Download Textual Studies in Ancient and Medieval Geometry by Wilbur Richard Knorr (auth.) PDF
By Wilbur Richard Knorr (auth.)
For textual experiences in relation to the traditional mathematical corpus the efforts by way of the Danish philologist, 1. L. Heiberg (1854-1928), are in particular major. starting along with his doctoral dissertation, Quaestiones Archimedeae (Copen hagen, 1879), Heiberg produced an magnificent sequence of variants and important stories that stay the root of scholarship on Greek mathematical four technology. For comprehensiveness and accuracy, his variants are exemplary. In his textual stories, as additionally within the prolegomena to his variants, he rigorously defined the extant proof, prepared the manuscripts into stemmata, and drew out the results for the nation of the textual content. five in regards to his Archimedean paintings, Heiberg occasionally betrayed indicators of the philologist's occupational ailment - the tendency to rewrite a textual content deemed on subjective grounds to be unworthy. 6 yet he did so much less frequently than his fashionable 7 contemporaries, and never as to detract considerably from the price of his versions. In interpreting textual questions concerning the Archimedean corpus, he tried to use up to attainable facts from the traditional commentators, and in a few circumstances from the medieval translations. it's the following that possibilities abound for brand spanking new paintings, extending, and in a few circumstances superseding, Heiberg's findings. For at his time the supply of the medieval fabrics was once restricted. in recent times Marshall Clagett has accomplished a monstrous severe version of the medieval Latin culture of Archimedes,8 whereas the bibliographical tools for the Arabic culture are in sturdy order due to the paintings of Fuat Sezgin.
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Sample text
It is clear that he knew of the closely related method in Philo's Belopoeica (discussed as PB in chap. 3), 26 I. Ancient Texts on Geometric Problems even if he presents this different method in his own Belopoeica. For instance, both Hero and Philo insert their methods in the context of the same problem, the scaling of catapults of given throw weight. For further remarks on the relation of Hero to Philo, see chap. 3, by notes 5-6. "Interestingly, Eutocius' wording of the Heronian method uses an alternative expression, of its "having the position ZBH;' which differs from HB, but may be considered closer to it than to the reading "let the position be" of HM.
In keeping with the commentator's paraphrastic manner, already noted, some features may be assigned to him: the inversion of ratios in [i], for instance, and the inclusion there of the remark on parallels. The coincidence of Euclidean references in [h], ostensibly linking HE and AJ cannot be considered significant, since this is an obvious place for a source reference, and the two versions actually cite different theorems. At one point HE agrees with the particular reading ofHB, its shorter version of [g]; moreover, the lettering in HE can follow from that in HB merely by transposing Z, H, whereas the agreement of HE with any other version is rather more remote.
Elements VIII 12, IX 4. For further discussion of the Aristotelian passage, see T. L. Heath, Mathematics in Aristotle, pp. 44-47. 32Parallels in the version of Nicomedes provide striking confirmation of this inference; cf. chap. 2. 33See note 11. 1) assigns specific models to Berosus, Aristarchus, Eudoxus (and Apollonius), Scopinas, Parmenion, Theodosius and Andrias, Patrocles, Dionysodorus, and Apollonius. This list is analyzed by S. Gibbs (Greek and Roman Sundials, chap. , p. 63). c. (cf. ). Since Apollonius was active only several decades later, this Parmenion could have transmitted an Apollonian cube duplication only in a writing of his own maturity, when Apollonius would still have been young.