By Wilbur Richard Knorr (auth.)
For textual stories in relation to the traditional mathematical corpus the efforts by means of the Danish philologist, 1. L. Heiberg (1854-1928), are specifically major. starting together with his doctoral dissertation, Quaestiones Archimedeae (Copen hagen, 1879), Heiberg produced an striking sequence of versions and important reviews that stay the root of scholarship on Greek mathematical four technology. For comprehensiveness and accuracy, his variations are exemplary. In his textual experiences, as additionally within the prolegomena to his variants, he conscientiously defined the extant facts, geared up the manuscripts into stemmata, and drew out the results for the kingdom of the textual content. five with reference 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 favourite 7 contemporaries, and never as to detract considerably from the price of his variants. In studying textual questions pertaining to 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 new paintings, extending, and in a few situations superseding, Heiberg's findings. For at his time the provision of the medieval fabrics used to be constrained. in recent times Marshall Clagett has accomplished a sizeable serious version of the medieval Latin culture of Archimedes,8 whereas the bibliographical tools for the Arabic culture are in solid order because of the paintings of Fuat Sezgin.
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Extra resources for Textual Studies in Ancient and Medieval Geometry
Example text
I, p. 270. I suspect that the circumlocution in these instances with Proclus and Pappus may indicate the author's use of a secondary source. But even if that is the case, it need not detract from the accuracy of the citation, as Pappus' quotation of Hero reveals. " SThe term deixis (from deiknynai, to "show" or "prove") ought to mean "proof;' "specimen;' or "exhibition" (cf. ). But Pappus' statement seems to have a more specific geometric meaning, that is, something displayed or presented in a geometric manner, hence, a construction.
Pp. 24; Pappus, op. cit. (Book IV), pp. 25; cf. also Pappus, op. cit. (Book III), pp. 24. The three versions are in literal agreement. 6PappUS, op. cit. (IV), p. 15-23. 7PappUS, op. cit. (IV), p. 26-32. BCf. Diocles' prop. 10, ed. Toomer, pp. 96-97 (lines 205-206): having found by means of two parabolas (cf. the second method of Menaechmus, in chap. 5) the two mean proportionals LN, LHbetween the given lines A, B, Diocles observes that A3:ND = A:B; thus if A = 2B, A3 = 2ND, whence A is the side of the double cube.
IV), p. 15-23. 7PappUS, op. cit. (IV), p. 26-32. BCf. Diocles' prop. 10, ed. Toomer, pp. 96-97 (lines 205-206): having found by means of two parabolas (cf. the second method of Menaechmus, in chap. 5) the two mean proportionals LN, LHbetween the given lines A, B, Diocles observes that A3:ND = A:B; thus if A = 2B, A3 = 2ND, whence A is the side of the double cube. ) Again, in his prop. , pp. 100-103), Diocles infers the cube multiplication from the finding of the two means. See also chap. 5. 90 n Hippocrates of Chios, see my Ancient Tradition, chap.