-37 n. 3 pass., 23916, 276 line 39, 277 line 23, 279 lines 9 40n, 264 n. 21, 270 line 35 bis, 275 line 7 (El. XIII) and 28, 280 lines 12 (El. XV) (El. IX), 337 n. 40, 347 n. 62, 353 n. 65, and 15 (El. XV), 281 lines 22 and 52363, 372, 431; see basis, conus rectus, 53, 282 line 69, 284 lines 3 (El. XVIII) diametros, latus rectum, piramis recta, and 10 (El. XVIII), 285 line 14 (El. XIX), superficies recta 286 line 41, 287 line 33, 288 lines 66 and

quadratus (adj.)\ see numerus, radix quadrilaterum: 367;____rectangulum: 378 quadrilaterus: 377-78, 383 quantitas: 60 line 47, 88n, 90 n. 36, 97n, 121 line 32, 131 lines 14-16, 139 line 70, 15960 n. 2, 162, 188 line 30, 189 line 32, 215 lines 9-12 and 19, 221 line 63, 223 line 7 et pass., 227 line 24, 267n, 368 bis, 377,394,458 bis; ___ continua: 207 line 28 quiescens: 162 quinquangulum: 385

545

546

ARCHIMEDES IN THE MIDDLE AGES redeo: 4 n. 5, 35 n. 6, 55 line 9, 68 n. 8, 96 n. 43, 116 line 4, 265 n. 23 redigo: 135 lines 47 and 49, 334 n. 34 reflectio: 111, 133 line 97; see angulus reflectionis reflecto: 97n, 130 line 5 (C.9), 162pass., 186 lines 20-21 (C.2), 189 lines 16 and 22, 190 lines 37-38, 227 lines 2 -3 (Passage 5), 261 n. 17, 263 n. 20, 265 n. 23, 331 n. 23, 364 bis, 375-77 reflexio: 162 pass., 186 line 25 (C.2), 187 line 12, 188 line 52, 376-77, 388; see angulus reflexionis, punctus reflexionis reflexus: 265 ns. 22—23; see linea reflexa refrango: 160 n. 2, 360, 364-65; 376 pass. regula: 130 lines 11 (C. 10) and 13 (C. 10), 131 line 14 et pass., 159 n. 2, 160 n. 5, 178, 191 lines 24 and 26 and 28, 192 line 31, 215 line 6 et pass., 218 line 80, 377; ____ plana quadrangularis: 130 line 9 (C.10) regulo: 131 line 26 relinquo: 162, 238 bis, 289 line 20 (EI. XXI), 378 reliqua: 278 line 25 bis reluceo: 214 line 4 (C.9) remaneo: 14-15n, 68 n. 8, 79n, 96 n. 42, 129 line 62 remotus: 30 n. 53, 46 line 19 (Prop. 4), 47 line 58, 58 line 20, 80 n. 26, 121 lines 38 and 40, 162 removeo: 22 reperio: 30 n. 55 repono: 134 line 35, 135 line 61 requiro: 133 line 2 res (= an algebraic unknown): 225 lines 21-22, 226 lines 23-24 (Passage 3) and 31-33, 227 line 27 reseco: 94-95n, 200 line 31, 212 line 53, 223 lines 17 and 21, 224 lines 6 -7 and 33, 264 n. 22, 377-78, 402, 414 residuum: 123 line 17, 125 line 32 bis, 126 line 52 bis, 211 lines 30-31 and 45-46, 225 line 45 bis resilio: 261 n. 17, 264 n. 20, 265 n. 23 resolutio (=analysis): 13-14 n. 33 pass., 17, 66n bis respicio: 84, 87n resto: 21, 84pass. resulto: 261 n. 17 reverbero: 263 n. 20 revolutio: 162, 185 line 11 (C .l), 186 line 9, 188 line 49, 201 line 36, 376 bis revolvo: 4 n. 5 pass., 44 line 8, 55 line 8, 162, 185 lines 10 (C.l) and 15, 188 lines 32 and 39 , 264 n. 21, 362-63, 374 bis, 378 ritum: 244 n. 6 rotula: 353 n. 65 rotunditas: 446, 450 rotundus: 226 line 27, 267n, 452; see columpna, conus rotundus, corpus rotundum,

figura, piramis rotunda, pyramis ortho­ gonia rotunda, pyramis rectangula rotunda, pyramis rotunda rubeo: 134 line 35, 135 line 56 sagitta or sagita: 13 n. 33 pass., 40, 44 line 9, 45 line 4 (Prop. 2) et pass., 46 lines 2 -3 and 22, 47 line 6, 55 line 9, 56 lines 4 -5 and 12 (Prop. 2), 57 line 4 et pass., 58 lines 4 and 24, 59 line 8, 117 line 28 et pass., 118 lines 42 and 44 and 51, 120 lines 3 -4 et pass., 123 line 6 (C.5) et pass., 124 line 13 et pass., 125 line 7 et pass., 126 line 41, 127 line 3 et pass., 130 lines 4 (C.9) and 6 (C.9), 162-63 n. 9, 182n, 186 lines 15 and 19, 187 line 28 bis, 200 line 20 bis et pass., 201 lines 37 and 45, 204 line 26 et pass., 205 lines 41 and 49, 207 lines 2 -3 et pass., 208 lines 33-34 and 49 and 69, 209 line 5 (C.5) et pass., 210 line 12 (C.6) et pass., 211 lines 20 and 37, 212 line 55 et pass., 213 line 20 et pass., 214 lines 3 (C.9) and 5 (C.9), 223 line 4 et pass., 224 line 3, 225 line 56 et pass., 226 lines 35-36 and 2 and 20, 227 line 3 (Passage 5) et pass., 228 lines 29-30, 247, 249, 320-21 n. 15, 325, 363 pass., 36 6 -7 9 pa ss., 381-82 pass. sal petrae: 381 sanguis: 136 lines 95-97 sarro ( = serro): 187 line 17 scalenus: 248, 270 lines 35-36, 416; see conus scalenus scalprum: 379-80 scientia: 13 η. 32 bis, 65 η. 5, 387-88, 409, 416 scindo: 59var., 134 lines 31-32, 135 line 69, 187 line 17, 287 line 30; see ferrum, instrumentum scio: 7 n. 18, 13 n. 32 scribo: 66npass., 260-61n, 263 n. 19, 267n, 276 line 24, 277 lines 12 (El. XI) and 15 and 17, 278 lines 50 and 55, 286 line 40, 287 line 32, 288 line 8, 289 line 16 (El. XXI) sculptus: 136 line 73 seco: 4 n. 5 pass., 7n pass., 8 n. 21 pass., 12 n. 31, 13 n. 33, 20 n. 42, 21 pass., 29 n. 49, 41, 44 line 15, 45 lines 1 (Prop. 2) and 6 (Prop. 2) and 9 (Prop. 2), 46 lines 1 and 22 and 25, 47 line 5, 48 lines 10 and 17, 55 lines 17-18, 56 line 11 (Prop. 1) et pass., 57 line 11 et pass., 58 lines 24 and 34, 59 lines 7 and 12, 60 line 22, 66n, 69 n. 11, 70 n. 13, 71n pass., 78-79 n. 23 pass., 80 n. 26, 82 n. 30, 83-85n pass., 87n pass., 88n pass., 90 ns. 36-37, 91 n. 38, 116 line 9 et pass., 118 line 2, 119 lines 12-13 (C.2) et pass., 120 lines 15 (C.3) and 9 and 18 (C.4), 125 lines 18 and 20,

INDEX OF LATIN MATHEMATICAL TERMS 137 lines 8 and 12 and 14, 138 lines 28-29, 162, 185 line 5 (C .l), 186 line 19 (C .l) et pass., 187 line 16, 189 line 34, 200 line 13 et pass., 204 line 8 et pass., 205 lines 2 (C .l) and 5 and 7, 206 line 11 (C.2) et pass., 207 line 16, 211 lines 17 and 35-36, 212 lines 49-50 and 56-57, 218 lines 6 and 9, 219 line 12 et pass., 220 line 43, 221 lines 70-71, 224 line 12, 225 line 17, 226 line 20, 227 lines 2 -3 (Passage 6) et pass., 237-40npass., 24344 ns. 5 -6 , 261 n. 16 pass., 262 n. 18 pass., 262-63 n. 19, 264 ns. 21-22, 266 n. 25, 267n, 270 lines 48-49 et pass., 271 line 73, 272 line 5 (El. II) et pass., 273 line 15 (El. IIII) et pass., 274 lines 7 and 15, 275 lines 7 (El. VIII) and 9 (El. IX), 276 line 32, 277 line 8 et pass., 278 line 10, 280 lines 20 and 8 (EI. XV), 281 line 14, 282 lines 67 and 70, 283 lines 4 and 17 and 25, 285 line 8 et pass., 287 line 11 et pass., 288 line 9, 289 lines 15 (El. XXI) and 17 (El. XXI) and 8, 311- 12n pass., 314-15 n. 11 pass., 317-18 n. 14 pass., 320n, 332 n. 29, 334 n. 34, 337 n. 40, 346 n. 58 pass., 347 n. 62 bis, 351-52n pass., 363, 370-71 pass., 373, 376-77, 379, 382-83, 389-90, 393 pass., 395 bis, 397-99 pass., 402-06 pass., 408 bis, 410-11, 413-14, 418, 421-24 pass., 426, 429-30 pass., 432, 434-37 pass., 439_40, 442, 444-45, 447 -4 8 pass., 45051, 453-54, 458 b i s ; ____, bifariam: 237, 264 n. 22, 277 line 14, 279 line 25, 287 line 37;____, dividue: 276 lines 23-24, 277 line 11 (El. XI), 279 line 28, 285 line 20 (El. XX), 287 line 8, 288 lines 7 -8 sectio or seccio: 11 n. 26, 12 n. 31, 13 ns. 32-33 pass., 21 pass., 30 n. 53, 45 line 5 (C.3), 46 line 19 (C.3), 57 lines 5 and 14, 58 line 18, 59 line 15, 66n, 71n pass., 78-79 n. 23, 80 n. 26pass., 83n, 85n, 87n pass., 88n pass., 90 n. 36 pass., 91 n. 38 pass., 93 n. 41 pass., 96 n. 42 pass., 97n pass .,116 line 11, 117 line 24 et pa ss., 118 line 43 et pass., 120 line 5 et pass., 122 lines 52-53 et pass., 123 line 4 (C.5) et pass., 124 line 17 et pass., 125 lines 8 and 16-17, 126 line 60, 127 line 9et pass., 128 lines 35 and 53 bis, 129 lines 71 and 73, 130 line 6 (C.9), 159 n. 2 pass., 160 n. 5, 162-63 n. 9 pass., 177, 186 line 4 et pass., 187 line 30 et pass., 188 line 26, 189 line 64 et pass., 190 line 35 et pass., 191 lines 81 and 85, 200 lines 18 and 25, 201 line 44, 204 lines 10 and 22 and 32, 205 line 40 et pass., 207 line 4 et pass., 208 line 48 et pass., 209 line 2 (C.5) et pass., 2101ine 16 et pass., 211 lines 16-18and36, 212 line 52 et pass., 213 lines 18-20 et pass., 214 lines 57 bis and 59 and 5 (C.9),

217 line 76, 223 lines 2 -3 and 10, 224 line 25 (Passage 1), 225 lines 52-53 and 57 and 18, 226 lines 29 and 36 and 23, 227 lines 4 (Passage 5) and 22, 236-40 n. 3 pass., 244 n. 6 , 264 n. 21 bis, 266 n. 25 pass., 267npass., 271 line 74, 273 line 7 (El. IIII), 280 lines 6 (El. XV) and 12 (El. XV), 285 lines 11-12 and 16 (El. XX), 287 lines 30 bis and 32-34, 289 line 15 (El. XXI), 311 —12n pass., 314-16 ns. 10-11 pass., 317-18 n. 14 pass., 320-21 n. 15, 331 n. 23, 333 n. 31, 334 n. 35, 335 n. 37, 346 n. 58 pass., 351-52n, 360 bis, 362-64 pass., 366, 369-72 pass., 375-76, 378-79, 383, 398 pass., 406, 410 bis, 412, 414, 431 pass., 436, 440-42 pass., 444, 454 pass.; ____addita: 8 n. 21, 9-10, 12 n. 31, 31, 39-40, 103, 108-09, 117 line 25, 137 line 107, 160, 176, 204 line 23, 218 line 93;____ ambligonia: 103,117var.,2041ine35;------, amblygonii coni: 74 n. 17;----- ampligonia: 71n, 73, 87n bis, 226 line 2 9 ;------amplygonia: 82 n. 30;____aucta: 363;------ com­ munis or vice versa: 44 line 16, 48 line 12, 55 line 18, 56 lines 2 (Prop. 2) and 15, 58 line 35, 59 lines 12 and 16, 69-70 n. 11 pass., 70 n. 13, 71n., 78-79 n. 23 pass., 80 n. 26 pass., 88n, 117var., 119 line 3 (C.3), 137 line 15, 138 line 47, 139 line 78, 185 line 4 (C .l), 186 line 20 (C .l) et pass., 200 line 14, 206 line 2, 219 line 13, 220 line 44, 221 line 71, 227 line 4 (Passage 6), 237-39, 261 n. 16 , 264 n. 21 pass., 265 ns. 22-23, 270 line 48 et pass., 271 lines 68-69, 273 lines 13 (El. V) and 15 (El. V), 274 lines 16 and 18, 280 lines 21 and 12 (El. XV), 281 line 24 et pass., 283 line 26, 285 lines 18-19 (El. XX) and 27,311-12npass.,314-15n. ll,3 1 7 -1 8 n . \4pass., 3 6 4-65,390bis, 393-94, 397-99, 404-06pass., 408, 421, 424 bis, 439, 45354, 4 5 8 ;____, communis et triangularis: 364;____coni or vice versa: 67, 237, 239, 244 n. 6, 285 line 3, 314 n. 10, 436; ____conica or vice versa: 30 n. 53, 71n, 88n pass., 90 n. 36 bis, 236 n. 3, 242n, 264 n. 21 pass., 270 lines 61 and 63, 271 lines 71-74, 278 line 44, 280 lines 2 (El. XV) and 5 (El. XV) and 16 (El. XV), 286 line 45, 332 n. 27, 333 ns. 30 and 32, 334 n. 33, 353 n. 65 pass., 388 bis, 404, 431, 436; ___ defectio (=ellipse): 312 bis, 315 b i s ; ___ diminuta (= ellipse): 8 n. 21, 9-10, 11 ns. 26 and 28, 12 n. 31, 103, 117 lines 26- 27, 160 , 204 line 24, 325, 376; ____ diminuta ( = small segment of pa­ rabola): 325, 363; cf. sectio parabola diminuta; ____ eclipsis(Z): 204 line 36; ___ ellipsis: 315, 318n bis; cf. ellipsis; ___ hyperbole: 176, 260n, 312 bis, 315— 16 n. 11, 317-18 n. 14; cf. hyperbole;

547

548 ARCHIMEDES IN THE MIDDLE AGES ___ hyperbolica: 286 lines 54-55 and 57, 25, 206 line 18, 207 line 23, 208 line 41, 417 bis; ___ muchefi: 137var.; ____ 278 lines 5 and 12-13 and 18, 360, 366mukefi: 8 n. 21, 9-10, 12 n. 31, 13 n. 33 67, 375-77 bis, 96- 97 n. 43 pass., 108, 117 lines semidimetiens: 345 n. 58, 402 pass. 23-25 et pass., 118 line 42 et pass., 120 semidyameter: 68 n. 8 bis, 71n, 79n, 88n, 90 lines 9 and 20, 122 line 2, 123 line 2, 124 n. 36 pass., 214 line 5 (C.10), 215 line lines 18 and 20 and 2, 125 line 12, 129 lines 9 et pass., 217 line 79 1-2, 159 n. 2 pass., 160, 162 pass., 168— semis: 2llvar., 381 69, 173, 185 line 1 et pass., 186 line 25 semissa: 218var. (C .l) et pass., 187 line 28 et pass., 188 semita: 13-14 n. 33 line 22 et pass., 189 line 9, 190 lines sententia, communis: 263 n. 19, 282 lines 48-49 and 66, 191 lines 2 and 4 -5 , 192 72-73 and 90, 283 line 43, 284 line 54, lines 37-38, 201 line 45, 204 line 20 285 line 15 (El. XIX), 286 line 17, 287-88 et pass., 205 lines 38-39 et pass., 207 lines 41-42 and 56, 289 line 19 (El. XXI), lines 8 bis and 17-18, 209 lines 1 (C.5) 367-68, 373, 382, 396, 399-400pass., 402 and 18 and 1 (C.6), 210 line 17 et pass., pass., 404, 406 pass., 411-12 pass., 416, 214 lines 1-2 (C.9), 217 lines 66 and 74, 223 420, 433 bis, 436, 438, 440 bis, 444, line 1, 224 lines 2 and 9, 225 lines 2 and 9, 448-51 pass. 226 line 20, 227 lines 1-2 (Passage 6) and separo: 7n, 13 n. 33 pass., 134 line 33, 223 9 (Passage 6) and 23, 324; ____ mukefi line 5, 265 n. 23, 320n bis addita: 71n, 109, Wlvar., 140 line 85, 204 sexangulum: 385 bis line 35; ___ mukefi diminuta: 71n, 117 signo: 56 line 16 (Prop. 1) and 13 (Prop. 2), var., 204 line 36; ___ opposita: 10 n. 23, 57 lines 8 and 10, 58 lines 8 and 26, 71n, 11 n. 26, 12 ns. 28 and 31, 23n, 87n; 80 n. 26, 97n, 119 lines 15 and 12 (C.3), ___orthogonii coni: 237;____ ortogonia: 120 line 15 (C.3), 123 line 3, 127 lines 2 201 line 4 6 ;____oxigonia: 71n, 80 n. 26, and 10 and 13-14, 131 line 40, 132 line 73, 103, 117var., 204 line 36; ___ oxygonii 138 lines 27 and 29, 139 line 61, 206 lines coni: 71n, 237;____parabola or parabolae 14 (C.2) and 13 (C.3) and 16 (C.3), 209 or vice versa: 91 n. 38 bis, 93 n. 41 bis, line 2 (C.6), 212 lines 1 and 9 and 12, 215 94-95n, 97n, Wlvar., 120 line 2, 127 lines line 30, 217 line 60, 219 line 26, 220 line 55, 2 and 17, 128 line 33, 162, 168, 185 line 227 line 9 (C.6), 272 lines 2 (El. Ill) and 3 (C .l), 187 lines 14-15, 201 line 46, 204 20 (El. Ill), 273 line 12 (El. IIII), 288 line 34, 207 line 1, 212 lines 1 and 16, 213 line 64, 346 n. 58 bis, 365 lines 29-30, 225 line 1, 267n, 320n bis, signum: 261 n. 16, 262 n. 18, 270 line 40, 273 331 n. 23, 360-82 pass.·, cf. parabola; lines 16 (El. IIII) and 9 (El. V) and 16 ___ parabola diminuta: 329, 3 7 7 -7 9 ;____ (El. V), 274 lines 33 and 7 -8 , 275 lines parabole: 260η, 31 Inez's, 314-15 η. 11,317 5 (El. VIII) and 7 (EI. IX), 276 lines 11 η. 14 bis; cf. parabole; ___ parabolea: and 25, 277 line 9 (El. XI) et pass., 278 331 η. 23; ____ parabolica: 265 η. 23; lines 11 and 15, 279 lines 12-13 et pass., ___ pyramidalis: 13 η. 32, 21, 29-31, 280 line 21 et pass., 281 line 18 et pass., 71η; ____ pyramidis: 30-31, 266 η. 25; 282 line 70 et pass., 283 line 5 et pass., ----- rectangula: 71η, 73, 103, Wlvar., 168, 285 lines 8 and 16 (El. XX), 286 lines 46 185 line 4 (C .l), 204 line 34, 331 n. 23 and 53 bis, 287 line 3 et pass., 288 line 59 b is ; ___ , rectanguli coni: 74 n. 17, 242n; et pass., 289 line 11 (El. XXII), 389-90 ----- yperbola: 204 line 35; cf. yperbola pass., 393-400 pass., 402-04 pass., 406 segmentum: 20 ns. 42-43, 213var., 244 n. 5, bis, 4 1 0 -14pass., 417-21 pass., 425pass., 261 n. 16, 262-63 ns. 18-19, 271 lines 3 428 bis, 434-35 pass., 437 bis, 439-40, (El. I) and 9, 272 lines 6 (El. II) and 3 442 bis, 4 4 5 -4 8 pass., 451-54 (El. Ill) and 5 (El. Ill), 273 line 8 (El. similis: 21 pass., 66n, 70 n. 13 pass., 84, 221 n il) and 13 (El. IIII), 276 line 3, 315, 331 line 67, 226 line 23 (Passage 4), 238-39 n. 23, 334 n. 35, 367, 369, 372-74, pass., 265 n. 23, 266 n. 25, 271 line 15, 4 0 1 -0 4 pass., 4 3 4 -4 6 pass., 442 276 lines 17-18, 284 line 12 (El. XVIII), semicirculus: 178, 218 line 87, 238, 264 n. 22, 288 line 59, 289 line 24 (El. XXI), 367, 273 lines 16 (El. V) and 18 (El. V), 274 375, 377, 402-03 pass., 408,411-12,414, lines 26 (El. V) and 27 (El. VI), 111 line 432, 437, 450, 453, 456-60 12 et pass., 281 lines 15 and 17, 288 line similitudo: 353 n. 65 8, 289 line 16 (El. XXI), 332 n. 29 pass., sinus rectus: 138 line 38, 139 line 65 bis, 367, 319 pass., 413-14 219 line 35, 220 lines 58-59, 226 line 22 semicircunferentia: 397 sinus versus: 138 lines 37-38, 139 line 69 semidiameter: 31n, 115 line 36, 120 line 17 bis, 219 lines 34-35, 221 lines 62-63, (C.3), 121 lines 26 and 45, 130 lines 8 226 lines 22-23 (C.10) and 12 (C.10), 131 lines 14-15 and situo: 134 line 10, 162

INDEX OF LATIN MATHEMATICAL TERMS 18, 263 n. 19, 271 lines 77 and 79, 273 situs: 70 n. 13 bis lines 8 -9 (El. V), 274 lines 34-35 et p a ss., sol: 97n, 135 line 54; see corpus solis, 275 line 13 (El. VIII), 276 lines 2 and 4, radians, radius 277 lines 2 and 7, 278 line 47 bis, 280 solaris: 97n, 381 lines 6 (El. XVI) and 10 (El. XVI), 281 solidum: 263 n. 19pass. line 54, 282 line 101; see linea structim solidus: 377, 431 bis, 455 bis; see figura, materia stylus: 353 n. 65, 377-78 sollicitudo: 13 n. 32 spatium or spacium: 66n, 162, 277 line 11 subcontrarie: 239, 312 bis, 315 bis, 318n bis subfero: 278 lines 24-25 (El. XI), 278 line 56, 289 line 16 (El. XXI), 315, 317-18 n. 14 pass., 346 n. 58, subicio: 238, 285 line 19 (El. XIX) subintro: 365 401, 413 species: 67, 239, 312n pass., 315-16 n. 11 submergo: 134 line 36 subscribo: 364 bis pass. subsulto: 352n specularis: 387; see superficies specularis subtendo: 68 n. 8, 219var., 279 line 18, concava 281 line 44, 282 lines 85 and 95, 317 n. speculum: 13 n. 32 bis, 97n, 129 line 3, 14 bis, 346 n. 58, 363, 366, 400, 420 130 lines 6 (C.10) and 10 (C.10), 135 bis, 428, 452-53, 456 pass., 459-60 line 60, 136 line 80, 137 line 104, 159pass. 60 n. 2 pass., 162 pass., 182n bis, subtensa ( = subtended side): 271 lines 2 -3 189 lines 8 -9 and 15, 200 lines 26-27, 201 (El. I) et pass., 212 line 7 (El. II) lines 36 and 38, 214 line 2 (C.9), 215 line et pass., 273 lines 11 (EI. IIII) and 14 7, 218 line 88, 223 line 2, 227 line 2 (EI. IIII), 274 line 17, 282 line 58 (Passage 5) bis, 261 n. 17 pass., 263 n. succumbo: 408 bis, 429 20, 265 n. 22, 331 n. 23 pass., 360-61 sufficio: 30 n. 55 pass., 364-65p a ss., 375-77pass., 379-81 sulphur: 381 pass., 387-88; see the references to the summitas or sumitas: 46 line 3, 48 line 22, De speculis comburentibus under Alhazen 311 —12n pass., 314-16 n. 11, 354n, 415 and to the Speculi almukefi compositio bis, 4 5 6 -5 9 pass. under Anonymous in the Index of Names; ___ annulare: 381; ____ Archimedis . summum: 377 annulare: 182n; ___ ardens: 200 line 4; sumo or summo: 20 n. 42pass., 21 pass., 30 η. 53, 83n pass., 117 line 34, 186 line 18 ___ comburens: 114 line 2, 159 n. 2, 178, (C .l), 188 line 41, 190 lines 53 and 61, 185 lines 2-3 (Proem), 203 lines 3 (Praef.) 238-39, 243n, 261 n. 16, 262 n. 18, 264 n. and 15-16, 217 lines 78-79, 323, 335 n. 21, 269 line 6, 279 line 29, 283 line 18, 285 36; ____combustivum: 115 lines 34-35, line 17 (El. XX), 288 line 5, 317-18 n. 14, 130 lines 3 -4 , 137 line 103, 214 line 3 346 n. 58, 347 n. 62 bis, 352n, 376-78, (C .10);____concavatum: 129 line 2, 214 381, 389-91,407,413,433 line 1 (C .9);___ concavum or vice versa: 97n, 261 n. 17 pass., 265 n. 22, 364sumptio: 387 superficialis: 433 65, 375-76; ____ mukefi annularis: 227 superficies: 4 n. 5, 5 n. 7, 7n, 8 n. 21 pass., line 1 (Passage 5); ___ orbiculare: 381; 40-41, 44 lines 15-16 and 1 (Prop. 1) and ___ parabolice concavum: 265 η. 22;-----6 (Prop. 1), 45 line 15 (Prop. 1) et pass., parabolicum; 263-64 η. 20 bis, 265 η. 23, 46 line 10 (Prop. 3) et pass., 47 line 28 362bis, 376pass., 381 bis;___ spericum: et pa ss., 48 lines 9-10 et pa ss., 49 line 50, 13 n. 32; ___ sphaerice concavum: 263 55 lines 18 and 1 (Prop. 1), 56 line 5 η. 20, 265 η. 22; ____ sphaericum con­ (Prop. 1) et pass., 57 line 3 (Prop. 3) et vexum: 29 η. 49; ___ urens: 361; -----pass., 58 line 10 et pass., 59 line 41 ustorium: 323, 331 n. 23, 360pass., 362, et pass., 60 line 32 et pass., 64n, 68 n. 8, 365 69-70 n. l l ,7 0 n . 13 bis, l l n p a s s ., 78-79 sphaera: 244 n. 5 bis, 262 n. 18 bis, 262-63 n. 23 pass., 80 n. 26 pass., 90 n. 36, 97n n. 19pass., 431 pass., 116 lines 10-11 and 17, 117 lines 21 sphaerice: 263 n. 20, 265 n. 22 and 28, 118 line 5, 119 lines 2 (C.2) and sphaericus: 261 n. 17; see speculum sphaeri­ 4 (C.3), 131 line 18, 132 lines 52 bis and cum convexum 56, 133 line 78, 134 line 30, 137 line 10, stagnum: 136 line 93 138 line 26 et pass., 139 lines 48 and 55 and stannum: 380-81 79, 159-60 n. 2, 162, 186 lines 11-12, 188 stilus: 188 lines 21-24 et pass. lines 40 and 46, 200 line 13 et pass., 204 sto: 7n, 48 line 11, 59 line 15, 117 line 19, line 10 et pass., 205 lines 5 and 1 (C.2), 120 line 19 (C.4), 207 lines 17 and 19, 226 206 line 9 (C.3), 215 line 14, 216 line 44, line 2 217 line 64, 218 line 11, 219 lines 18 and 24 structim: 237 bis, 261 n. 16 pass., 262 n.

549

550 ARCHIMEDES IN THE MIDDLE AGES and 33, 220 lines 40-42 et pass., 221 lines 69 and 72, 224 line 11, 237-39 pass., 261 n. 17 , 264 - 65 ns. 22-23 pass., 269 line 14 bis, 282 line 71, 311 —12n pass., 315, 317-18 n. 14, 331 n. 23, 346 n. 58, 347-48 n. 62 pass., 351-52n pass., 360, 362-66, 3 7 4-78pass., 380-83pass., 397-98, 400-01, 405 pass., 407, 418-23 pass., 426-27, 429-30, 433,438, 444, 453, 455-56pass., 4 5 7-58pass., 4 6 0 -6 1 ;____ communis: 90 n. 3 6 ;____concava: 13 n. 32, 96-97 n. 43 pass., 263 n. 20 bis, 265 n. 23 pass., 380-81; ____, concava et parabolica: 381;____conica or vice versa: 69-70 n. 11, 70 n. 13, 71n pass., 79n, 80 n. 26 pass., 186 line 29, 237, 239, 264 n. 21, 269 line 17, 270 lines 40-42 et pass., 273 line 13 (El. V), 274 line 18, 276 lines 43-44, 279 lines 7 -8 (El. XIIII), 280 line II (El. XIIII) et pass., 283 lines 6 -7 and 19-20 and 26-27, 285 lines 10-11, 315 pass., 333 n. 31 pass., 352n pass., 353 n. 65, 363-67, 389-90, 393, 397-98 pass., 405, 407-08 pass., 420-23, 430 bis, 436 pass., 438-39, 446 bis, 450-51 pass., 453-54, 457-58 pass.·,___ curva or vice versa: 40-41, 55 line 18, 56 lines 2 -3 (Prop. 2), 71n, 78 n. 23,80 n. 26, 104n, 119 line 4 (C.3), 132 lines 51-52 and 5556 and 72, 133 lines 79 and 81, 137 line 15, 139 lines 58 and 78-79, 185 line 13, 206 line 3 (C.3), 216 lines 40-41 and 43-44, 217 lines 58 bis and 65 and 68, 219 lines 13 and 39, 220 line 52, 221 lines 71-72, 227 line 8 (Passage 6 ) :____exterior: 133 line 4; ____ inflexa: 274 line 18, 280 line 15 (El. XIIII), 281 line 16, 381; __ para­ bola: 381;___ parabolica: 265 n. 23, 381; ___ piramidis: 4 n. 5 pass., 45 lines 3 (Prop. 2) and 7 (Prop. 2) and 5 (Prop. 3), 46line 11 (Prop. 3) ^fp ass., 48 lines 17—18, 56 lines 8 -9 (Prop. 1) and 3, 57 lines 5 -6 et pass., 58 lines 9 and 29 and 35-36, 59 lines 13-14, 119 line 9 (C.3), 206 line 10 (C .3 );____plana: 4 n. 5, 7n pass., 8 n. 21, 69-70 n. 11 pass., 70 n. 13, 71n pass., 78-79 n. 23 pass., 80 n. 26pass., 96 n. 43, 116 lines 9 and 15, 117 line 19, 118 line 3, 119 lines 3 (C.3) and 14 (C.3), 133 line 77 et pass., 137 line 14, 138 line 24 et pass., 139 lines 53-54 and 66, 162,185 lin e 5 (C .l), 186 lines 2 0 (C .l)an d 25 (C. 2) and 28, 188 lines 34 and 31 and 43, 200 line 9 et pass., 201 line 44 , 204 lines 8 and 13 and 16-17, 205 line 2 (C .l), 206 line 2, 217 lines 63-66 and 74, 219 line 12 et pass., 220 line 40 et pass., 227 lines 3 (Passage 6) and 5 (Passage 6) and 8 (Pas­ sage 6), 265 ns. 22-23 pass., 331 n. 23, 346 n. 58, 347 n. 62 bis, 351-52n pass., 363-64, 378, 382-83, 419-20, 427, 429,

432, 446, 453, 458 pass.·, ____ recta: 55 line 18; ____rectangula: 61 line 2; ____ specularis concava: 97η, 265 η. 2 3 ;____ triangularis: 200 lines 13 and 15; ____ trigona: 68 η. 8 superior: 131 lines 22-23 et pass., 215 line 17 et pass., 216 line 36, 221 lines 70 and 72, 264 n. 21, 377, 394; see punctus supremus supero: 286 line 39, 394-95, 434 bis, 436, 442-43 superpono: 135 line 42, 139 line 54, 220 line 48 supersedo: 265 n. 22 supervenio: 78 n. 22 suppositio: 392 pass., 394, 402, 420-21 pass., 424, 433, 439, 442-43, 448, 458 bis, 460 bis suprapono: 132 line 47 suscipio: 270 line 41, 278 lines 2 and 9, 279 lines 2 (El. XIII) and 12 and 23, 282 line 73, 365-66, 395 syzyges: 237 bis

tabula: 223 lines 11-12 and 14, 331 n. 23 tangens: 29 n. 49, 48 line 11, 278 lines 3 and 10, 279 lines 3 (El. XIII) and 3 (El. XIIII) and 8 (El. XIIII), 280 line 15 (El. XIIII) et pass., 281 lines 22-23 and 29 and 49, 282 line 97, 312 bis, 333 n. 31, 334 ns. 33 and 35, 370 pass., 372 bis; 397 pass., 447 bis, 450; cf. linea tangens; tangentes, non: 312p irn ., 316 n. 11 pass., 332 n. 27, 334 ns. 34-35, 346 n. 58, 347 n. 62; tangentes contrapositarum, non: 334 tango: 21 pass., 45 line 4 (Prop.. 3), 46 lines 11 (Prop. 3) and 15 (Prop. 3), 6 6 67n, 119 line 4 (C.2), 131 line 39, 139 line 54 et pass., 188 lines 23 and 50, 192 line 36, 206 lines 3 -4 (C.2), 215 line 30, 220 lines 49-51 and 57, 280 line 11 (El. XIIII) et pass., 281 lines 25 and 36 and 51, 282 lines 59 and 95 and 97, 333 n. 31 pass., 347 n. 62 pass., 351-52n pass., 364, 370-72 pass., 375 pass., 378, 383, 393, 3 9 7 -9 9 pass., 402-03, 405 bis, 408, 418— 23 pass., 425 bis, 427-31 pass., 445-46, 453-54 tartarum rubeum: 381 tellus: 261 η. 17 tendo: 200 line 7, 351η, 456 tergo: 136 line 98 terminalis: 58var. termino: 201 line 41, 243n bis, 264 η. 21, 271 line 78, 283 lines 12 and 24, 346 n. 58 pass., 363, 455 bis terminus: 57 line 19, 7 0 n. 11, 83npass., 88n, 91 n. 38, 117 line 34, 283 line 3, 333 n. 31, 337 n. 40, 346 n. 58, 348n, 377, 403 bis, 425, 427

INDEX OF LATIN MATHEMATICAL TERMS terra crocea: 134 line 12 tetragonicus: 61 line 4 theorema or theoreuma: 59 line 14, 60 lines 26 and 38, 74 n. 17, 93 n. 41 pass., 237, 244 n. 5, 262 n. 18, 364, 385-86, 392, 394, 396 pass., 401 bis, 403-04, 415-17pass., 425-26pass., 435,440,447, 450, 455, 457—60; ____, Pythagoricum: 385 theorematice: 409 thesis: 23n thyraeos (=thyreos): 238 tornatorium: 162 tracto: 203 line 4 traduco: 262 n. 18 , 267n traho: 44 line 5 (Proem), 45 line 9 (Prop. 1), 47 line 30, 48 line 48, 55 line 5, 186 lines 21 (C. 1) and 23 (C. 1) and 17 (C.2), 188 line 38, 189 lines 18 and 20 bis, 190 lines 36 and 50 and 68, 191 line 17, 227 line 22, 267n bis transcindo: 134 line 20 transduco: 244 n. 5 transeo: 4 n. 5, 7n pass., 11 n. 26, 12 n. 28, 22, 44 line 16, 45 lines 3 (Prop. 3) and 8 (Prop. 3), 46 lines 2 and 23, 47 line 6, 55 lines 17 and 3 (Prop. 1), 56 lines 13 (Prop. 1) and 12 (Prop. 2), 57 line 3 (Prop. 3) et pass., 58 line 24, 59 line 8, 60 line 24, 66n, 70 n. 11 bis, 116 lines 10 and 15 and 17, 118 lines 44 and 3, 119 lines 8 (C.2) and 14 (C.3), 120 line 19 (C.4), 121 line 22, 122 line 60, 123 line 4 (C.5), 125 line 16, 131 lines 31-32 and 34, 137 line 8, 138 lines 18 and 35, 139 line 76, 162 bis, 187 line 27, 189 lines 28-29, 190 line 35 et pass., 191 lines 84 and 27, 200 lines 9 and 12 and 24, 204 line 9 et pass., 205 lines 43 and 3, 206 line 7 (C.2), 208 line 52, 209 lines 3 (C.5) and 6 (C.5), 211 line 15, 215 lines 25-26, 216 line 54, 217 line 62-63 and 66-67, 218 line 7, 219 lines 26 and 33, 220 line 56, 221 line 69, 276 line 39, 316 n. 11, 36367, 372, 374-75, 377-78, 382 bis, 402-03, 406, 421 bis, 427, 429, 439, 451 bis, 454-55 transitus: 4 n. 5, 35n, 68 n. 8, 116 line 2, 203 line 2 (Def.) transversa (=linea transversa): 267n pass.·, cf. linea transversa transversus: 131 lines 30 and 35 and 38, 215 lines 24 and 26 and 29, 312, 315-16 η. 11 pass., 318n bis, 333 n. 31 triangularis: 71n, 186 line 30, 200 line 33, 217 line 66, 225 line 8, 408, 428, 442; see figura, sectio communis et triangularis, superficies triangularis triangulus or triangulum: 7n pass., 8 n. 21, 21 pass., 35 n. 6, 45 line 15 (Prop. 1), 46 line 9 (Prop. 3) et pass., 47 line 6, 48 line

9 et pass., 56 lines 13 (Prop. 1) and 15 (Prop. 1) and 14 (Prop. 2), 57 lines 12 and 28 and 2, 58 lines 4 -5 et pass., 59 lines 11 and 16, 60 lines 28-29 and 38, 64n, 68 n. 8 pass., 84 bis, 88n, 116 lines 3 and 16, 117 line 22, 118 line 9, 119 lines 13 (C.2) bis and 14 (C.2), 120 line 18 (C.4), 124 line 24, 132 line 65, 133 line 83, 137 lines 13 and 15, 138 line 16 et pass., 162 pass., 185 lines 10-11 (C .l) and 14-15, 186 lines 20 (C .l) and 11, 188 line 31 et pass., 189 line 65, 192 line 33, 200 lines 10-11, 203 line 3 (Def.), 204 lines 14 and 19-21, 205 lines 11-12, 206 lines 11-13 (C.2), 207 lines 16-17 and 19-20, 210 line 24, 216 line 52, 217 lines 69-70, 218 lines 7 and 9-10, 219 lines 13 and 19, 220 lines 41 and 44 and 59, 221 line 69, 225 line 9, 227 lines 2 (Passage 6) and 4 (Passage 6), 237-40 pass., 244 n. 6, 264 ns. 21-22 pass., 269 lines 5 and 22, 272 lines 18 (El. II) and 5 (El. Ill), 275 line 8 (El. VIII), 276 lines 27-29 et pass., 279 lines 14 and 16, 281 line 19 et pass., 282 lines 62-63 et pass., 283 line 4 et pass., 285 lines 6 -7 et pass., 287 line 20 (El. XXI), 289 line 14 (El. XXII), 311-12n pass., 31415 n. 11 pass., 317-18 n. 14 pass., 333 n. 31, 334 n. 34 bis, 346 n. 58, 347 n. 62, 351-52n, 362-68 pass., 372, 378, 38283, 385pass., 389bis, 393 - 94 , 396, 399400, 404-07, 416-18 pass., 432 bis, 4364 0 pass., 445, 453 bis, 458, 460 b i s \ ____, ab axe: 239 bis, 264 ns. 21-22 pass., 270 lines 51 and 64-65, 283 lines 2 -4 et pass., 284 line 45, 285 lines 8 -9 and 1 2 ;____, ab axe coni: 237, 247, 264 n. 21, 271 line 69, 273 lines 13-15 (El. V)and 23-24 (El. V), 274 lines 13 and 16,281 line 14 et pass., 283 lines 14-17, 285 lines 5 -6 ; ___ aequilaterus: 385;____ equiangulus: 8 4 ;_____, ex axe: 237 bis·,____isosceles: 275 lines 11-12 (El. VIII), 282 line 74; ____ orthogonius: 104n, 236 n. 3; ____ orthogonus: 185 line 8 (C .l), 188 line 28; ___ ortogonius: 200 line 5 ;____ per axem or axim: 311 —12n pass., 314-15 n. 11 pass., 317-18 n. 14pass., 333 n. 31, 367 pass., 397, 404 bis, 408-09, 427, 436-38, 440-41, 453, 457-58, 4 60;___ per axem coni: 389 pass., 391, 393, 398-99, 424 bis, 4 5 7 -5 8 ;___ rectangulus: 35 n. 6, 44 line 7, 55 line 7, 68 n. 8, 116 line 2, 185 line 8 (C .l), 186 line 9, 200 line 10, 203 line 2 (Def.), 264 n. 21, 269 line 4, 274 line 17, 276 line 27, 288 line 47, 351n, 362-64, 378, 382; ____ , rectangulum ac isosceles: 364;___ rectangulus atque isos­ celes: 376, 3 8 2 ;___ rectangulus et isos­ celes: 271 line 5, 272 line 7 (El. II), 362-64, 367;___ rectangulus isoceles or

551

552

ARCHIMEDES IN THE MIDDLE AGES isoscelis: 271 lines 2 (El. I) and 2 (El. II), 273 lines 10 (El. IIII) and 23 (El. IIII); ___ rectilinearis: 118 line 6, 205 line 6; ___ rectilineus or vice versa: 270 lines 49 and 53, 275 line 10 (El. VIII), 369, 394, 436 trigonus or trigonum: 44 line 8, 45 line 12 (Prop. 1), 46 line 10 (Prop. 3) et pass., 55 line 8, 58 lines 7 and 10, 66n bis., 69 n. 11, 70 n. 13, 71npass., 19npass., 80 n. 26 pass., 84-85n pass., 88n bis, 95, 128 line 42, 225 lines 10 and 19, 226 line 29, 227 lines 6 -7 (Passage 6), 346 n. 58, 351-52n pass.·, ____ acutus: 225 line 20; ____ amplus: 225 line 20; ___ curvilineum: 71n; ___ equiangulum: 79n; ____ isocheles: 225 line 1 1 ;____orthogonius: 45 line 11 (Prop. 1), 68 n. 8 ;___ rectangulus: 68 n. 8, 70 n. 13; ___ rectilineum: 71n trilaterus: 351n, 385 trocus: 186 line 17 (C .l) bis trunco: 363, 378, 381 typus: 330, 381 pass. umbilicum: 335 η. 37 uniformis: 188 line 54 uniformitas: 226 lines 19 and 22 uniformiter: 191 lines 7 and 17 unio radiorum: 185 line 7 (Proem) utilitas communis: 13 n. 32 vado: 55 line 3 (Prop. 1), 60 line 26, 104, 119 line 5 (C.2), 206 line 4 (C.2), 285 line 15 (El. XX) velocitas: 13 n. 32 venio: 66n pass., 263 n. 19, 270 line 59, 345 n. 58 (indexed sparingly) vergo: 238, 337 n. 40 veritas: 13 n. 32 vertex: 60 line 25, 67 pass., 68 n. 8 pass., 69-70 n. ll ,7 0 n . 13 pass., Tin pass., 79η pass., 80 η. 26 pass., 87n bis, 90 η. 36 bis, 121 lines 38-39, 123 lines 15 and 19, 124 line 17, 185 line 12, 186 lines 19 (C .l) and 29, 208 lines 34-35, 209 lines 14 and 17, 210 line 16, 231-39pass., 244 ns. 5 -6 , 260-61 ns. 16-17, 262 n. 18 bis, 263 n.

19bis, 264-65 ns. 2 1 -2 2 pass., 265 n. 23, 269 line 15 et pass., 270 lines 40 and 48 and 59, 271 lines 68 and 73, 273 lines 6 -7 (El. V), 275 line 5 (El. VIII), 279 lines 2 (El. XIIII) and 5 (El. XIIII), 280 line 14 (El. XIIII) et pass., 281 line 13, 282 lines 99-100, 283 lines 2 and 15, 284 line 45, 285 line 15 (El. XX), 314-15 n. 11 pass., 317-18 n. 14 pass., 333 n. 31 pass., 334 n. 34, 346 n. 58 pass., 347 n. 62bis, 351-52npass., 363-72p a ss., 37476, 378 bis, 381-82 bis, 389 bis, 391, 393 bis, 397-99, 404-05, 419, 425 bis, 436-38 pass., 450-51, 453, 455 bis, 458 bis verticalis: 334 n. 34 verto: 264 n. 21, 269 line 22 vesica: 135 line 49 vestigium: 162 bis via instrumenti: 97n pass. viola: 135 line 67 virga: 130 line 7 (C.10), 134 lines 9 and 14 and 20, 214 line 5 (C.10), 377 pass. visibilis: 29 n. 49 visibilitas: 65 n. 5 visus: 29 n. 49 volvo: 45 line 12 (Prop. 1), 265 n. 23 ydolum: 136 line 97, 137 line 101 ymaginabilis: 70 n. 13 ymaginatio mechanica: 82 n. 30 ymaginor: 70 n. 13, 82 n. 50, 121 line 22, 132 line 59, 133 line 79, 137 line 14, 139 line 74, 162 bis ymago: 136 lines 70-71 yperbola or yperbole: 66-67n pass., 71n, 72-73, 74 n. 17, 87n pass., W lv a r., 204 line 35; cf. hyperbola; see sectio yperbola ypotenusa (=side of a cone): 324; ___ piramidis: 104n, 118 line 11, 205 lines 1 2 -1 3 ;___ , pyramidis: 247 ypotesis or ypothesis: 60var., 111, 121 line 42, 126 line 55, 128 line 43, 132 lines 63 and 65, 138 line 24, 186 line 21 (C.2), 189 line 27, 208 line 38, 211 line 20, 212 line 47, 216 line 51, 219 line 23; cf. hypothesis zabulum ( = sabulum): 134 line 26

Index of Manuscripts Cited

Brugge, Stadsbibl. 512: 19 n. 41 Cambridge Peterhouse Coll. Libr. 209: 19 n. 41 Trinity Coll. Libr. 0.5.30(1311): 19 n. 41 Dijon, Bibliotheque Anciens Fonds 441(226): 161, 161-63 n. 9; Figs. 5.2-5.3 Edinburgh, Royal Observatory 9-11-3(20): 19 n. 41 Erfurt, Stadtbibl., i.e. Wissenschaftliche Allgemeinbibliothek Amplon. F. 392: 19 n. 41 Escorial, Real Bibl. del Escorial J. III.31: 314, 314-16 n. 11

I have occasionally added to the manuscript numbers the abbreviatory siglum which I have used for the manuscript, since often reference to a manuscript is made in terms of the siglum alone. However, I have not in­ dexed the sigla in the variant readings to the edited texts.

Florence Bibl. Medicea Laurenziana Ashburn. 975 ( = MS F of Speculi almukefi compositio): 99, 103, 108, 110-13; Fig. 4.1-4.3 Bibl. Naz. II. III. 324 (Magliab. XX.52): 19 n. 41 Koprillii 952 (Arabic): 18 n. 37 Leiden, Bibl. der Rijksuniversiteit Cod. Or 14(6) (Arabic): 34 n. 5 Lincoln, Cathedral Chapter Libr. 238 (A. 7. 9): 159 η. 1 London British Library Cotton Tiberius B. IX (=M S C of Spec­ uli almukefi compositio): 99, 103, 108-13; Figs. 4.7-4.8, 4.10, 4.13 Royal 12 G VII: 19 n. 41 Sloane 306: 19 n. 41; Figs. 1.8-1.9 Royal College of Physicians 383(36): 19 n. 41, 31n; Fig. 1.9 Modena, Bibl. Estense II. D4 (Greek; abbr. Est): 236 ns. 1-2, 238, 240n Munich, Bay. Staatsbibl. 10269: 19 n. 41 Nuremberg, Stadtbibl. Cent. V, App. 6 (Greek): 184, 236 η. 1

Oxford Bodl. Libr. Canon, gr. 106: 236 η. 1 Canon Misc. 480 ( = MS O of Speculi almukefi compositio): 99, 102-03, 108,110-13; Figs. 4.1-4.4,4.12-4.13 D’Orville 70 (=M S O of De duabus lineis): 40; Figs. 2.2-2.4 Marsh 667 (Arabic): 4 n. 5, 7n Corpus Christi Coll. 150: 19 n. 41 260: 159 η. 1, 160 n. 2 Paris, Bibl. Nat. grec 2342 (= G r MS p of Apollonius): 235 η. 1 suppl. gr. 451: 236 η. 1 lat. 7247: 19 n. 41 7434 (= M SP of Version B of De duabus lineis): 40, 42-43, 159-60 ns. 1-5; Figs. 2.1-2.4 9335: 3, 4 n. 5, 7n, 8 n. 21, 10η, 11 ns. 26 and 28, 12 n. 31, 13 ns. 32-33, 172-73 16199: 19 n. 41 Saint-Omer, Bibl. Munic. 605: 19 n. 41 Vatican City Library Vat. gr. 203 (= G r MS v of Apollonius): 68, 75, 86, 235-36 ns. 1-2 206 (= G r MS V of Apollonius): 235-56 η. 1 218: 75n Pal. lat. 1355: 19 n. 41 Venice, Bibl. Naz. Marc, gr. 518: 235-36 η. 1 gr. 305 ( = Gr MS E of Archimedes): 245 n. 8 f.a. 327: 65 n. 4, 243n Verona, Bibl. Capitolare 206 (=M S V of Speculi almukefi com­ positio): 103, 108, 110-13; Figs. 4 .1 4.3, 4.12-4.13 Vienna, Nationalbibl. 5176: 42-43 5203: 174, 184 n. 30 5258 ( = MS R of Speculi almukefi com­ positio, i.e. Regiomontanus’ auto­ graph): 108, 110-13, 174-75; Figs. 4.1-4.3, 4.5-4.7, 4.12-4.13, 5.11, 5.13, 5.16-5.17 5277: 42-43, 263, 263-65 ns. 20-23 5322: 19 n. 41

555

Index of Apollonian Definitions and Propositions

First Definitions: 4 -7 , 12-13, 19 n. 40, 237, 240, 242, 249 Second Definitions: 11-12, 239, 241-42 Propositions 1.1: 239, 241, 248 1.2: 8, 36, 39, 248 1.3: 8, 19, 70, 104, 239, 241, 248, 436 1.4: 19, 36, 39, 71, 80, 89, 248, 437 1.5: 19, 80, 82, 239, 241 1.7: 68 n. 6 1.9: 81 1.11:8-10, 15, 17,66,94, 100-01, 104-06, 146, 149, 171, 209 line 71, 311n, 31415 n. 11, 316, 317 n. 14, 318n, 410 1.12: 8-10, 89, 108, 311-12n, 315, 316 n. 11, 317-18 n. 14, 430 1.13: 8, 10, 12, 312, 315-16 n. 11, 318n 1.14: 11, 25, 30, 65, 89-90 1.15: 82 1.16: 12

For general references to Apollonius the reader should also consult the Index of Names and Works.

559

1.17: 1.20: 1.21: 1.35:

91 n. 37, 239-40n, 241 68 n. 6, 105, 252 37-38, 40, 257 15, 17- 18, 66, 92-93, 100-01, 10506, 149, 171, 212 line 58, 229. 255, 333-34 I. 60: 89 n. 35 II. 1: 38, 40, 384, 409 II.4: 23, 25, 27-31, 65, 74, 82 n. 30, 83, 85, 258, 312, 316 n. 11, 318n, 409 II.8: 23-24, 27, 29-31, 65, 85-86, 262 (in fact 11.12) 11.12: 262 11.14: 39-40, 348, 384, 409 11.15: 25, 30-31 11.16: 26, 28, 30-31, 65, 90 11.17: 91 n. 37 11.38: 240n, 241 II. 39: 240n, 241 III. 20: 68 n. 6 V.34: 30-31

Index of Names and Works

Where names occur in a text and translation, references are to the pages of the translation only. However, all persons referred to in un­ translated passages appear in this index. Excepted are citations in the footnotes to proposition numbers of the Elements of Euclid; such cita­ tions can be found abundantly in many notes in this volume.

Academia Bolognese, 353 Adelard of Bath, see Euclid Alberius de Pontetremulo, 34 n. 2 Alberti, Leon Battista, 174 Albertus Magnus, 107 n. 10, 155 Alhazen ( = Ibn al-Haytham): his De speculis comburentibus, 3 -4 , 10, 13-18, 64, 76 η. 19, 91-92, 94, 96, 97η, 98-101, 106-07, 120, 159, 165-66, 168-69, 171, 173-75, 236, 261, 261-62 η. 17, 263-65, 319, 320η, 321, 323-24, 326, 328, 330-31,35758; for Gerard of Cremona’s translation see Gerard; his Perspectiva, 18-20, 21-22 n. 43, 23-31, 64, 65 n. 5, 80, 85-87, 89-92, 98, 103, 357, 359; “ The Problem of Alhazen” , 29; mentioned, 174n. 20,242 Alphraganus ( = al-FarghanI), 375 Amodeo, F., 332 Anonymous: De duabus lineis semper ap­ proximantibus sibi invicem et numquam concurrentibus, 33-61, 64, 69-70, 72, 100-02, 104, 108, 236, 248-49, 256-58, 260, 337-44, 351, 354, 356, 358-60; De sectione optimi speculi comburentis: vo­ catur Mukefi, 159; De speculo parabolico, 263-65; Libellus de proporcionibus thebith, 42, 59var.; Liber de curvis superficiebus Archimenidis, see Johannes de Tinemue; Speculi almukefi compositio, 17, 43, 70, 99-158, 160 n. 5, 165-71, 17375, 179-83, 195n, 228-30, 232-33, 236. 242, 247-50, 252-58, 260-61, 262 n. 17, 265 ns. 22-23,266,316, 319, 321-33,337, 339, 345, 350, 354-59; version of Regio­ montanus, see Regiomontanus Anthemius, 13, 76 n. 19 Apollonius of Perga: his Comparison o f the dodecahedron with the icosahedron, 64n; his Conics, 3-17, 19, 21-22, 24-25, 29, 30-31, 35-40, 49, 63-71, 73-77, 78 n. 23, 79-83, 85-90, 91 ns. 37-38, 92-94, 98, 100-06, 108, 110, 112, 140-43, 146-47, 149, 164, 170-71, 173, 175, 182-84, 19697, 203 lines 4 and 9, 204 lines 11 and 31, 205 line 40, 209 line 71, 212 line 58, 229, 231 n. 2, 235-42, 243n, 245-50, 252, 255, 257-58, 262-63, 311-19, 320n, 32324, 326, 328, 331-34, 335 ns. 36-37, 336-37, 346-49, 351n, 353, 355, 357-59, 362, 384, 387-88, 409-10, 430, 436; see Eutocius; for translations of the Conics see Commandino, Gerard of Cremona, Maurolico, Memmo; for individual prop­ ositions and definitions of the Conics see separate index; \De] loco resolutorio, 238, 241; mentioned, 20, 73, 76-77, 98, 111, 387 Arafat, W., 3 n. 2, 15n Archimedes: his Conoids and Spheroids, 63, 97n; his Equilibrium o f Planes, 63,

313, 388; his Floating Bodies, 63, 67, 317 n. 13, 388; the Lemmata attributed to, 29; his Measurement o f the Circle, 353 n. 64; his Quadrature o f the Parabola, 63, 92, 347; his Sphere and the Cylinder, 73-74; his Spiral lines, 26, 28; mentioned 13, 37n, 64, 74, 92 n. 40, 100, 104, 245, 249, 311, 314, 331, 335 n. 38, 358, 387; see Eutocius Aristaeus, 64n, 74, 92 Aristotle, 75n, 386, 416, 418-19, 429, 431 Bacon, Roger: his De compositione medi­ cinarum, 99-100; supposed author of the Speculi almukefi compositio, 99-100, 160n, 265 n. 22, 335 n. 38 Banii Musa, 29-30, 43n Barozzi, Francesco, 266, 319, 336 n. 39, 337 n. 41, 340, 345, 350, 352-58, 384-461 (Text) Bauch, G., 245 n. 10 Bembo, Pietro, 313, 314 n. 8 Bessarion, Cardinal, 235-36 η. 1, 245 n. 8, 313 Biancano, P.(?), 335 n. 38 Boncompagni, B., 33 η. 1, 353 n. 64 Bonucci, A., 174 n. 20 Borelli, Giovanni, 332 Borgnet, A., 107 n. 10 Boyer, Μ. N., 353 n. 64 Bredon, Simon, 99, 113 Calcagnini, Celo, 337, 351n, 384, 430-31 Calixtus III (Pope), 235n Camerarius, Joachim, 266 n. 25 Campanus of Novara: his version of the Elements, 35n, 64n, 69 n. 9, 78 n. 22, 90 n. 37, 101, 102 n. 6, 141, 229, 405; mentioned, 20, 24 Cantor, M., 245 n. 10, 248n Cardano, Girolamo, 266, 335 n. 38, 338, 345, 345-46 ns. 58-59, 347-52, 354, 356, 384, 397 n. 2, 399 ns. 9 and 11, 417-26, 428-29, 431, 445, 460 Cato, 193 Cavalieri, Bonaventura, 335 Clagett, M.: “ A Medieval Latin Transla­ tion” , 34 n. 3; Archimedes 7, 3 n. 3, 18 n. 38, 29 n. 46, 30 n. 55, 43n, 104n, 353 n. 64; Archimedes 2, 3 η. 1, 42 n. 14, 63 ns. 1-2, 66-67n, 68 n. 7, 74 n. 17, 92 n. 39, 97n, 170n, 172 ns. 12-15,173 n. 19,243-44 n. 5, 245 ns. 7 -8 , 250n; Archimedes 3, 41n, 65 n. 4, 75n, 173 n. 18, 175 n. 22, 243n, 245 ns. 7-10, 313 ns. 2 and 4, 316 n. 12, 317 n. 13, 321, 332 n. 26, 338 n. 44; “ Life and Works of Giovanni Fontana” , 99 ns. 3 -4 ; “ Works of Francesco Mauro-

563

564

INDEX OF NAMES AND WORKS

ARCHIMEDES IN THE MIDDLE AGES lico” , 313 n. 7, 314 ns. 8 -9 , 331 ns. 24-25, 332 n. 26 Commandino, Federigo: his version of Apol­ lonius’ Conics, 6 n. 17, 316-17, 317-18 n. 14, 319, 353, 355, 359, 409; his version of Archimedes’ On Floating Bodies, 317 n. 13; mentioned, 63, 353 n. 64 Coner, Andreas, 245, 311 Conon, 387 Contarini, Jacomo, 353 Courtenay, Richard, 172 Cremonensis, Jacobus, 243, 247 Curtze, M., 182n D ee,John, 113 Devreesse, R., 235-36 η. 1 Dijksterhuis, E. J., 63 D iodes, 15n, 262 Dionysodorus, 244 n. 5, 262 Du Cange, C., 161 n. 7 Durer, Albrecht, 266-68 Emden, A. B., 99 n. 2 Este, Ippolito d ’, 337 Euclid; his Conics, 74, 92; his Elements, 16, 23-26, 35, 40, 42, 49, 55-56, 60-61, 64n, 65, 69, 72, 78, 81, 90, 91 n. 38, 101, 141, 143-48, 150, 153, 157, 167-68, 176, 194, 197-98, 204 line 7, 206 line 11 (C.2), 207 lines 21 (C.3) and 23 (C.4), 208 line 54, 214 line 53, 229, 231, 292-97, 299-310, 318n, 323-24, 328, 330, 337, 340, 349-50, 360, 362, 365-76, 378-79, 382-85, 387407,410-14,419, 421-25,427-39,441-44, 446-49, 451-53; Adelard II version, 35; Campanus version, see Campanus; Zamberti version, see Zamberti; his Loci, 241; his Specularia, 264; mentioned, 20,69-71, 92, 174 n. 20 Eudemus, 314 Eutocius: his commentary on Apollonius’ Conics, 63, 68, 75-78, 86, 98, 236, 24041, 243-44 n. 5, 249, 317, 318n, 335 n. 37, 358, 384, 409-10; his commentaries on Archimedes, 236 n. 2, 358; his commen­ tary on Archim edes’ Equilibrium o f Planes, 63, 67-68; his commentary on Archimedes’ On the Sphere and Cylinder, 63, 66-68, 73-74, 86, 92, 98, 242, 243-44 n. 5, 245, 247n, 260, 262, 384 Fabio Vigili of Spoleto, 236 η. 1 al-Farghani, see Alphraganus Filelfo, Francesco, 235n Fine, Oronce, 105, 321-31,335 ns. 36 and 38, 354, 356, 359, 360-83 (Text), 384, 405 n. 2, 406 n. 8, 407, 425-28, 450 Folkerts, M., 245 n. 10 Fontana, Giovanni, 99 ns. 3 -4 , 172-74, 200-02 (Text), 357

Frederick II, 33, 34 n. 2 Fusoris, Jean, 18, 96, 105, 107, 113, 161, 163-72, 185-99 (Text), 322, 357, 359 Geminus, 69, 76, 35In, 384, 431 Gerard of Cremona: version of Alhazen’s De speculis comburentibus 3, 10, 13, 1517, 31, 64; and see Alhazen; fragmentary translation of Apollonius’ Conics, 3-12, 35, 39, 64, 70, 72-73, 82, 89, 101-02, 108, 111, 159 η. 1, 160, 173-75, 182-83, 184 n. 30, 231 n. 2, 240-42, 247-49, 323, 357; mentioned, 172, 353 n. 64 Ghetaldi, Marino, 334-35 Giosepho da Padova, see Joseph Schalit ben Jakob Gogava, A. H., 99, 101, 110, 113, 179, 31920, 321 n. 15, 322-23, 331, 355 Gruemberger, P. (?), 335 n. 38 Halley, E., 30 n. 53, 318-19 Heath, T. L., 11 n. 25, 26, 28n, 29 ns. 46-47, 37n, 63, 69 n. 10, 75n, 100 n. 5a, 249n Heiberg, J. L.: ed. of Gerard’s translation of Alhazen’s De speculis comburentibus (with E. Wiedemann), 3 n. 2, 13 n. 33, 96 n. 43, 169n, 262 n. 17, 265 n. 23, 326 ns. 19-23; ed. of Apollonius’ Conics, 3 n. 3, 4 ns. 4 -5 , 5 ns. 6-11, 6 ns. 12-16, 8 ns. 1 9 -2 1 ,9n, 10η, 11 ns. 24 and 26-28, 12 ns. 29-31, 17n, 18 n. 36, 29 ns. 50-51, 30 ns. 52 and 54, 36n, 37n, 38n, 39n, 70 n. 12, 76 ns. 20-21, 80 n. 25, 8ln, 82 n. 29, 86n, 89 n. 35, 91 n. 37, 105, 184 n. 28, 235n, 236 ns. 1-2, 240-41, 250n, 313, 319; ed. of Archimedes, 243-44 n. 5, 247n; “ Die Kenntnisse des Archimedes iiber die Kegelschnitte” , 63; “ Eine arabische Schrift iiber die Parabel und parabolische Hohlspiegel” (with E. Wiedemann), 113, 323 Henry, Abbot, 34 n. 2 Hilal ibn Abi Hilal al-Himsi, 7n Huillard-Breholles, J. L. A., 33 n. 2 Hultsch, F., 74 n. 18 Hurtado de Mendoza, Don Diego, 338 Huxley, G. L., 76 n. 19 Hypsicles, 64n Ibn Abi Usaybia, 34 n. 4 Ibn al-Haytham, see Alhazen Ibn Shem-Tob, see Samtou, Rabbi Isidore of Miletus, 170n, 244 n. 5 Jacobus Cremonensis, 64, 65 n. 4 Johannes de Tinemue (probable author of Liber de curvis superficiebus), 40-41, 104, 143, 205 line 13 John XXIII (Anti-Pope), 172

John of Palermo: 33-34, 40, 54, 248, 260, 358; and see Anonymous: De duabus lineis Jordanus de Nemore, 19,20n. 41,30,3In, 42 Joseph Schalit ben Jakob, 338 al-Karajl, 33 η. 1 Kepler, Johann, 335 al-Khayyaml, 33 η. 1, 34 n. 4 Knorr, W. R., 26n Krause, M., 18 n. 37 La Hire, Philippe de, 335 n. 37 Leonardo Fibonnaci Pisano, 33, 43 Lindberg, D. C., 3 n. 2, 18 n. 37, 100 n. 5, 161 n. 8 Madan, F., 40n Magini, Giovanni Antonio, 335 n. 38 Maimonides, Moses (= Rabbi Moyses Aegyp­ tius), his Dux seu director dubitantium, 336-39, 346, 349, 352, 356-57, 384, 38687, 418, 454 Margoliouth, G., 338 ns. 41 and 43 Mason, John, 323, 360 Maurolico, Francesco: his version of Apol­ lonius’ Conics, 313-16, 317 n. 14, 359; his edition of Archimedes, 316 n. 12, 332 n. 26; his Cosmographia, 313-14; his De lineis horariis liber tertius, 266, 316, 331-34; Index lucubrationum Maurolici, 331-32; mentioned, 63, 245, 256, 311, 314 n. 8 Memmo, Giambattista, his version of Apol­ lonius’ Conics, 236,311-14,316,317 n. 14, 318-19, 346, 353, 355, 359, 409 Memmo, Giovanni Maria, 311 Menaechmus, 259-60, 261 n. 16 Michaud, L., 324n Midorgius, C., see Mydorge Mirot, L ., 161 n. 6 Mizauld, Antoine, 324, 361-62 Moerbeke, William of, 63 - 64, 65 n. 4, 66, 68, 73-75, 76 n. 19, 86, 92-93, 100, 235n, 243, 244 n. 5, 245 n. 8, 247, 311, 313, 317 n. 13, 358 Moise Provenzale (= Rabbi Moyses N ar­ bonensis), 338-45, 348-51, 356, 384, 418, 431-54 (Text) Mo(ot, Simeon, 338, 338-39 n. 46, 340, 344 Mugler, C., 249-50n Murdoch, J. E., 64n Mydorge, Claude, 333 n. 30 Nebbia, G., 34 n. 4 Nicomedes, 242 Nix, L. M. L., 4 n. 5, 5 ns. 6-11, 6 ns. 12-16, 319

Paleotti, Camillo, 352-53, 385 Pappus, 26, 74-75, 241, 317. 355, 384, 416 Paravicini Bagliani, A., 76 n. 19 Peletier, Jacques, 351-53, 356, 384-85, 398 n. 3, 428-31 Pines, S., 336 n. 39 Pio di Carpi, Alberto, 236 n. 2 Plato, 429 Plato of Tivoli, 353 n. 64 Porta, Giambattista della, 331, 335 n. 38 Poulle, E., 161 n. 6, 172 n. 16, 321 Proclus, 20, 22-23, 25, 384, 431 Profiat, Duran, 337 n. 41, 339, 356-57 Prometheus, 324, 362 Ptolemy, 75n, 113, 319

Ravius, Christianus, 6 η. 17 Regiomontanus: his version of the Speculi almukefi compositio, 101, 105, 107, 110, 112-13, 175-83, 203-33 (Texts), 250, 256-57, 260, 266, 319, 322, 324, 359; mentioned 64n, 65, 235, 236 η. 1, 243n, 245 Richard, Claude, 6 n. 17 Risner, F., 18 n. 37, 19-20, 29, 31n, 65 n. 5, 69 n. 8, 70 ns. 11 and 13, 71n, 75 n. 19, 78 ns. 22-23, 80 n. 26, 82 ns. 28 and 30, 85n, 87n, 89 n. 34, 91 n. 38, 93 n. 41, 94n, 97n, 319, 326 n. 20 Roder, Christian, 182 Rose, P. L., 353 n. 64

Sabra, A. I., 18 n. 37, 29 n. 48, 30 n. 53 Sacerdote, G., 338—39 ns. 41 and 46 Samtou, Rabbi, ( = Ibn Shem-Tob), 337-38 n. 41, 384, 454-61 (Text and Com.) Sancto Vincentio, Gregorius a, 333 n. 30 Serenus, 82, 317, 387 al-Sijzi, Ahmad ibn Muhammad ibn Abdu ’l-Jalfl, 34 Simplicius, 75n Solomon ben Isaac, 338 n. 41, 339 Sorbonne College Library, 113,167,194,322 Spiazzi, G., 353 n. 64 Steinschneider, M., 338 n. 43

Taliaferro, R. C., 8 ns. 19-20, 9n, 11 ns. 24 and 27, 18 n. 36, 29 ns. 50-51, 30 ns. 52 and 54, 36n, 37n, 38n, 39n, 70 n. 12, 81n, 82 n. 29 Tartaglia, Niccolo, 313 Thabit ibn Qurra, 42, 59var. Theodorus, Magister, 33 η. 1, 34 η. 2 Theodosius of Bithynia, 236 η. 1 Thiene, Giulio, 353 Toomer, G. J., 15n al-Tusi, 35 n. 6

565

566 ARCHIMEDES IN THE MIDDLE AGES Unguru, S.: “ A Very Early Acquaintance” , 65 n. 5, 71n; “ Pappus in the 13th Cen­ tury” , 75n; his ed. of Witelo, 29 n. 49, 65 n. 5, 68 n. 8, 69 n. 11, 70 n. 13, 71n, 78 ns. 22-23, 80 n. 26, 82 ns. 28 and 30, 83n, 87n, 88n, 89 n. 35, 90 ns. 36-37 Valla, Giorgio, 236-50, 260, 262, 311, 313 η. 1, 325, 351n, 353, 384 Vogel, K., 33 η. 1 Walther, Bernhard, 184, 236, 246, 314 Watson, A. G., 99 η. 1, 113 Werner, Johann: his Commentarius . . . in undecim modos, 260-62, 265 η. 23; his Commentatio . . . in Dionysodori . . . problema, 260, 262-63 ns. 18-19; his Libellus super vigintiduobus elementis conicis, 39, 105, 2 4 3 -4 4 η. 5, 245-60, 264, 264-65 ns. 21-22, 266, 269-310 (Text), 322, 324-26, 330, 332-34, 335-36 n. 38, 344, 346-47, 350, 354-59, 384, 390 ns. 5 and 7, 392 ns. 5 and 8, 395 n. 9, 396 ns.

10-11, 414-18, 426, 431; mentioned, 244, 245 n. 10, 264 n. 20 Wickersheimer, E ., 161 n. 6, 172 n. 17 Wiedemann, E., see Heiberg, J. L. Winter, H. J. J., 3 n. 2, 15n Witelo and his Perspectiva, 20, 25, 29 n. 49, 3 1 ,6 3 -6 6 ,6 8 -7 5 ,7 6 n. 28,77-98,99-101, 102 n. 6, 104-07, 111-12, 140, 149, 161, 163,165-66,168-75,193-94,196,203 line 6, 235n, 241-42, 247-48, 266, 313, 316, 319, 321, 323-24, 326 ns. 20-22, 327-28, 330-31, 335 ns. 36 and 38, 357, 359-60, 405, 425, 427 Woepcke, F., 34 n. 4 Wyckof, D., 107 n. 10 Zamberti, Bartolommeo, his version of Euclid, 246n, 247 Zedler, J. H., 324n Zeuthen, H. G., 63 Ziegler, Jakob, 337, 35In, 431 Zinner, E ., 113, 174 n. 21, 175, 183n, 184 ns. 28-30