Mathematical Reconstructions Out, Textual Studies In: 30 Years in the Historiography of Greek Mathematics
Revue d'histoire des mathématiques, Tome 4 (1998) no. 1, pp. 131-142. 
@article{RHM_1998__4_1_131_0,
     author = {Saito, Ken},
     title = {Mathematical {Reconstructions} {Out,} {Textual} {Studies} {In:} 30 {Years} in the {Historiography} of {Greek} {Mathematics}},
     journal = {Revue d'histoire des math\'ematiques},
     pages = {131--142},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {4},
     number = {1},
     year = {1998},
     zbl = {0927.01003},
     language = {en},
     url = {http://archive.numdam.org/item/RHM_1998__4_1_131_0/}
}
TY  - JOUR
AU  - Saito, Ken
TI  - Mathematical Reconstructions Out, Textual Studies In: 30 Years in the Historiography of Greek Mathematics
JO  - Revue d'histoire des mathématiques
PY  - 1998
SP  - 131
EP  - 142
VL  - 4
IS  - 1
PB  - Société mathématique de France
UR  - http://archive.numdam.org/item/RHM_1998__4_1_131_0/
LA  - en
ID  - RHM_1998__4_1_131_0
ER  - 
%0 Journal Article
%A Saito, Ken
%T Mathematical Reconstructions Out, Textual Studies In: 30 Years in the Historiography of Greek Mathematics
%J Revue d'histoire des mathématiques
%D 1998
%P 131-142
%V 4
%N 1
%I Société mathématique de France
%U http://archive.numdam.org/item/RHM_1998__4_1_131_0/
%G en
%F RHM_1998__4_1_131_0
Saito, Ken. Mathematical Reconstructions Out, Textual Studies In: 30 Years in the Historiography of Greek Mathematics. Revue d'histoire des mathématiques, Tome 4 (1998) no. 1, pp. 131-142. http://archive.numdam.org/item/RHM_1998__4_1_131_0/

[1] Artmann (Benno) [1985] Über voreuklidische ‘Elemente', deren Autor Proportionen vermied, Archive for History of Exact Sciences, 33 (1985), pp.291-306. | MR | Zbl

[2] Artmann (Benno) [1991] Euclid's Elements and its Prehistory, in Peri Tōn Mathēmatōn (Apeiron, 24-4), Mueller (I.), ed., Alberta: Academic Printing & Publishing, 1991, pp.1-47. | MR | Zbl

[3] Becker (Oskar) [1932/33]Eudoxos-Studien I: Eine voreudoxische Proportionenlehre und ihre Spuren bei Aristoteles und Euklid, Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik, Abt.B, Bd. II, pp.311-330. | JFM | Zbl

[4] Beckmann (Friedhelm) [1967] Neue Gesichtspunkte zum 5. Buch Euklids, Arch. Hist. Exact Sci., 4 (1967), pp.1-144. | MR | Zbl

[5] Berggren (J. Lennart) [1984] History of Greek Mathematics: A Survey of Recent Research, Historia Mathematica, 11 (1984), pp.394-410. | MR | Zbl

[6] Berggren (John L.) and Thomas (Robert S.D.) [1996] Euclid's Phaenomena: A Translation and Study of a Hellenistic Treatise in Spherical Astronomy, New York: Garland, 1996. | MR | Zbl

[7] Bowen (Alan C.) [1982] The Foundations of Early Pythagorean Harmonic Science: Archytas, Fragment 1, Ancient Philosophy, 1 (1982), pp.79-104.

[8] Bowen (Alan C.) [1991] Euclid's Sectio canonis and the History of Pythagoreanism, in Science and Philosophy in Classical Greece, Bowen (A.C.) and Rochberg-Halton (F.), eds., New York: Garland, 1991, pp.164-187. | MR

[9] Burkert (Walter) [1972] Lore and Science in Ancient Pythagoreanism, trans. E.L. Minar, Jun. Cambridge, Mass.: Harvard University Press, 1972.

[10] Caveing (Maurice) [1994-98]Essai sur le savoir mathématique dans la Mésopotamie et l'Egypte anciennes, Lille: Presses universitaires de Lille, 1994 (= vol.1); La figure et le nombre. Recherches sur les premières mathématiques des Grecs, Lille: Presses universitaires du Septentrion, 1997 (= vol.2); L'irrationalité dans les mathématiques grecques jusqu'à Euclide, Lille: Presses universitaires du Septentrion, 1998 (= vol. 3). | MR | Zbl

[11] Centrone (Bruno) [1996] Introduzione ai Pitagorici, Roma-Bari: Laterza, 1996.

[12] Dicks (D.R.) [1959] Thales, Classical Quarterly, NS 9 (1959), pp.294-300.

[13] Euclide [1990] Les Éléments, trad. et commentaires par Bernard Vitrac, Paris: Presses universitaires de France, 1990-, 4 vols., 2 vols to date, vol.3 to appear in December 1998.

[14] Fowler (David H.) [1987] The Mathematics of Plato's Academy, Oxford: Clarendon Press, paperback edition with corrections, 1990. A revised second edition in preparation.

[15] Fowler (David H.) [1994] The Story of Discovery of Incommensurability, Revisited, in Trends in the Historiography of Science, Gavroglu (K.), Christianidis (J.) and Nicolaïdis (E.), eds., Dordrecht: Kluwer Academic Publishers. A revised version to be included in the second edition of [Fowler 1987], pp.221-235. | MR

[16] Freudenthal (H.) [1966] Y avait-il une crise des fondements des mathématiques dans l'antiquité?, Bulletin de la Société mathématique de Belgique, 18 (1966), pp.43-55. | Zbl

[17] Fritz (Kurt Von) [1945] Discovery of Incommensurability by Hippasus of Metapontum, Annals of Mathematics, 46 (1945), pp.242-264. | MR | Zbl

[18] Gardies (Jean-Louis) [1988] L'héritage épistémologique d'Euxode de Cnide, Un essai de reconstitution, Paris: Vrin, 1988. | Zbl

[19] Grattan-Guiness (Ivor) [1996] Numbers, Magnitudes, Ratios and Proportions in Euclid's Elements: How Did He Handle Them?, Historia Mathematica, 23 (1996), pp.355-375. | MR | Zbl

[20] Heath (Sir Thomas L.) [1921] A History of Greek Mathematics, 2 vols., Oxford: Clarendon Press, 1921, Reprint, New York: Dover Publications, 1981.

[21] Huffman (Carl A.) [1985] The Authenticity of Archytas Fr.1, Classical Quarterly, 35 (1985), pp.344-348.

[22] Huffman (Carl A.) [1993] Philolaus of Croton: Pythagorean and Presocratic, Cambridge: Cambridge University Press, 1993. | MR

[23] Jones (Alexander) [1991] The Adaptation of Babylonian Methods in Greek Numerical Astronomy, Isis, 82 (1991), pp.441-453. | MR | Zbl

[24] Jones (Alexander) [1996] On Babylonian Astronomy and its Greek Metamorphoses, in Tradition, Transmission, Transformation, Jamil Ragep (F.) and Ragep (S.P.), eds., pp.139-155. Leiden: Brill, 1996. | MR | Zbl

[25] Knorr (Wilbur R.) [1975] The Evolution of the Euclidean Elements, Dordrecht: Reidel, 1975. | MR

[26] Knorr (Wilbur R.) [1978] Archimedes and the pre-Euclidean Proportion Theory, Arch. Hist. Exact Sci., 19 (1978), pp.211-290. | MR | Zbl

[27] Knorr (Wilbur R.) [1986] The Ancient Tradition of Geometric Problems, Boston: Birkhäuser, 1986. Reprint, New York: Dover Publications, 1993. | MR | Zbl

[28] Knorr (Wilbur R.) [1989] Textual Studies in Ancient and Medieval Geometry, Boston: Birkhäuser, 1989. | MR | Zbl

[29] Knorr (Wilbur R.) [1996] The Wrong Text of Euclid: On Heiberg's Text and its Alternatives, Centaurus, 38 (1996), pp.208-276. | MR | Zbl

[30] Mueller (Ian) [1981] Philosophy of Mathematics and Deductive Structure in Euclid's ‘Elements', Cambridge, Mass.: The MIT Press, 1981. | MR | Zbl

[31] Mueller (Ian) [1991] On the Notion of a Mathematical Starting Point in Plato, Aristotle, and Euclid, in Science and Philosophy in Classical Greece, Bowen (A.C.) and Rochberg-Halton (F.), eds., New York: Garland, 1991, pp.59-97. | MR

[32] Netz (Reviel) [forthcoming] The Shaping of Deduction in Greek Mathematics, Cambridge: Cambridge University Press, 1999 (forthcoming). | MR | Zbl

[33] Neuenschwander (Erwin) [1972/73] Die ersten vier Bücher der Elemente Euklids, Arch. Hist. Exact Sci., 9 (1972/73), pp.325-380. | MR | Zbl

[34] Neuenschwander (Erwin) [1974/75] Die stereometrischen Bücher der Elemente Euklids: Untersuchungen über den mathematischen Aufbau und die Entstehungsgeschichte, Arch. Hist. Exact Sci., 14 (1974/75), pp.325-380. | MR | Zbl

[35] Saito (Ken) [1985] Book II of Euclid's Elements in the Light of the Theory of Conic Sections, Historia Scientiarum, 28 (1985), pp.31-60. | MR | Zbl

[36] Saito (Ken) [1986] Compounded Ratio in Euclid and Apollonius, Historia Scientiarum, 31 (1986), pp.25-59. | MR | Zbl

[37] Saito (Ken) [1994] Proposition 14 of Book V of the Elements - A Proposition that remained a Local Lemma, Revue d'histoire des sciences, 47 (1994), pp.273-284. | MR | Zbl

[38] Szabó (Árpád) [1964] Ein Beleg für die voreudoxische Proportionenlehre29-35, Archiv für Begriffsgeschichte, 9 (1964), pp.151-171.

[39] Szabó (Árpád) [1969] Die Anfänge der griechischen Mathematik, München: Oldenbourg, 1969. | MR | Zbl

[40] Unguru (Sabetai) [1975] On the Need to Rewrite the History of Greek Mathematics, Arch. Hist. Exact Sci., 15 (1975), pp.67-114. | MR | Zbl

[41] Van Der Waerden (B.L.) [1954] Science Awakening, trans. Arnold Dresden, New York: Oxford University Press, 1954; 3rd. ed., 1971. | MR

[42] Van Der Waerden (B.L.) [1979] Die Pythagoreer, Zürich: Artemis Verlag, 1979. | MR

[43] Vitrac (Bernard) [1993] De quelques questions touchant au traitement de la proportionnallité dans les Éléments d'Euclide, Thèse de doctorat de l'École des hautes études en sciences sociale, Paris, sous la dir. de Dhombres (J.), soutenue le 17/12/1993.

[44] Vitrac (Bernard) [1996] Mythes (et réalités?) dans l'histoire des mathématiques grecques anciennes, in Goldstein (C.), Gray (J.) et Ritter (J.), éd., L'Europe mathématique, Paris: Éditions de la Maison des sciences de l'homme, 1996, p. 33-51. | MR | Zbl

[45] Vogt (Heinrich) [1908/09]Die Geometrie des Pythagoras, Bibliotheca Mathematica, III. Folge, 9 (1908/09), pp.15-54. | JFM

[46] Zeller (Eduard) [1844-1852] Die Philosophie der Griechen in ihrer geschichtlichen Entwicklung, 5.Ed., Leipzig, 1923. Reprint, Hildesheim, 1990.

[47] Zhmud (Leonid) [1997] Wissenschaft, Philosophie und Religion im frühen Pythagoreismus, Berlin: Akademie Verlag, 1997