Bibliography The following list of cited works is divided into ancient, medieval and modern writings, where, for convenience, I take the 7th century to separate the ancient and medieval periods. Among the ancient and medieval titles I cite manuscripts when a published version is not available. When multiple entries occur for a given modern author, I have listed the titles in the order of publication. Ancient Sources Anonymus. Prolegomena tes tou Ptolemaiou megales syntaxeos: Vat. ms. gr. 1594 (Vati- can, 10th cent.), f. lr-9r; Marc. ms. gr. 313 (Venice, 10th cent.), f. lr-28r; B.N. ms. gr. 2390 (Paris, 13th cent.), f. lr-13v -. Introduction to the Syntaxis = Prolegomena ... Syntaxeos -. [Introduction, excerpt on isoperimetric figures]: see F. Hultsch, Pappi Collectio, III, pp. 1138-65 -. see also J. Mogenet (1956) Anthemius of Tralles. Peri paradoxon mechanematon (On Paradoxical Mechanisms, a fragment), ed. J.L. Heiberg, Mathematici Graeci Minores, Copenhagen: A.F. & Son, 1927, pp. 78-87 -. see also G.L. Huxley; and R. Rashed Apollonius. Quae graece exstant, ed. J.L. Heiberg, 2 vol., Leipzig: Teubner, 1891-93 (repr. Stuttgart, 1974) -. Conicorum libri octo, ed. E. Halley, Oxford, 1710 -. see also H. Balsam; T.L. Heath (1896); P. Ver Eecke (1924) Archimedes. Opera Omnia, cum Commentariis Eutocii, ed. lL. Heiberg, 2nd ed., 3 vol., Leipzig: Teubner, 1910-15 (repr. Stuttgart, 1972) -. see also A. Czwalina; T.L. Heath (1897); EJ. Dijksterhuis; C. Mugler; P. Ver Eecke (1921) Aristotle. Opera (I-II, Aristoteles Graece, ed. I. Bekker, 1831; III, Aristoteles Latine, interpretibus variis, 1831; IV, Scholia in Aristotelem, ed. C.A. Brandis, 1836; V, Index
35
Embed
Bibliography - Springer978-1-4612-3690-0/1.pdf · Bibliography The following list of cited works is divided into ancient, medieval and modern writings, where, for convenience, I take
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Bibliography
The following list of cited works is divided into ancient, medieval and modern writings, where, for convenience, I take the 7th century to separate the ancient and medieval periods. Among the ancient and medieval titles I cite manuscripts when a published version is not available. When multiple entries occur for a given modern author, I have listed the titles in the order of publication.
Ancient Sources
Anonymus. Prolegomena tes tou Ptolemaiou megales syntaxeos: Vat. ms. gr. 1594 (Vatican, 10th cent.), f. lr-9r; Marc. ms. gr. 313 (Venice, 10th cent.), f. lr-28r; B.N. ms. gr. 2390 (Paris, 13th cent.), f. lr-13v
-. Introduction to the Syntaxis = Prolegomena ... Syntaxeos -. [Introduction, excerpt on isoperimetric figures]: see F. Hultsch, Pappi Collectio, III,
pp. 1138-65 -. see also J. Mogenet (1956) Anthemius of Tralles. Peri paradoxon mechanematon (On Paradoxical Mechanisms, a
fragment), ed. J.L. Heiberg, Mathematici Graeci Minores, Copenhagen: A.F. H~st & Son, 1927, pp. 78-87
-. see also G.L. Huxley; and R. Rashed Apollonius. Quae graece exstant, ed. J.L. Heiberg, 2 vol., Leipzig: Teubner, 1891-93
(repr. Stuttgart, 1974) -. Conicorum libri octo, ed. E. Halley, Oxford, 1710 -. see also H. Balsam; T.L. Heath (1896); P. Ver Eecke (1924) Archimedes. Opera Omnia, cum Commentariis Eutocii, ed. lL. Heiberg, 2nd ed., 3 vol.,
Leipzig: Teubner, 1910-15 (repr. Stuttgart, 1972) -. see also A. Czwalina; T.L. Heath (1897); EJ. Dijksterhuis; C. Mugler; P. Ver Eecke
(1921) Aristotle. Opera (I-II, Aristoteles Graece, ed. I. Bekker, 1831; III, Aristoteles Latine,
interpretibus variis, 1831; IV, Scholia in Aristotelem, ed. C.A. Brandis, 1836; V, Index
818 Textual Studies in Ancient and Medieval Geometry
Aristotelicus, ed. H. Bonitz, 1870), Berlin (Academia litterarum regia borussica): G. Reimer
-. Aristoteles Latinus, G. Verbeke (series ed.), Brussels: Desclee de Brouwer and Leiden: Brill
Boethius. De institutione arithmetica libri ii, De institutione musica libri v, ed. G. Friedlein, Leipzig: Teubner, 1867
-, trans. De sophisticis elenchis, ed. B.G. Dod, in Aristoteles Latinus, VI: 1-3, 1975 CAG = Commentaria in Aristotelem Graeca (Academia litterarum regia borussica),
Berlin: G. Reimer Damianus. Kephalaia ton optikon hypotheseon (Chapters of the optical hypotheses), ed.
R. Schone, Damianos: Schrift aber Optik, Berlin: Reichsdruckerei, 1897 Damascius. Vitae Isidori Reliquiae, ed. C. Zintzen, Hildesheim: G. Olms, 1967 Diocles. On Burning Mirrors, ed. GJ. Toomer, Berlin/Heidelberg/New York: 1976 -. see also R. Rashed Diophantus of Alexandria. Opera Omnia, ed. P. Tannery, 2 vol., Leipzig: Teubner,
1893-95 -. see also R. Rashed (1984); J. Sesiano Domninus of Larissa. Encheiridion arithmetikes eisagoges (Manual of the Arithmetic
Introduction): in J.F. Boissonade, Anecdota Graeca, Paris, 1832 (repr. Hildesheim: G. Olms, 1962), IV, pp. 413-429
-. see also P. Tannery (1906) -. Pos esti logon ek logou aphelein (fragment, "How to subtract a ratio from a ratid'): see
ed., ed. E.S. Stamatis, 4 vol., 1969-73) -. see also T.L. Heath (1926) -. Elementa XlV-XV, Scholia in Elementa, and "Prolegomena critica," ed. J.L. Heiberg
(Euclidis Opera, vol. 5), Leipzig: Teubner, 1888 (2nd ed., in two parts, ed. E.S. Stamatis, 1977)
-. Data (Opera Omnia, vol. 6), ed. H. Menge, Leipzig: Teubner, 1896 -. see also S. Ito -. Optica, Opticorum recensio Theonis, Catoptrica (Opera Omnia, vol. 7), ed. J.L.
Heiberg, Leipzig: Teubner, 1895 -. Phaenomena, Scripta musica (Opera Omnia, vol. 8), ed. H. Menge, Leipzig: Teubner,
1916 Eutocius of Ascalon. Commentaria in Conica: in Apollonii quae graece exstant, ed. J.L.
Heiberg, vol. II, Leipzig: Teubner, 1893 (repr. Stuttgart, 1974) -. Commentarii in Libros de Sphaera et Cylindro, Dimensionem Circuli, de Planorum
Aequilibriis: in Archimedis Opera Omnia, ed. J.L. Heiberg, vol. III, Leipzig: Teubner, 1915 (repr. Stuttgart, 1972)
Hero of Alexandria. Opera, 5 vol. (I, Pneumatica, ed. W. Schmidt, 1899; II, Mechanica, ed. L. Nix and [Ptolomeil De speculis, ed. W. Schmidt, 1900; III, Mechanica and Dioptra, ed. H. Schone, 1903; IV, Definitiones and Geometrica, ed. J.L. Heiberg, 1912; V, Stereometrica, ed. J.L. Heiberg, 1914), Leipzig: Teubner.
-. Metrica: see also E.M. Bruins -. Belopoeica: see E.W. Marsden Hypsicles. Book XIV of the Elements: see Euclidis Opera Omnia, ed. J.L. Heiberg,
vol. 5 Iamblichus of Chalcis. In Nicomachi Introductionem Arithmeticam Liber, ed. H. Pistelli,
1973 Joannes Philoponus. In Aristotelis Analytica Posteriora Commentaria, ed. M. Wallies
(CAG, vol. 13, pt. 2), Berlin: Reimer, 1909 Marinus of Neapolis. Vita Procli, ed. 1.F. Boissonade (1814), repro with the English trans
lation by K.S. Guthrie (1925), in Marinos of Neapolis. The Extant Ubrks, ed. A.N. Oikonomides, Chicago: Ares, 1977
Menelaus of Alexandria. Sphaerica, ed. E. Halley, Oxford, 1758 Nicomachus of Gerasa. Harmonikon Encheiridion, ed. K. von Jan, Musici Scriptores
Graeci, no. 5, Leipzig: Teubner, 1895 (repr. Hildesheim: G. Oims, 1962) -. Introductionis arithmeticae libri ii, ed. R. Hoche, Leipzig: Teubner, 1866 Pappus of Alexandria. Collectionis quae supersunt, ed. F. Hultsch, 3 vol., Berlin: Weid-
mann, 1876-78 (repr. Amsterdam: A.M. Hakkert, 1965) -. see also A. Jones; P. Ver Eecke (1933) -. Commentaries on Ptolemy: see A. Rome (1931) -. Commentary on Euclid's Book X: see W Thomson and G. Junge Philo of Byzantium. Belopoeica: see E.w. Marsden Philoponus: see Joannes Philoponus Plato. Opera, ed. 1. Burnet, (Oxford Classical Texts), 5 vol., Oxford: Clarendon Press,
1900-07 (repr. 1977) Plutarch of Chaeronea. Scripta Moralia, ed. WR. Paton, I. Wegehaupt, et aI., 7 vol.,
[no publ.], 1964 Proclus Diadochus. In Primum Euclidis Elementorum Librum Commentarii, ed. G. Fried
lein, Leipzig: Teubner, 1873 (repr. 1967) -. see also G.R. Morrow -. In Platonis Timaeum Commentaria, ed. E. Diehl, 3 vol., Leipzig: Teubner, 1903-06
(repr. Amsterdam: A.M. Hakkert, 1965) Ptolemy of Alexandria. Opera quae exstant omnia, ed. 1.L. Heiberg, 2 vol. (I, 2 pts., Syn
taxis mathematica, 1898); II, Opera astronomica minora: Phaseis, Hypotheseis, Inscriptio Canobi, Procheiron kanonon diataxis, Analemma, Planisphaerium, etc., 1907), Leipzig: Teubner
-. Almagest = Syntaxis mathematica -. see also K. Manitius; GJ. Toomer (1984) Quintilian. Institutionis oratoriae libri xii, ed. L. Radermacher, corr. V. Buchheit, Leip
zig: Teubner, 1959 Serenus of Antinoeia. Opuscula (De sectione cylindri, De sectione coni), ed. J.L. Heiberg,
Leipzig: Teubner, 1896 Simplicius. In Aristotelis de Caelo Commentaria, ed. J.L. Heiberg (CAG 7), Berlin:
Reimer, 1894 -. In Aristotelis Physica Commentaria, ed. H. Diels, 2 vol. (CAG 9-10), Berlin: Reimer,
1882-95 Synesius of Cyrene. Opuscula, ed. N. Terzaghi, Rome: Regia officina polygraphica, 1944 -. Hymnes, ed. C. Lacombrade, Paris: Les Belles Lettres, 1978 -. see also A. Fitzgerald Syrianus. In Metaphysica Commentaria, ed. W Kroll (CAG 6, pt. 1), Berlin: G. Reimer,
1902 Themistius. In Aristotelis Physica Paraphrasis, ed. H. Schenkl (CAG 5, pt. 2), Berlin: G.
Reimer, 1900
820 Textual Studies in Ancient and Medieval Geometry
-. In Libros Aristotelis De Caelo Paraphrasis (Hebrew and Latin), ed. S. Landauer (CAG 5, pt. 4), Berlin: G. Reimer, 1902
Theon of Alexandria. In Claudii Ptolemaei Magnam Constructionem Commentariorum Lib. XI, ed. 1. Camerarius, Basel: 1. Walder, 1538
-. see also A. Rome (1936; 1943) -. Commentaries on Ptolemy's Handy Tables: see 1. Mogenet (1985); A. Tihon (1978) Theon of Smyrna. Expositio rerum mathematicarum ad legendum Platonem utilium, ed. E.
Hiller, Leipzig: Teubner, 1878 (repr. New York and London: Garland, 1987) Vitruvius. De Architectura, ed. V. Rose, 2nd ed., Leipzig: Teubner, 1899 -. see also M.H. Morgan
Medieval Sources
Abu Bakr al-Harawl. [On the trisection of an angle], B.N. ms. arab. 2457, no. 45alt (Paris), f. 194r-195r: see Part II, text A
Abu Jacfar al-Khazin. [On the trisection of an angle], Bod!. ms. Hunt. 237 (Oxford), f. 103v-104v: see Part II, text A3
-. Ff stikhraj kha~~ain bain kha~~ain (On the construction of two lines between two lines), B.N. ms. arab. 2457, no. 47 (Paris), f. 198v-199r: see Part II, text F
-. see also R. Lorch (1986) Abu 'I-Rashid cAbd al-Hadi. Qaul mansub ila Arshimfdis fl misa~at al-da'ira (Writing
attributed to Archimedes on the measurement ofthe circle) [Recension of Dimension 0/ the Circle, with preface, "Theorems applicable to the book of Archimedes"]' Columbia University ms. Smith 45, no. 4 (New York): see Part III, chap. 7, Appendix I
Adelard of Bath. [Latin translation of Euclid's Elements]: see H.L.L. Busard (1983) Al).mad ibn Musa. Qaul fl tathlfth al-zawiya (Writing on the trisection ofthe angle), Bod!.
ms. Thurston 3 (Oxford), f. 131 v-132r; Bod!. ms. Marsh 720, f. 260v: see Part II, texts B,B*
-. see also 1. P. Hogendijk (1981) Anonymus. [Arabic translation of Archimedes' Dimension o/the Circle], ms. Fatih 3414,
no. 1 (Istanbul), f. 2v-6v (cf. Sezgin, GAS, V, p. 131): see Part III, Appendices to chaps. 3 and 4
-. [Arabic translation of Archimedes' Sphere and Cylinder], ms. Fatih 3414, no. 2 (Istanbul), f. 7r-8r, 9r-59r (cf. Sezgin, GAS, V, p. 129)
Anonymus. [Hebrew translation of Archimedes' Dimension o/the Circle], Vat. ms. Hebr. 384, f. 412r-412v: see Part III, Appendices to chaps. 3 and 4
Banu Musa, Kitab macrifa misa~a al-ashkiil al-basf~a wa- 'I-kurfya (Book of the Knowledge of Measurement of Plane and Spherical Figures), in the recension of al-Tusi: see al-Tusi, Rasa'il, II, no. 1
-. Verbafiliorum: in M. Clagett, Archimedes in the Middle Ages, I, chap. 4 -. see also H. Suter (1902); and Al).mad ibn Musa al-Bironi, Abu Rail).an Mul). b. Al).mad. Rasa'il. Hyderabad: Osmania University, 1948 -. Istikhraj al-awtar fi 'l-da'ira (The Construction ofthe Chords in the Circle), in Rasa'il,
no. 1; see also Suter (1910-11) Gerard of Cremona. Liber Arsamithis de mensura circuli, or De quadratura circuli trac
tatus [Latin translation of Archimedes' Dimension o/the Circle]: see Part III, Appendices to chaps. 3 and 4; and M. Clagett, Archimedes in the Middle Ages, I, chap. 2, sect. 2
Bibliography 821
-. [Latin translation of Euclid's Elements]: see H.L.L. Busard (1984) Grosseteste, R.: see R.C. Dales ibn al-Haytham: see 1. al-Dabbagh; and 1.P. Hogendijk (1985) Johannes de Tinemue (John of Tynemouth). Liber de curvis superficiebus: see M. Clagett,
Archimedes in the Middle Ages, I, chap. 6, sect. 2 Jordanus de Nemore: see B.B. Hughes al-Jurjani, Abu Sacid al-parir. Masa'il handasfya (Geometric Questions), Dar al-Kutub
ms. riya<;1. 41m (Cairo), f. 69r-71 v (cf. Sezgin, GAS, V, 263) al-Kashi: see P. Luckey Pachymeres, Georgios. Quadrivium (sc. Syntagma ton tessaron mathematon), ed. P. Tan
nery, (Studi e Testi 94), Vatican City: Biblioteca Apostolica Vaticana, 1940 Plato of Tivoli. In quadratum circuli [Latin translation of Archimedes' Dimension of the
Circle]: see Part III, Appendices to chaps. 3 and 4; and M. Clagett, Archimedes in the Middle Ages, I, chap. 2, sect. 1
Qalonymus b. Qalonymus. [Hebrew translation of Archimedes' Sphere and Cylinder], Bodl. ms. Laud or. 93 (Oxford), f. Ir-28v; Bodl. ms. hebr. d. 4, f. 108r-141v
al-Quhi, Abu Sahl. Maqala fi stikhraj al-kha~~ain bain al-kha~~ain . .. wa-qismat alzawiya bi-thalathat aqsam (Writing on the construction of the two lines between the two lines ... and the division of the angle in three parts), Dar al-Kutub ms. riya9. 40m (Cairo), f. 226v-227r: see Part II, text E
-. see also A. Sayili al-Sijz!, cAbd ai-Jam. [On the trisection of the angle], B.N. ms. arab. 2457, no. 33
(Paris), f. 16Or: see Part II, text D -. Risala fi qismat al-zawiya al-mustaqimat al-kha{{ain bi-thalathat aqsam mutasawiya:
trans. as "Traite de la trisection de l'angle rectiligne;' by F. Woepcke, in lltlgebre d'Omar Alkhayyami, pp. 117-127
Suidae Lexicon. [10th century Greek historical and literary dictionary], ed. A. Adler, 5 vol., Leipzig: Teubner, 1928-38
Thabit ibn Qurra. Qismat al-zawiya ... bi-thalathat aqsam (Division of the angle ... into three parts), B.N. ms. arab. 2457, no. 45 (Paris), f. 192v-194r: see Part II, text C
-. Kitab fi 'l-Qaras{un: see K. Jaouiche; and W.R. Knorr (1982) al-Tus!, Na~!r aI-Din. Rasa'il, 2 vol., Hyderabad: Osmania University, 1939-40 -. [Recension of the Arabic translation of Archimedes' Sphere and Cylinder], in Rasa'i!,
II, no. 5 -. [Recension of the Arabic translation of Archimedes' Dimension of the Circle], in
Rasa 'ii, II, no. 5, pp. 127-133: see Part III, chap. 7, Appendix II -. [Scholium to Conics V 52, on the construction of two mean proportional lines], Bodl.
ms. Marsh 667 (Oxford), f. 106r: see Part II, text M cUmar al-Khayyam. Maqalafi 'l-jabr wa-1-muqabala: see F. Woepcke (1851) William of Moerbeke. [Latin translations of Archimedes from the Greek]: see M. Clagett,
Archimedes in the Middle Ages, II
Modern Studies
AMA = Archimedes in the Middle Ages: see M. Clagett Arendt, F. "Eine Interpolation des Eutokios in unserem Apolloniostext," Bibliotheca
822 Textual Studies in Ancient and Medieval Geometry
Asmus, R. "Hypatia in Tradition und Dichtung;' Studien zur vergleichenden literaturgeschichte, 1907, 7:11-44
Aujac, G. "Le rapport di isou (Euclide V, definition 17): Definition, utilisation, transmission;' Historia Mathematica, 1986, 13:370-386
Balsam, H. Des Apollonios von Perga sieben Bucher aber Kegelschnitte, Berlin: G. Reimer, 1861
Becker, 0. "Eine voreudoxische Proportionenlehre und ihre Spuren bei Aristoteles und Euklid" (Eudoxos-Studien I), Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, 1933,2 (Abt. B): 311-333
-. "Das Prinzip des ausgeschlossenen Dritten in der griechischen Mathematik" (EudoxosStudien IV), Quellen und Studien, 1936,3 (Abt. B): 370-388
Berggren, 1.L. "Spurious Theorems in Archimedes' Equilibria of Planes, Book I;' Archive for History of Exact Sciences, 1976-77, 16: 87-103
-. ')\ Lacuna in Book I of Archimedes' Sphere and Cylinder;' Historia Mathematica, 1977,4: 1-5
-. ')\ Coincidence of Pappos' Book VIII with al-Binini's Taltdid;' Journal for the History of Arabic Science, 1978,2: 137-142
-. "The Correspondence of Abu Sahl al-Kuhi and Abu ISQaq al-~abi: A Translation with Commentaries;' Journalfor the History of Arabic Science, 1983, 7: 39-124
-. Episodes in the Mathematics of Medieval Islam, New YorklBerlin/Heidelberg/London/ Paris/Tokyo: Springer, 1986
Boll, H. "Heliodorus": see PW Brandis, C.: see Aristotle Bregman, 1. Synesius of Cyrene, Philosopher-Bishop, Berkeley/Los Angeles/London:
University of California Press, 1982 Bruins, E.M. Codex Constantinopolitanus (palatii veteris no. 1), I: Reproduction of
the Manuscript, Leiden: Brill, 1964 (includes Greek text of Herds Metrica, Geometrica, etc.)
Bulmer-Thomas, I. "Eutocius of Ascalon;' DSB, 4 (1971): 488-491 -. "Isidorus of Miletus;' DSB, 7 (1973): 28-30 Burkert, W. Lore and Science in Ancient Pythagoreanism, Cambridge: Harvard University
Press, 1972 (trans. from the German, ~isheit und Wissenschaft, Nuremberg: H. Carl, 1962)
Busard, H.L.L. "Ein mitte1alterlicher Euklid-Kommentar, der Roger Bacon zugeschrieben werden kann;' Archives internationales d'histoire des sciences, 1974, 24: 199-218
-. The Translation of the Elements of Euclid from the Arabic into Latin by Hermann of Carinthia (?), Books I-VI, Leiden: Brill, 1968; Books VII-XlI, Amsterdam: Mathematisch Centrum, 1977
-. "Der Traktat De isoperimetris, der unmittelbar aus dem Griechischen ins Lateinische iibersetzt worden ist;' Mediaeval Studies, 1980,42: 61-88
_. The First Latin Translation of Euclid's Elements Commonly Ascribed to Adelard of Bath, Toronto: Pontifical Institute of Mediaeval Studies (Studies and Texts, 64), 1983
-. The Latin Translation of the Arabic Version of Euclid's Elements Commonly Ascribed to Gerard of Cremona, Leiden: Brill, 1984
-. The Mediaeval Latin Translation of Euclid's Elements, Made Directly from the Greek, (Boethius, vol. 15), Stuttgart: F. Steiner-Verlag-Wiesbaden, 1987
Cantor, M. [Review of Nokk, Zenodorus' Abhandlung aber die isoperimetrischen Figuren], Zeitschriftfiir Mathematik und Physik (Literaturzeitung), 1861,6: 1-3
-. [Review of Hultsch, Pappi Collectio, II] , Zeitschrift for Mathematik und Physik (hist.lit. Abth.), 1877,22: 173-179
Bibliography 823
Carruccio, E. Mathematics and Logic in History and in Contemporary Thought, London: Faber and Faber, 1964
Clagett, M. "The Medieval Latin Translations from the Arabic of the Elements of Euclid;' Isis, 1953, 44: 16-42
-. "King Alfred and the Elements of Euclid;' Isis, 1954,45: 269-277 -. "The De curvis superjiciebus Archimenidis," Osiris, 1954, 11: 295-358 -. The Science of Mechanics in the Middle Ages, Madison: University of Wisconsin Press,
1959 -. Archimedes in the Middle Ages: I, The Arabo-Latin Tradition (Madison: University of
Wisconsin Press, 1964); II, The Translations from the Greek by William of Moerbeke (Philadelphia: American Philosophical Society, 1976); III, The Fate of the Medieval Archimedes 1300-1565 (Philadelphia, 1978); IV, A Supplement on the Medieval Latin Traditions of Conic Sections (Philadelphia, 1980); V, Quasi-Archimedean Geometry in the Thirteenth Century (Philadelphia, 1984)
-. see also E.A. Moody and M. Clagett Coolidge, 1.L.L. A History of Geometrical Methods, Oxford: Clarendon Press, 1940 (repr.
New York: Dover, 1963) Courant, R. and H. Robbins. What is Mathematics? An Elementary Approach to Ideas and
Methods, 4th ed. (repr.), Oxford/New York, etc.: Oxford University Press, 1978 Czwalina, A. Archimedes ~rke, 5 vol., Leipzig: Teubner, 1922-25 al-Dabbagh,1. ["Ibn al-Haytham. Tract on isoperimetric figures" (Russian translation and
commentary)], Istoriko-matematicheskie Issledovaniya, 1966, 17: 399-448 Dales, R.C. RDberti Grosseteste ... Commentarius in VIII Libros Physicorum Aristotelis,
Boulder: University of Colorado Press, 1963 Derenbourg, H. and H.PJ. Renaud, Les manuscrits arabes de l'Escurial, vol. 2, fasc. 3
("Sciences exactes et sciences occultes"), Paris: Librairie Orientaliste P. Geuthner, 1941
Diels, H. and W. Kranz. Die Fragmente der Vorsokratiker, 6th ed., 3 vol., Dublin/Zurich: Weidmann, 1966
Dijksterhuis, EJ. Archimedes, Copenhagen: E. Munksgaard, 1956; repro with a bibliographical supplement, '~rchimedes after Dijksterhuis;' by W.R. Knorr, Princeton: University Press, 1987
Dilgan, H. "Sur un theoreme isoperimetrique d'Ibn-i-Haitham;' Actes du IJC-! Congres International d'Histoire des Sciences (Barcelona and Madrid, 1-7 Sept. 1959), Barcelona: Universidad de Barcelona and Paris: Hermann & Cie., I, pp. 453-460
Dold-Samplonius, Y. "al-Khazin, Abu Jacfar Mu~ammad ibn al-l:Iasan al-Khurasani;' DSB, 7 (1973): 334-335
Drachmann, A. "Philo of Byzantium;' DSB, 10 (1974): 586-589 -. "Ctesibius (Ktesibios);' DSB, 3 (1971): 491-492 DSB = Dictionary of Scientific Biography, ed. C.c. Gillispie, 16 vol., New York: C. Scrib
ner's Sons, 1970-80 Dumontier, 1.: see c.E. Ruelle Emden, A.B. A Biographical Register of the University of Oxford to A.D. 1500, 3 vol.,
Oxford: Clarendon Press, 1957-59 Etienne, E. and 1. Roels. "Deux aspects particuliers du probleme des moyennes dans
Pappus d'Alexandrie," Revue des questions scientifiques, 1986, 157: 179-198 Fitzgerald, A. The Letters of Synesius of Cyrene (trans., with intro. and notes), Oxford:
University Press and London: H. Milford, 1926 -. The Essays and Hymns of Synesius of Cyrene (trans., with intro. and notes), 2 vol.,
Oxford: University Press and London: H. Milford, 1930
824 Textual Studies in Ancient and Medieval Geometry
Foley, V.: see W. Soedel and V. Foley Folkerts, M. "Adelard's Versions of Euclid's Elements;' in C. Burnett, ed., Adelard of Bath:
An English Scientist and Arabist of the Early Twelfth Century, London: Warburg Institute (Surveys and Texts 14), 1987, pp. 55-68
Fowler, D.H. "Ratio in Early Greek Mathematics;' Bulletin of the American Mathematical Society, 1979, 1 (n.s.): 807-846
-. The Mathematics of Plato's Academy: A New Reconstruction, Oxford: Clarendon Press, 1987
Gericke, H. "Zur Geschichte des isoperimetrischen Problems;' Mathematische Semesterberichte, 1982, 29: 160-187
Gibbs, S.L. Greek and Roman Sundials, London and New Haven: Yale University Press, 1976
Gow, A.S.F. and D.L. Page. The Greek Anthology: Hellenistic Epigrams, Cambridge: University Press, 1965
Grant, E. A Source Book in Medieval Science, Cambridge: Harvard University Press, 1974 Gudemann. "Sporos": see PW Guthrie, W.K.C. A History of Greek Philosophy, 6 vol., Cambridge: Cambridge University
Press, 1962-81 Hartner, W. "The Principle and Use of the Astrolabe;' in A Survey of Persian Art, ed. A.V.
Pope, London and New York: Oxford University Press, 1939, pp. 2530-2554 (repr. in W. Hartner, Oriens-Occidens, Hildesheim: G. Oims, 1968, pp. 287-311)
Haskins, C.H. Studies in the History of Mediaeval Science, Cambridge: Harvard University Press, 1924; 2nd ed., 1927 (repr. New York: F. Ungar, 1960)
-. The Renaissance of the Twelfth Century, Cambridge: Harvard University Press, 1927 (repr. Cleveland and New York: World Publishing Co., 1957)
Heath, T.L. Apollonius of Perga: Treatise on Conic Sections, Cambridge: Cambridge University Press, 1896
-. The Works of Archimedes, Cambridge: Cambridge University Press, 1897; Supplement: The Method of Archimedes, 1912 (repr. New York: Dover, n.d.)
-. A History of Greek Mathematics, 2 vol., Oxford: Clarendon Press, 1921 (repr. New York: Dover, 1981)
-. The Thirteen Books of Euclid's Elements, 2nd ed., 3 vol., Cambridge: University Press, 1926 (repr. New York: Dover, 1956)
-. Mathematics in Aristotle, ed. A.M. Heath, Oxford: Clarendon Press, 1949 Heiberg, 1.L. Quaestiones Archimedeae, Copenhagen: R. Klein, 1879 -. Philologische Studien zu griechischen Mathematikem, (from Supplementbiinde der
lahrbiicher fUr classische Philologie): I, "Ueber Eutokios" (1880, 11: 357-384); II, "Ueber die Restitution der zwei Bucher des Archimedes Peri Sphairas kai Kylindrou" (1880, 11: 384-398); III, "Die Handschriften Georg Vallas von griechischen Mathematikern" (1881, 12: 377-402); IV, "Ueber den Dialekt des Archimedes" (1883, 13: 543-566); V, "Interpolationen in den Schriften des Archimedes" (1883, 13: 566-577)
-. "Die arabische Tradition der Elemente Euklid's;' ZeitschriftfUr Mathematik und Physik (hist.-lit. Abth.), 1884,29: 1-22
-. "Eine mittelalterliche Ubersetzung der Syntaxis des Ptolemaios;' Hermes, 1910,45: 57-66
-. "Noch einmal die mittelalterliche Ptolemaios-Ubersetzung," Hermes, 1911, 46: 207-216
Hintikka,1. and V. Remes. The Method of Analysis: Its Geometrical Origin and Its General Significance, Dordrecht: Reidel, 1974
Bibliography 825
Hoeg, C. "Johann Ludvig Heiberg" (obituary), lahresbericht aber die Fortschritte der klassischenAltertumswissenschaJt, 1931,57 (233), pt. 4 (Nekrologe), pp. 38-77
Hogendijk, J.P. "On the trisection of an angle and the construction of a regular nonagon by means of conic sections in medieval Islamic geometry;' preprint nr. 113, University of Utrecht: Department of Mathematics, March 1979
-. "How Trisections of the Angle Were Transmitted from Greek to Islamic Geometry;' Historia Mathematica, 1981,8: 417-438
-. Ibn al-Haytham's Completion of the Conics, New YorklBerlin/Heidelberg/Tokyo: Springer, 1985
-. ':.\rabic Traces of Lost Works of Apollonius;' Archive for History of Exact Sciences, 1986, 35: 187-253
Hughes, B.B. The De Numeris Datis of lordanus de Nemore: A Critical Edition, Analysis, Evaluation and Translation, Ph.D. diss., Stanford University, 1970
Hultsch, F. "Domninos" and "Eutocius": see PW Huxley, G.L. Anthemius of Tralles: A Study in Later Greek Geometry (Greek, Roman and
Byzantine Monographs, no. 1), Cambridge, Mass., 1959 Ito, S. The Medieval Latin Translation of the Data of Euclid, Tokyo: University of Tokyo
Press and Boston/Basel/Stuttgart: Birkhauser, 1980 Jackson, D.E.P. "The Arabic Translation of a Greek Manual of Mechanics;' Islamic Quart
erly, 1972, 16: 96-lO3 -. "Towards a Resolution of the Problem of ta heni diastemati graphomena in Pappus' Col
lection Book VIII," Classical Quarterly, 1980, 30 (n.s.): 523-533 Jaouiche, K. Le livre du Qaraszun de Thabit ibn Qurra, Leiden: Brill, 1976 Jones, A. Pappus of Alexandria: Book 7 of the Collection, 2 vol., New York/Ber
lin/Heidelberg/Tokyo: Springer, 1986 King, D.A. "Notes on the Sources for the History of Early Islamic Mathematics" [essay
review of F. Sezgin, Geschichte des arabischen Schrifttums, vol. 5], lournal of the American Oriental Society, 1979, 99: 450-459
-. A Catalogue of the Scientific Manuscripts in the Egyptian National Library, Cairo: General Egyptian Book Organization (in collaboration with the American Research Center in Egypt and the Smithsonian Institution), 1981
Kliem. "Sporos": see PW Knaack, G. "Eratosthenes": see PW Knorr, W.R. The Evolution of the Euclidean Elements: A Study of the Theory of Incommen
surable Magnitudes and Its Significance for Early Greek Geometry, Dordrecht: D. Reidel, 1975
-. ':.\rchimedes and the Measurement of the Circle: A New Interpretation;' Archive for History of Exact Sciences, 1976, 15: 115-140
-. ':.\rchimedes and the Elements: Proposal for a Revised Chronological Ordering of the Archimedean Corpus;' Archive for History of Exact Sciences, 1978, 19: 211-290
-. ':.\rchimedes and the pre-Euclidean Proportion Theory;' Archives internationales dhistoire des sciences, 1978,28: 183-244
-. Ancient Sources of the Medieval Tradition of Mechanics: Greek. Arabic and Latin Studies of the Balance, Florence: Istituto e Museo di Storia della Scienza (monograph no. 6 of the Annali dell7stituto), 1982
-. "The Hyperbola-Construction in the Conics, Book II: Ancient Variations on a Theorem of Apollonius," Centaurus, 1982, 25: 253-291
-. "Infinity and Continuity: The Interaction of Mathematics and Philosophy in Antiquity;' in N. Kretzmann (ed.), Infinity and Continuity in Ancient and Medieval Thought, pp. 112-145, Ithaca and London: Cornell University Press, 1982
826 Textual Studies in Ancient and Medieval Geometry
-. "Techniques of Fractions in Ancient Egypt and Greece;' Historia Mathematica, 1982, 9: 133-171
-. ''The Geometry of Burning-Mirrors in Antiquity;' Isis, 1983,74: 53-73 -. "On the Transmission of Geometry from Greek into Arabic;' Historia Mathematica,
1983,10: 71-78 -. ')\ncient Versions of Two Trigonometric Lemmas;' Classical Quarterly, 1985, 35:
362-391 -. ')\rchimedes and the pseudo-Euclidean Catoptrics: Early Stages in the Ancient Geo
metric Theory of Mirrors;' Archives internationales d'histoire des sciences, 1985, 35: 28-105
-. "Euclid's Tenth Book: An Analytic Survey;' Historia Scientiarum (Tokyo), 1985,29: 17-35
-. [rev. of l Sesiano, Books Wto VII ofDiophantus' Arithmetica . .. ], American Mathematical Monthly, 1985, 92:150-154
-. The Ancient Tradition of Geometric Problems, Boston/Basel/Stuttgart: Birkhiiuser, 1986
-. ')\rchimedes' Dimension of the Circle: A View of the Genesis of the Extant Text;' Archive for History of Exact Sciences, 1986,35: 281-324
-. "The Medieval Tradition of a Greek Mathematical Lemma;' Zeitschrift fUr Geschichte der arabisch-islamischen Wissenschaften, 1986, 3: 230-261
-. "On Two Archimedean Rules for the Circle and the Sphere;' Bollettino di Storia delle Scienze Matematiche, 1986,6: 145-158
-. "The Medieval Tradition of Archimedes' Sphere and Cylinder;' in E. Grant and lE. Murdoch (eds.), Mathematics and its Applications to Science and Natural Philosophy in the Middle Ages: Essays in Honor of Marshall Clagett, Cambridge: University Press, 1987,pp.3-42
-. ')\rchimedes after Dijksterhuis: A Guide to Recent Studies": see EJ. Dijksterhuis (1987)
-. "Paraphrase Editions of Latin Mathematical Texts: De Figuris Ysoperimetris;' Mediaeval Studies (to appear 1990)
-. ''John of Tynemouth alias John of London: Emerging Portrait of a Singular Medieval Mathematician" (available in preprint, 1989)
Kozhukhova, G.M. ["The Arabic Version of Archimedes' Dimension of the Circle' (in Russian)], Istoriko-matematicheskie Issledovaniya, 1980,25: 315-316
Kramer, E. "Hypatia of Alexandria;' DSB, 6 (1972): 615-616 Krause, M. "Stambuler Handschriften islamischer Mathematiker;' Quellen und Studien
zur Geschichte der Mathematik, Astronomie und Physik, 1936,3 (Abt. B): 437-532 Kunitzsch, P. [Ibn al-$ala~]. Zur Kritik der Koordinatenilberlieferung im Sternkatalog des
Almagest, Gottingen: Akademie der Wissenschaften (Abhandlungen, phil.-hist. Klasse, 3rd ser., 94), 1975
Lacombrade, C.: see Synesius Lang, M. "Herodotos and the Abacus," Hesperia, 1957,26: 271-287 Lemay, R. "Gerard ofCremona;' DSB, 15 (1978): 173-192 Lloyd, A.C. "The Later Neoplatonists;' Part IV of The Cambridge History of Later Greek
and Early Medieval Philosophy, ed. A.H. Armstrong, Cambridge: University Press, 1967
Lloyd, G.E.R. "The Alleged Fallacy of Hippocrates of Chios;' Apeiron, 1987, 20: 103-128.
Lorch, R. "Some Remarks on the Arabic-Latin Euclid;' in C. Burnett, ed., Adelard of
Bibliography 827
Bath: An English Scientist and Arabist of the Early Twelfth Century, London: Warburg Institute (Surveys and Texts 14), 1987, pp. 45-54
-. 'l\biJ Jacfar al-Khazin on Isoperimetry and the Archimedean Tradition," Zeitschriftfiir
Geschichte der arabisch-islamischen Wissenschaften, 1986,3: 150-229 Lorent, H. "Sur les traces des pas d1\rchimede:' Mathesis, 64, suppl. I, 1955 LSJ = H.G. Liddell, R. Scott and H.S. Jones, A Greek-English Lexicon, Oxford: Claren
don Press, 1983 (repr. of 9th ed., 1940, with Supplement of 1968) Luckey, P. [al-Kash!]. Der Lehrbrief aber den Kreisumfang, Berlin: Akademie der
Wissenschaften (Abhandlungen, Klasse f. Math. u. algem. Naturwissen., 1950, nr. 6), 1953
Manitus, K. Des Claudius Ptolemiius Handbuch der Astronomie, 2 vol., Leipzig: Teubner, 1912-13
Marsden, E.W. Greek and Roman Artillery: Technical Treatises, Oxford: Clarendon Press, 1971 (includes Greek text with translation of Hero's Belopoeica, Philo's Belopoeica, etc.)
Mercier, R. "Studies in the medieval conception of precession:' Archives internationales dhistoire des sciences, part I, 1976,26: 197-220; part II. 1977,27: 33-71
Mogenet, 1. 17ntroduction a lltlmageste, Brussels: Academie Royale de Belgique (Memoires, 51, fasc. 2), 1956
-. 'THistoire des isoperimetres chez les Grecs," in Scrinium Lovaniense: Melanges histo
riques Etienne van Cauwenbergh, Universite de Louvain: Recueil de travaux dhistoire et de philologie, 4 ser., fase. 24, 1961. pp. 69-78
-. Le "Grand Commentaire" de Theon dltlexandrie aux Tables Faciles de Ptolemee, Livre I (critical edition, revised and completed with a commentary by A. Tihon), Studi e Testi 315, Vatican City: Biblioteca Apostolica Vatieana, 1985
Moody, E.A. and M. Clagett. The Medieval Science of Weights (Scientia de ponderibus) , Madison: University of Wisconsin Press, 1960
Morgan, M.H. Vitruvius: The Ten Books on Architecture, Cambridge: Harvard University Press, 1914 (repr. New York: Dover. 1960)
Morrow, G.R. Proclus: A Commelltarv Oil the First Book of Euclid:5 Elements, Princeton: University Press, 1970.
Mueller, I. Philosophy of Mathematics and Deductive Structure in Euclid:5 Elements, Cambridge: MIT Press, 1981
Muller, W. "Das isoperimetrische Problem im Altertum ," Sudh(iffs Archiv, 1953, 37: 39-71
Mugler, C. Les Oeuvres dltrchimMe, 4 vol., Paris: Les Belles Lettres, 1970-74 Murdoch, lE. "Euclides Graeco-Latinus. A Hitherto Unknown Medieval Latin Transla
tion of the Elements of Euclid Made Directly from the Greek:' Harvard Studies in Classical Philology, 1966, 71: 249-302
-. "The Medieval Euclid: Salient Aspects of the Translations of the Elements by Adelard of Bath:' Revue de Synthese, 1968,89: 67-94
-. "Euclid: Transmission of the Elements," DSB, 4 (1971): 437-459 Neuenschwander, E. "Die ersten vier Bucher der Elemente Euklids." Archive for History
of Exact Sciences, 1973,9: 325-380 -. "Zur Ueberlieferung der Archytas-Uisung des delischen Problems," Celltaurus, 1974,
18: 1-5 Neugebauer, 0. "The Early History of the Astrolabe," Isis, 1949,40: 240-256 (repr. in
Astronomy and History: Selected EssQ\'s. New York/Berlin/Heidelberg/Tokyo: Springer, 1983, pp. 278-294)
828 Textual Studies in Ancient and Medieval Geometry
-. A History of Ancient Mathematical Astronomy, 3 vol., Berlin/Heidelberg/New York: Springer, 1975
Nokk, [no init.]. Zenodorus'Abhandlung iiber die isoperimetrischen Figuren, nach den Ausziigen, welche uns die Alexandriner Theon und Pappus aus derselben iiberliefert haben, Beilag z. d. Freiburger Lyceums-Programme, 1860
Parker, R.A. Demotic Mathematical Papyri, Providence: Brown University Press, 1972 Pedersen, 0. A Survey of the Almagest, Odense University Press, 1974 Pendlebury, R. "On a Method of Finding Two Mean Proportionals," Messenger of
Mathematics, 1873 (2, ser. 2): 166-169 Pfeiffer, R. History of Classical Scholarship: From the Beginnings to the End of the
Hellenistic Age, Oxford: Clarendon Press, 1968 Powell, 1U. Collectanea Alexandrina, Oxford: Clarendon Press, 1925 (repr. 1970) Praechter, K. "Hypatia" and "Syrianos": see PW PW = Pauly-Wissowa: Paulys Real-Encyclopiidie der classischen Altertumswissenschaft,
2nd ed., ed. G. Wissowa et aI., 24 vol. in 43, Stuttgart: 1B. Metzler, 1894-1963; 2nd ser. 10 vol. in 19, 1914-72; for the following articles: "Domninos;' Hultsch, 5 (1905): 1521-25 "Eratosthenes von Kyrene;' Knaack, 6 (1909), 358-389 "Eutocius;' Hultsch, 6 (1909): 1518 "Heliodoros;' Boll, 8, pt. 1 (1912): 18-19 "Hypatia;' Praechter, 9, pt. 1 (1914): 242-249 "Parmenion;' H. Riemann, 18, pt. 4 (1949): 1567-69 "Sporos, griechischer Grammatiker;' Gudemann, 2nd ser., 3, pt. 2 (1929): 1879-81;
"S. von Nikaia, Mathematiker;' Kiiem, ibid., 1881-83 "Syrianos;' K. Praechter, 2nd ser., 4, pt. 2 (1932): 1728-75 "Theon von Alexandria;' K. Ziegler, 2nd ser., 5, pt. 2 (1934): 2075-80
Rashed, R. Diophante. Les Arithmetiques, vol. 3-4 (of projected 4 voL), Paris: Les Belles Lettres, 1984
-. Diocles, Anthemius de Tralles, Didyme . .. : Sur les miroirs ardents (edition of the Arabic texts with French translation), Paris: Les Belles Lettres, in preparation.
Rawlins, D. "Eratosthenes' Geodesy Unraveled: Was There a High-Accuracy Hellenistic Astronomy?" Isis, 1982, 73: 259-265
Remes, u.: see 1 Hintikka and U. Remes Reynolds, L.D. and N.G. Wilson, Scholars and Scribes, 2nd ed., Oxford: Clarendon
Press, 1974 Riemann, H. "Parmenion": see PW Rist, 1M. "Hypatia;' Phoenix, 1965, 19: 214-225 Roels, 1: see E. Etienne and 1 Roels Rome, A. Commentaires de Pappus et de Theon d:4lexandrie sur 1:4lmageste: I, Pappus,
Commentaire sur les livres 5 et 6, Rome: Biblioteca Apostolica Vaticana, 1931; II, Theon, Commentaire sur les livres 1 et 2, Vatican City, 1936; III, Theon, Commentaire sur les livres 3 et 4, Vatican City, 1943
Ruelle, C.E. "Texte inedit de Domninus de Larisse sur l'arithmetique;' (with explanatory note by 1 Dumontier), Revue de Philologie, 1883, 7 (n.s.): 82-94
Saito, K. "Compounded Ratio in Euclid and Apollonius;' Historia Scientiarum (Tokyo), 1986, 31: 25-59
Saliba, G. "The Meaning of al-jabr wa'l-muqabalah;' Centaurus, 1972, 17: 189-204 Sambursky, S. "John Philoponus," DSB, 7 (1973): l34-l39 Sams6, 1 "aI-Khazin, Abu DjaCfar ... al-Khurasani;' Encyclopedia of Islam, 2nd ed.,
Leiden: Brill, 1978, IV, pp. 1182-83
Bibliography 829
Sarfatti, G.B. Mathematical Terminology in Hebrew Scientific Literature of the Middle Ages (Hebrew with English summary), Jerusalem: Magnes Press (The Hebrew University), 1968
Sato, T. ':.\rchimedes' On the Measurement of a Circle Proposition 1: An Attempt at Reconstruction," Japanese Studies in the History of Science (= Historia Scientiarum, Tokyo), 1979, 18: 83-99
-. "Quadrature of the Surface Area of the Sphere in the Early Middle Ages-Johannes de Tinemue and Bam! Musa;' Historia Scientiarum, 1985,28: 61-90
Sayili, A. "The Trisection ofthe Angle by Abu Sahl Way jan ibn Rustam AI Kuhl" (Arabic text with Turkish and English translations), Belleten (Ankara: Societe d'histoire turque), 1962,26: 693-700
Schmidt, W. "Zur Geschichte der Isoperimetrie im AItertum;' Bibliotheca Mathematica, 1901,2 (3rd ser.): 5-8
Schneider, I. Archimedes: Ingenieur. Naturwissenschaftler und Mathematiker, Darmstadt: Wissenschaftliche Buchgesellschaft, 1979
Schoy, C. "Graeco-Arabische Studien," Isis, 1926,8: 21-40 Sesiano,1. Books IV to VII of Diophantus' Arithmetica in the Arabic Translation Attributed
to Qus~a ibn LCtqa, New York/Heidelberg/Berlin: Springer, 1982 Sezgin, F. Geschichte des arabischen Schrifttums, V (Mathematik bis ca. 430 H.), Leiden:
Brill, 1974 de Slane, Ie Baron. Catalogue des manuscrits arabes (Bibliotheque Nationale, Departe
ment des Manuscrits), Paris: Imprimerie Nationale, 1883-95 Soedel, W. and V. Foley, "Ancient Catapults;' Scientific American, March 1979, 240:
150-160 Sorabji, R. (ed.). Philoponus and the Rejection of Aristotelian Science, London and Ithaca,
N.Y.: Cornell University Press, 1987 Steiner,1. "Einfache Beweise der isoperimetrischen Hauptsatze," Crelle's Journal, 1836,
18: 281-296 (repr. in Gesammelte ~rke, ed. K. Weierstrass, Berlin: G. Reimer, 1882, II, pp. 75-91)
Steinschneider, M. Die hebraeischen Obersetzungen des Mittelalters und die Juden als Dolmetscher, Berlin: Bibliographisches Bureau, 1893 (repr. Graz: Akademische Druckund Verlagsanstalt, 1956)
-. Die Mathematik bei den Juden, Hildesheim: G. Olms, 1964 (repr. of editions Berlin/Leipzig, 1893-99 and Frankfurt, 1901)
Sturm, A. Das delische Problem [in three parts], XXIX-XXXI Program des k. k. OberGymnasiums der Benedictiner zu Seitenstetten, Linz, 1895-97
Suter, H. Die Mathematiker und Astronomen der Araber und ihre ~rke, Leipzig: Teubner, 1900
-. "Uber die Geometrie der S6hne des Musa ben Schakir;' Bibliotheca Mathematica, 1902, 3 (ser. 3): 259-272
-. "Das Buch der Auffindung der Sehnen im Kreise von AbU'I-RaiJ.!an MuJ.!. el-Blruni," Bibliotheca Mathematica, 1910-11, II (3rd ser.): 11-78
Tannery, P. La Geometrie grecque. comment son histoire nous est parvenue et ce que nous en savons, Paris: Gauthier-Villars, 1887
-. Memoires scientifiques: "Sciences exactes dans l'antiquite;' 3 vol., ed. 1.L. Heiberg and H.G. Zeuthen, Toulouse: Privat and Paris: Gauthier-Villars, 1912-15, for the following papers: "Larticle de Suidas sur Hypatia" (1880), I, pp. 74-79 "I.:arithmetique des Grecs dans Pappus" (1880), I, pp. 80-105 "I.:article de Suidas sur Ie philosophe Isidore" (1881), I, pp. 111-117
830 Textual Studies in Ancient and Medieval Geometry
"Sur les fragments d'Eudeme de Rhodes relatifs a l'histoire des mathematiques" (1882), I,pp.168-177
"Sur Sporos de Nicee" (1882), I, pp. 178-184 "Sur la mesure du cercie df\rchimede" (1882), I, pp. 226-253 "Serenus df\ntissa" (1883), I, pp. 290-299 "Domninos de Larissa" (1884), II, pp. 105-117 "Eutocius et ses contemporains" (1884), II, pp. 118-136 "Notes critiques sur Domninos" (1885), II, pp. 211-222 "Un fragment des Metriques de Heron" (1894), II, pp. 447-451 "Sur un fragment inedit des Metriques de Heron df\1exandrie" (1894), II, pp. 452-454 "Sur la religion des derniers mathematiciens de l'antiquite" (1896), II, pp. 527-539 "Le manuel d'introduction arithmetique du philosophe Domninos de Larissa" (1906),
III, pp. 255-281 Taran, L. "Nicomachus of Gerasa;' DSB, 10 (1974): 111-114 Thaer, C. "Die Wiirfelverdoppelung des Apollonios;' Deutsche Mathematik, 1940, 5:
241-243 Theisen, W. "Liber de visu: The Greco-Latin Translation of Euciid's Optics;' Mediaeval
Mass.: Harvard University Press and London: W. Heinemann, 1939-41 (repr. 1957) -. see also I. Bulmer-Thomas Thomson, W. and G. Junge, The Commentary of Pappus on Book X of Euclid's Elements,
ed. and trans. from the Arabic, Cambridge: Harvard University Press, 1930 Tihon, A. Le "Petit Commentaire" de Theon d:4.lexandrie aux Tables Faciles de Ptolemee,
(Studi e Testi 282), Vatican City: Biblioteca Apostolica Vaticana, 1978 -. "B1oge: Joseph Mogenet;' Isis, 1981,72: 265-266 -. see also 1 Mogenet (1985) Toomer, G.l "The Mathematician Zenodorus;' Greek, Roman and Byzantine Studies,
1972,13: 177-192 -. "Theon of Alexandria," DSB, 13 (1976): 321-325 -. Ptolemy's Almagest, New YorkiBeriin/HeidelbergiTokyo: Springer, 1984 Unguru, S. "Pappus in the Thirteenth Century in the Latin West;' Archive for History of
Oxford: Clarendon Press, 1787 Ver Eecke, P. Les Oeuvres completes d:4.rchimede, Paris/Brussels: Desciee, 1921 (2nd ed. ,
2 vol., Liege: Vaillant-Carmanne, 1960) -. Les Coniques d:4.pollonius de Perge, Bruges: Desciee, De Brouwer, 1924 -. Pappus d:4.lexandrie: La Collection mathematique, 2 vol., Paris/Bruges: Desciee, De
Brouwer, 1933 Victor, S.K. Practical Geometry in the High Middle Ages: Artis cuiuslibet consummatio
and the Pratike de geometrie, Philadelphia: American Philosophical Society (Memoirs 134), 1979
van der Waerden, B.L. Science Awakening, Groningen: P. Noordhoff, 1954 (repr. New York: 1 Wiley & Sons, 1963)
Waithe, M.E. "Hypatia of Alexandria;' in A History of Women Philosophers, I, ed. M.E. Waithe, pp. 169-195, Dordrecht: M. Nijhoff, 1987
Weaver, lH. "The Duplication Problem," American Mathematical Monthly, 1916, 23: 106-113
Bibliography 831
-. "Pappus. Introductory Paper;' Bulletin of the American Mathematical Society, 1916-17, 23: 127-135
Wehr, H. A Dictionary of Modern Written Arabic, 3rd ed., ed. J.M. Cowan, Ithaca, NY.: Spoken Language Services, Inc., 1976 (from the German edition, Wiesbaden: O. Harrassowitz, 1971)
von Wilamowitz-Moellendorff, U. "Ein Weihgeschenk des Eratosthenes," Nachrichten der k. Gesellschaft der Wissenschaften zu Gottingen, phil.-hist. Klasse, 1894, pp. 15-35 (repr. in Kleine Schriften, Berlin: Akademie Verlag and Amsterdam: A.M. Hakkert, 1971, II, pp. 48-70)
Wilson, N .G. Scholars of Byzantium, London: Duckworth and Baltimore: Johns Hopkins University Press, 1983
-. see also L.D. Reynolds and N.G. Wilson Woepcke, F. l:4lgebre d'Omar Alkhayyami, Paris: B. Duprat, 1851 -. "Sur une me sure de la circonference du cercle, due aux astronomes arabes, et fondee
sur un calcul d'Aboul Waffi.;' Journal Asiatique, 1860, 15: 281-320 Wright, J.K. "Notes on the knowledge oflatitudes and longitudes in the middle ages;' Isis,
translation of Part III of the Russian edition, with the author's new notes and bibliographical citations], Paris: 1. Vrin, 1976
Ziegler, K. "Eutokios von Askalon;' in Der Kleine Pauly, Lexikon der Antike, Munich: A. Druckenmiiller, 2 (1975): 468
-. "Theon": see PW
Index
References are to the pages where the specified items are discussed. Entries with suffix "n" or "nn" followed by one or more numerals refer to the note or notes, respectively, so numbered, appearing on the indicated pages. In cases where a whole chapter is devoted to the discussion of an item, the part and number (or letter) of the chapter are given; for instance "III9" refers to Part III, chapter 9. The symbol "-+" is used for cross-referencing. Since for most subject headings only those discussions are cited in which the actual terms ofthe heading appear, it will in general be essential to consult the cross-referenced headings as well. Where a subheading also appears elsewhere as a heading, cross-referencing is often omitted; e.g., in the entry "Pappus, on cube duplication;' one should understand "-+ cube duplication" as an implicit cross-reference. The elements '~bu", "al-" and "ibn" are not counted in the alphabetization of Arabic names, nor is the word "De" in that of Latin titles.
analytic works of (lost) 214-215, 240n12, 241n19, 242n26
in Arabic 229, 248-249 commentaries on 5-6, 235-236,
244n74, 755, 765, 767, 770; of Eutocius 226, 228-230, 245n82, 765-771; of Hypatia 406, 755, 765, 769-770; -+ Pappus, lemmas on the Conics
on compound ratio 158 Conics, proposition numbers of
125n102; suppressed first edition of 231, 244n53; in Arabic 218,222, 259-260, 306; variants in mss. 286
Conics II 4: 284; text 331,333, 367-368 [-+ Eutocius, hyperbola construction; angle trisection, of Thiibit]; II 8: text 257, 326, 356; II 12: 279-280, 335, 369; IV 30 (35): text 257, 327, 357
on constructions 55-56, 118 cube duplication, in Philoponus (AJ)
Il, (PK) 13; in Eutocius (AE) 81; via conics 54, 75n40, 77; -+ cube duplication, of Apollonius
On Plane Loci 797n45 sundial of 28n34, 53
approximation 75n36; of cubic roots 536 of curves 121n39 of square roots 156, 522-523,
540-542, 546; Hero's rule for 493n15, 592n42; values for 492n9 [-+ Archimedes, on square roots]
of ratio of circumference to diameter of circle (1t) 230, 544; Archimedean values of 127n133 [-+ Archimedes, Dim. circ., prop. 3]; alternative values 541,550, 591n29, 593(nn52-57), 816n2; of Ptolemy 397n22
axiom on convergence (')\rchimedeanEuclidean axiom") 408, 418n26; Latin variant 684n104
axiom on including (convex) arcs 63, 72n6, 386, 417n9, 603, 682n80 [-+ rectification]
axiom on least distance 382, 399n41, 406
on balances 496, 506n12 centers of gravity 243n45, 594n58 chronology of works 418n15 citations of Euclid 381-382, 399n37,
408-409, 418n33 cited, in AI 159, 167, 186,700-702,
717-719,726-728; in Geminus 52; in Proclus 729; in Simplicius 730, 734, 737; in Theon 742n14 [-+ Hero; Pappus; Proclus]
commentaries on 6; Eutocius 226, 229-230
on compound ratio 158 conical solids ( surfaces) of 598-60 1 ,
747n57,776 on conics 223n16 corpus of writings, evolution of 531 n51 crown problem of 51On40 and cube duplication (Heronian) 53 editing of corpus 409-410 heptagon problem 307 on infinite 737 on inscribed polygons 735-736,
749(nn82-83,86) and isoperimetrics 502-503,729-730,
733-738 on measurement of sphere (Sphere and
Cylinder) 377, 503, 538, 596, 605-606; rule for volume of sphere 493n16; on spherical sectors 612n30
mechanical writings of 531n51 on mechanisms 129n152 medieval text of Sphere and Cylinder
528, 532n55; in Arabic 442-450; in Hebrew 442-450; in Latin 598; adaptations 610 [-+ De curvis superjiciebus; BanO MOsa]
on parabolic segment, area of 377, 498-501,508n33
on ratio of cylinder and cube 208n9, 605 [-+ indivisibles]
sector theorem 431, 435 [-+ Hero, on Archimedes]; medieval form 422
solid problem of 85-87, 101, 116-117, 222, 223nI4,230-231, 722, 743n26, 746n56
on spirals 95
Index 835
on square root approximations 492n9, 504
style 508n33, 509n38 synthenti summation lemma for ratios
744n33 triangle rule 51On40
Archimedes, Dimension of Circle, survey of textual tradition 11112; table 806
as extant in Greek (DC) 495-497, 503-505, 537-538, 541; date 453n35; as known to Eutocius 1II6 [-+ Eutocius]; style 403, 527, 771-774; defects 375,477-478,496, 514, 548
prototype (OC*) 1II6, 422-423, 495-496,503-505; date 608; provenance 753-756, 774, 779-780; relation to AI/AI* 689, 702, 733-734
older prototype (A*) 495-496, 502-505,806-807; relation to Sphere and Cylinder 527, 808
prop. I (circle theorem) as extant (OC) III2; text 411-414; 422-435, 536-538,547,700,702; prototype (A*) 1II2; text 411-413; prototype (OC*) 424-425, 431-435; versions in Pappus (P) and Theon (T) 1111; citations of circle theorem 376-380
prop. 2 (area of circle), as extant 1II4, 397n23, 506n7; text 484; prototype (OC*) 479-483; citations of 478
prop. 3 (approximation of ratio of circumference and diameter) III4, 397n23, 497, 503-505, 536-541; text 485-489; algorithm for 511n48; rounding off technique for 504, 512n50; alternative values 397n23, 502; citations of 480-481
medieval translations III3-4, 615n58, 805; text of Arabic (in English translation) 436-438, 484-489; Hebrew and Latin variants 422,438-441, 489-491; facsimiles, of Arabic (AF) 455-463, of Hebrew (H) 464-465, of Latin (LP, LG) 466-475 [-+ Gerard of Cremona; Plato of Tivoli; Quadratura circuli]; tradition of AF 544-551; Arabic adaptations III7
Archytas 26n22, 113, 128(nnI51-152), 142, 147, 150, 158; cube duplication of 53, 79-80, 110; -+ cube duplication, of Archytas
836 Textual Studies in Ancient and Medieval Geometry
area of circular sectors 505n3; -- Archimedes, sector theorem
area of circular segments 507n24; -- Hero, on circular segments
Arendt, F. 243n49, 493n14 Aristaeus 72n7, 75n40, 77, 123n83, 215,
223n15, 228, 237, 240n12, 241n21 Aristarchus 28n34, 530n38, 592n43, 698 Ariston 144 Aristotle, on applied science 74~n70; on
astronomy 128n150; cited 682n76; commentaries on 6; on isoperimetrics 730-731, 734, 737-738, 748n67, 811; locus problem 57nIl; on parts (mathematical) 57n12; on zoology 93, 123n89, 747n64, 751n9l
[Aristotle], Mechanics 496, 506n8 arithmetic, relative to geometry 157-159,
171(nn19,21,24), 181, 21On48, 550, 593n47; verbal expression of numerals 593n50
arithmetic operations 155, l72n34; division by table 757-759,761-764;
text from Theon 780-784,786-787; text from Introduction to Almagest 787-793
expression and manipulation of large numbers 539-540, 545-546, 591n18, 592n40; in Quadratura circuli (Gerardian, Florence and Glasgow versions) 665-667; reduction of ratios 667
long division 757, 759-760; text from Theon 784-786, 802-804
long multiplication 522-523, 591n19 sexagesimal methods of 550,757,759,
781,783,786,788, 796n31 [-- division by table; long division]; notation 764, 790-791
tabular methods of 763, 789-791, 796(nn22,26)
Artis cuiuslibet consummatio 672-676, 811
astrolabe 699, 795n11. 814, 816n12; -- Theon of Alexandria, commentary, On Small Astrolabe
astronomical corpus, minor 698; -- intermediate corpus
continually (aei) 448-449; medieval terminology for 434, 449
continuity and divisibility 646, 653 convergence,
Archimedean (Sph. Cyl. I 1-6) 385, 407-408,497,602,612n36
Euclidean 383-385, 402-403, 406-407, 501-502, 507nl9 [-> Euclid, Elements Xl; XII 2]; in Latin 683n93
Euclidean alternative form (Elements, XII 16) 497, 506n16, 507n19, 537-538, 601-602, 613n38-39; in Latin 598-600, 646 [--> Bam) Musil.; De curvis superficiebusl
Eudoxean 406-407 in Pappus (alternative) 744n38
convergence enhancement 51 On42, 591n29
Coolidge, J.L.L. 241n17, 742n13, 744(nn33-34)
838 Textual Studies in Ancient and Medieval Geometry
Ctesibius of Alexandria 41-42, 56n5, 129n152, 145
cube duplication, anonymous, in Pappus 14; 112, 228 of Apollonius (in Eutocius, AE) II; 78,
113; (in Philoponus, AJ) II; (in Philoponus, PK) 249, 259-261; text 251-253, 321, 323
of Archytas 100-110, 289 of Diodes 39n8, 113-114; and Sporus
89-90 of Eratosthenes 16; Ill, 115, 228 of Eudoxus 108, 112 of Abu Bakr al-Harawl lIA; 220, 222,
225,271,287,302,305-307; text 251-253, 320, 322, 364-366
of Hero II (in Belopoeica, HB) 41, 45, 51, 119n8; (in Mechanica, HM) II, 51; (in Eutocius, HE) II, 45, 51-52; (in Pappus, HP) II
in Eutocius (survey) 15, 769-770 of al-Khazin 254, 262-264; text
254-255, 322-324, 352-354 of Menaechmus 39n8, 94-100,
114-115, 225 of Nicomedes 108, Ill, 115, 245n83,
249 of Nicomedes (in Eutocius) 316-318;
text 312-315, 342-345; (in alKhazin) IIF; text 311-315,341-342
of Pappus 87-93, 114, 227, 238; ->
attributed to Plato of Philo of Byzantium 113; in
Belopoeica (PB) 13, 25nlO; in Eutocius (PE) 13, 78; in Philoponus (PJ) 13; the same, attributed to Apollonius (PK) 13, 36-38
attributed to Plato 36-38, 78-80, 109, 112-113, 536; and Pappus 89-93
of al-Quhl lIE, 220; text 301-303, 339-340
of Sporus 87-93, 114, 124n92; -> of Diodes
of al-Tus! 264-265, 302; text 255-256, 324-325, 355
curves, as solid sections 104, 107-108, 128n150; on surfaces 128n150
De curvis superficiebus (CS) Ill8; adaptations of (medieval) 628-631,
672-673; -> De piramidibus ancient provenance (as prototype CS*)
497, 507n17, 538, 595-596, 608-610, 776-780, 809-810; relation to AI 608-610,689,718, 733-734
area expressions in 453n40 arithmetic estimate of sphere volume
604-606 convergence method in 538, 613n38 influence of 595-596 lemma on sphere volume 603-604 mss. 679(nn28-29) on proportion of circumferences and
diameters 497, 506n16, 507n19, 538, 613n40
and De quadratura circuli 614n55, 617, 620-627, 635-637, 646, 672; citations of De quad. circ. 606, 615n58
on rectification of curves and surfaces 613n44; -> rectification hypothesis
relation to Archimedes' Sph. Cyl. 596, 598-603, 609-610
relation to Baml Musa (VF) 596, 598-603, 608
style 596-598,621-623, 678n18, 776-780
cylinders, isoperimetric 720-722, 745n53, 746n56
cylindric line 104, 107 Cyril, patriarch of Alexandria 754
Eudoxus ofCnidus 26n22, 113, 128n151, 418n21; cited by Eratosthenes 142, 147, 150; by Hero 51On40; in Introduction to Almagest 159, 167, 186; astronomy of 126n124, 128n150; cube duplication of 78-89; sundial of 28n34
Eulalius 794n2 Eutocius 6, 11, 254, 615;
alleged author of Introduction to Almagest 17; 67-68, 788, 801n11O; --> Mogenet
and Ammonius 167, 169n5 in Arabic 127n132, 262, 447, 809; in
al-Tusi547, 549; possible use by Baml Musil 539-543
on Archimedes' circle theorem (Dim. Circ., prop. I) 424, 432-433, 452(nn21,32), 607
on Archimedes' estimates of circle ratio (n)494n38, 504-505, 510n41
on Archimedes' Sph. Cyl. 16: 418n24, 445-447,516; on 110: 516-520; text 533
citations: of Conics 306; of Ptolemy commentaries 417
commentaries 155-156; on Apollonius 222, 224n39, 231, 237-238, 245n81, 446,765-771; on Archimedes 63, 410, 445-447, 482-483, 757; on Ptolemy, alleged 164-166, 169n5, 175n7l,230
on compound ratio 17 on cube duplications 15; 39n16, 217,
222, 262-264, 295, 300, 798n68; of Apollonius (AE) II; of Philo (PE) 13, 41; --> cube duplication
date 26n22, 229-230 on Diocles 308 editing of Archimedes commentaries
99, 807 [--> Isidore of Miletus] on Eratosthenes 16; 67-68,
73(nn9-1O), 74n23, 115-116 on hyperbola construction, 284,
743n26; text 280-281, 336-337 on loci 228, 236, 241n20 on Nicomedes 29-33 on rectification of circle 613n44 religion of 167, 176(nn85-86), 177n87 sources of 18, 24, 26(nn21-22), 45,
Gerbert 673 Gericke, H. 742n13, 749n79 Gervase of Essex 595, 635-636 Gibbs, S. 28n34, 53 "givens": ---+ terminology Gordanus 638, 676, 680n59, 683n90; dat-
ing of 670; ---+ Quadratura circuli Grabmann, M. 612n27 graphical construction: ---+ construction Greaves, D. 190 Gregory, D. 798n66 Gregory, 1. 591n29 groove (of instrument) 30, 79, 132, 146,
150n2; ---+ construction, mechanical; terminology
Grosseteste: ---+ Robert Grosseteste
Index 841
Gudemann, [n.i.] 123(nn87,88)
al-I:Jajjaj 442, 612n25 al-Harawi, Abu Bakr 6,41, 54-55, 77,
249; on conics 290-291; cube duplication of IIA [---+ cube duplication]
al-Harawi, Abu '1-I:Jasan 296 Hartner, W. 795n 11 Haskins, C.H. 611n12, 614n57, 687n147,
688n150, 741nl ibn al-Haytham (Alhazen) 8nll, 318,
104, 108, 110 Heraclides 58n24, 230, 483, 494n38 Hermann of Carinthia 597-598, 612n25 Hero of Alexandria 5, 75n40, 793nl;
on analysis 242n27 on arches (Kamarika, lost) 9 and Archimedes, citations of 230,
805-807; for approximation of circle ratio (re) 397n23, 481. 483, 493n18, 502; for more accurate value (attributed) 496-497; for rule for area of circle (cf. Dim. eire., prop. 2) 397n23, 477-478, 493n14, 615n58; for circle theorem (cf. Dim. eire., prop. I) 377, 379, 397n23, 405; for sector theorem 377, 379, 495, 503; for measurement of parabola 397n15, 509n35
on circular segments 377, 497-502 cube duplication of 71, 81; in Mechan
ica (HM) and Belopoeica (HB) 11; in Eutocius (HE); ---+ cube duplication
on curvilinear areas 507n20
842 Textual Studies in Ancient and Medieval Geometry
Hero of Alexandria (cont.) on fractions 530n43 and Philo 41-42; on catapults 143 on polygons 492n9 practical geometry in mechanics
152n31 rule for triangle 536; -> Archimedes sources 51Onn40-41, 531 n51 on sphere, arithmetic estimate for
on Archimedes' circle ratio estimate (7t) 481, 483, 492n8
on Archimedes' circle theorem (Dim. eire., prop. 1) 378
on Archimedes' rule for area of circle (Dim. eire., prop. 2) 478, 492n8
on area of circular segments, aUr. to Archimedes 509n34
excerpts of Proclus in 453 (nn34-35) on isoperimetrics 747n63 on length of circular arcs 507n25 on sphere, arithmetic rule for 493n16 scholia 494 (nn25-26)
Hierocles 754 Hiller, E. 131, 153n47 al-l:Iimsi 256, 277, 284 Hintikka, 1. and U. Remes 242n27 Hipparchus 417nl Hippocrates of Chios 32, 56nll, 108,
hyperbola 85; for angle trisection 56, 297 for auxiliary problem of al-Sijzi 297 construction of 213-214, 217,
223(nn5,14), 230-234, 236-237, 274, 287-288; in Apollonius (Conics II 4) 231, 233, 281-282, 284; text 331,333; in Eutocius 230-234,249; text 336-337; in al-Khiizin 263, 289-291,317; in Pappus 230-234; in Thabit 283-285; text 277-278, 330, 332
for cube duplication 54-55 [-> cube duplication, of al-Harawi]
in isoperimetric cylinders problem 746n56
as locus of constant product 125n103 with Menaechmus 94-100 for solution of problems 213, 222
Hypsicles 73n7, 592n43, 745n43, 750n86
Iarnblichus 5,167, 176n79, 751n87, 796n36
Ibrahim ibn Sinan 229 impossible (adynaton, atopon) 384, 403,
417n6, 427, 636; Latin terminology 685n127; -> proofs, indirect
Neuenschwander, E. 126(nnI26-127) Neugebauer,o. 169n5, 743(nnI9,2I),
795nll, 816n12 neusis constructions 38, 117-118,
120n32; alternative formulations of 219,
285-288 for angle trisection 213-219,287 relative to circle and chord 228 via conchoid 30-31, 311 via conics 34; via hyperbola 272 and cube duplication 55-56; of Hero
53; of Pappus 91, 114; of Sporus 89; effected via hyperbola 260-261
for spirals 95 Nicomachus of Gerasa 157-158, 170n 17 ,
on Apollonius' cube duplication 54; on his Neuses (lost) 288
in Arabic 217,228-229,273; -+ Jackson
on Archimedes 805-807; approximation to circle ratio (n) 378, 480, 483; circle theorem (cf. Dim. Circ., prop. I) IIIl, 401-403, 405, 495, 511n46, 607; text P 387-392; sector theorem 377, 382, 384-387, 495-497; text S 394-396; measurement of sphere 716
cited in Eutocius 178, 236, 765, 798n62; in Introduction to Almagest 155,160,187,202,789,792-793
classification of problems 71 commentaries on Ptolemy 227, 691; on
Book I (lost) 380-381, 385-387; cited by Eutocius 157-159, 165
on compound ratio 160, 162 on construction by instrument 318 on cube duplication 14; 71, 217,
240(nn13-16); own method 71-72, 87-93
on division 175n76, 763-764, 787-793
on Eratosthenes 131-136 and Geminus 52 on hyperbola construction 230-234 on isoperimetric figures (PI) 11110,
497,502-503, 615n6O, 774-776, 811; contents 692; compared with other accounts 723-725; lost version (PI*) 691, 693, 697-698, 701-702, 704,710-711,715,725-728,730, 734, 736; on isoperimetric solids 51On44
lemma on circumference-diameter proportion 497, 511n46, 602, 613n42
lemma on volume of sphere 614n50 lemmas on Apollonius' Conics 228,
234-238,410, 767-768, 797n45, 798n58
lemmas on Euclid's Optics 242n29 Mechanics (cf. Collection VIII) 75,
87-88, 112, 228-229, 235, 273 on neusis for Archimedes' Spirals 95 on Nicomedes 29-33,50 originality 88, 92-93; modern assess-
ments of 226, 239n3 on rule for volume of sphere 493nl6 sources 92, 531n51, 716 on square roots 156
846 Textual Studies in Ancient and Medieval Geometry
part (mathematical term) 57n12, 654, 696 Pedersen, 0. 687n148 Perseus 128n150 Peyrard, F. 398n36 Philo of Byzantium 14, 41-42, 75n40;
date 145; Belopoeica 143-145; cube duplication (PB) 41-45,51-52; in Eutocius (PE) 44-45, 48-52 [-> cube duplication]; on mechanisms 129n152; style 43-44,143-145
Philo of Gadara 230,505,541, 591n24 Philo of Tyana 223n 17 Philoponus, John (Joannes) 6, 11, 28n30,
113; and Ammonius 169n5 on Apollonius' cube duplication, Hero
nian form (AJ) II; Philonian form (PK) 13, IIA; alternative (PJ) 13
on astrolabe 699 commentaries on Aristotle 21, 45,
796n35 date 26n22 on instrumental construction 16, 318 on Delian oracle 57n18, 140 on isoperimetrics 730-731, 735 sources 21, 26n22, 51 style 46, 798n69
for planes (area) 28n29, 106-107, 505n4, 697. 700-702, 745n48
for solids (volume) 717. 720, 733. 745(nn43,49-50), 800n97
terminology, in Greek (to h~po tr3n ... ) 106-107, 378-380; in Arabic 284, 425. 434, 449; in Hebrew 449; in Latin (ductus) 621,647,656-657. 677n15, 683(nnl01-I03)
proofs, alternative 94, 96, 98-99. 114, 125n114. 272-273. 300, 446, 497; general (contrasted to inductive) [--> induction]; indirect 383. 399n45, 538, 592n38. 597, 600-602, 611n19, 636, 686n129, 713, 7641--> impossible]
proportionality, of circular arcs and sectors 386, 398n36, 399n49, 407, 495-497, 502, 505n4; of circumferences and diameters 496-497, 502. 506(nn6,16), 507n19, 536. 538-539, 590n8, 602, 613n40; of areas and perimeters of regular polygons 684n 117; of cylinders and cubes 605
proportions, terminological variants in Greek 696; Arabic 285; Hebrew 449; Latin 622, 630-631
Ptolemy (king) Ill, 115, 131-132, 134. 144, 147,150; III (Euergetes) 144. 152n34; IV (Philopator) 144-145; V (Epiphanes) 145, 153n38
Ptolemy (Klaudios Ptolemaios) 5, 152n24,417nl;
Almagest (Syntaxis), Book I 155
Index 847
[--> Introduction to Almagest]; Latin translation 614n57; citations in Latin 645, 682n80, 686(nnI38-139)
approximation of circumferencediameter ratio (rr) 550, 593n53; on Archimedean values 480, 483, 503, 505n4
on Archimedean circle theorem (Dim. eire., prop. 1) 378, 505n4
on chords 645, 682n80; table of 75n33, 541-543,550, 591n29: --> chords
commentaries on: --> Arcadius; Eutocius; Hypatia; Pappus; Theon
On Gravities 230 on isoperimetrics 690, 736 on mean motion of planets 757-758.
780, 786-788 on obliquity of ecliptic 530n38 on planisphere 699 on proportionality of arcs and sectors
505n4 on spherics 175n61
Pythagoras 176, 813; Pythagorean theorem: --> Euclid, Elements I 47
Qalonymos b. Qalonymos 6. 421, 441. 450, 451(nn3,14)
quadratrix 58n26, 92-93, 114; for angle division 214; for circle quadrature: --> Sporus
De quadratura circuli, LG (translation of Dim. eire. by Gerard of Cremona) 617,619,623-624,627,641. 648-649. 663, 665. 667-668, 682n73. 687n147, 810; text 467, 469.471,473,475; variants from Arabic 438-441,489-491; titles in mss.614n52
adaptations of III9; overview 617-618, 668-677, 810
Abbreviated Version (AV) 648-649; --> Roger Bacon
Cambridge Version (C) 625-631; and other versions: Naples 635; Corpus Christi 655-663; and De cun'is superficiehus 628-631; and De ysoperimetris 680n46
Corpus Christi Version (Cor) 655-663; and Vatican Version 645
Florence Version (F) 614n54, 618-624, 799n85; and other versions: Cam-
848 Textual Studies in Ancient and Medieval Geometry
De quadratura circuli (cant.) Florence Version (F) (cant.)
bridge 626-631; Naples 631-635; Corpus Christi 655-663; Glasgow 665-668; and De curvis superfieiebus 620-624; --+ John of Tynemouth
Glasgow Version (Gg) 663-668 Gordanus Version (Go) 638-640; and
other versions: Munich 640-643, 648; Vatican 644-648,650,654-655
Munich Version (M) 640-643 Naples Version (N) 631-637; and other
versions: Gordanus 638-640; Munich 640-643; --+ Gerard of Brussels
in Questio of Albert of Saxony (QA) 649-655
Vatican (ps.-Bradwardine) Version (V) 644-648; and Abbreviated Version 648-649; and Questio of Albert 649-655
mss. of LG and adaptations 618, 624-625, 628, 635-636, 638, 641, 648, 655, 663, 669, 677(nn5,7), 681n73, 683(nn85,90), 684nl13, 685nI20,686n131
quadrivium 674 al-Quhi 6, 54-55, 216, 249;
angle trisection of lIE; --+ angle trisection; al-Sijzi
on approximation of circumferencediameter ratio (n) 544, 592n36
on Archimedes' Dim. eire., doubts 543-544
on Archimedes' heptagon problem 307 on centers of gravity 592n36, 594n58 citation of Conics 222, 245n81, 306 cube duplication of lIE; --+ cube dupli-
cation and al-Harawi 259
Quintilian 732, 748n64, 749n81, 811 Qust,li ibn Luqa 6, 11,447-450,809;
proposed as translator of Dim. eire. 535, 549, 551
Rashed, R. 318,448, 592n40, 795n14 Abu 'I-Rashid, cAbd al-Hadi 6, 450n2,
451n7, 494n35, 617, 671, 799n85, 809-810; question of identity 543; version of Dim. eire. (AR) 421, 543-546; text 552-576; possible use by al-Tusi 547,549-550; style 544-546, 551
ratio, compound 122n70, 208nl; in Domni
nus 201-207; in Eutocius 155-159, 162-164, 177-185; in Introduction to Almagest 155-156, 159-164, 185-201; relation to di'isou 171n25
duplicate 122n70 epimorios 208n2 in relation to number 158, 171n27,
174n53, 208n5, 531n44, 539, 600 subtraction of 159, 161, 175(nn61,63),
185, 187-190, 202-204, 21On35; rule for 209(nn2l ,27), 21On43
synthenti, form in Pappus and Archi-medes 711
--+ terminology Rawlins, D. 530n38 rectification of curved lines and surfaces,
in accounts of cube duplications, of Apollonius 16-17; of Banu Musil 79; of Hero 12-14; of Pappus 91-92; of Philo 42-44; of Plato 79, 92; of Sporus 89
flexible 83 of Nicomedes' conchoid 30 rod or guideline (Eratosthenes) 135,
140, 142, .146 sliding or moving 12-18, 22, 42-44,
263; ---> neusis
al-~abi, Abu Is~aq 592(nn34,36) al-~aghani 296 Saito, K. 171n25 Saliba, G. 242n27 salinon 498 al-Samau'al 242n27 Sams6, J. 254 Samson and Delilah 673 Sarfatti, G. 449, 451n3 Sato, T. 396n7, 423, 451n16,
452(nn17-18),613n37 Sayili, A. 301 schesis (relation), and ratio 208n3 Schneider, I. 396n2 scholastic 239, 617, 640-641, 648-649,
482, 543, 742n17, 797n45, 798n63; in De curvis superficiebus 61On7; to Euclid 171 n26; to Heronian corpus 492n7, 493n16, 494(nn25-26), 509n34; in Abu 'I-Rashid 561-562; (as commentary) 155, 164-165, 172n34, 178,231,235-238, 244n72, 495,767-768
Schoy, C. 307-308 secant product 34-36, 39n25; ---> Euclid,
Elements III 36 sections, of planes 105; of solids 104, 107 sectors, exterior 417n7, 529n16,
632-633, 680(nn52,54), 681n71; similar 429, 51On45
segment of circle, area approximation 498, 500-502; ---> Hero
on Archimedes' circle theorem (T; cf. Dim. eire., prop. I) IIII; 401-406, 423-435, 511n46, 513, 607,805; text 387-391, 392-393
on Archimedes' estimate of circle ratio (n) 479, 480-482, 493(nnI8,20)
on area of circle, arithmetic estimate (cf. Dim. eire., prop. 2) 493n14, 479-480, 483, 503, 614n48, 753
cited, by Eutocius 157-159, 165, 178;
in Introduction to Almagest 155, 698-699, 723, 741n3
commentaries: On Small Astrolabe 698-699, 743n21; On Small Astronomer 698-699, 723; On Hero's Metrica 243n44, 479, 493n15, 741n3; On Ptolemy's Almagest IIII, lIllO, 227, 754, 756; On Ptolemy's Tables 175n63, 417nl, 793n2, 795n13
on compound ratio 170n15, 17ln20, 174n60, 175n61, 21On48
editions of Euclid 398n36, 452n 17, 748n73, 816n4
on Hypatia 756, 762, 808 on isoperimetric figures (TI) II11O;
169n3, 615n60, 774-776, 811; contents 692; summary of comparisons 723-725; on solids 51On44; variants in mss. 709, 747n61
lemma to Archimedes' circle theorem (T) 403-405, 427-428, 518-520, 529n22, 544, 753; text 414-416, 534
on long division 757-764, 770-771; texts 780-787, 802-804
on proportionality of arcs and sectors 506n4
relation to Pappus 227, 240n7, 398n36, 482, 796n38
edition of Banu Musa 79-80, 103-105, 119n16, 127n139, 536, 549-550, 601, 611n23
edition of intermediate curriculum 546-547
and al-Harawi 259, 262-265 on rectification of circle, hypothesis of
542, 613n44 style 264-265, 547-551
Unguru, S. 242n29 unrolling (anaploun, exaploun) 379,
398n25
Ver Eecke, P. 243n35, 492n3, 742(nnI3-14),745n52
Victor, S.K. 686(nn135-140), 687(nnI43,145-146)
Vieta, F. 158 Vitruvius 24,42, 128n152, 51On40 van der Waerden, B.L. 240(nn3,4),
796n28
Abu 'l-Wafii' 549,582, 593(nn52,57), 809 Waithe, M.E. 794n4, 795n16 Wallies, M. 48 Weaver, J.H. 122n74 von Wilamowitz-Moellendorff, U. 16;
74n23 , III, 115, 245n83 Wilson, N.G. 531n28 Witelo 229 Woepcke, F. 224(nnI9,31), 294, 307,
593n57 Wright, J.K. 688nl49
Ya'akov b. Makhir 6,442,450, 451nl4 Youschkevitch, A.P. 750n86
852 Textual Studies in Ancient and Medieval Geometry
De ysoperimetris 595, 614(nn45,57), 680n46, 689, 741n1, 743n18; adaptations 686n132, 687n147, 688(nn154,157), 741n1, 810, 816n3; and John of Tynemouth 676; citation of Archimedes' circle theorem 607