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By D'Ooge, Martin Luther; of Gerasa. Nicomachus; Robbins, Frank Egleston; Karpinski, Louis Charles

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Eratosthenes, of course, makes his appearance in connection with his famous 'sieve' (1. 13), hut there are two other places where with the aid of Theon we can detect a suggestive similarity. This is seen most clearly in the theorem of the' three rules' for deriving the various ratios from equality;' and there was perhaps another kindred matter in which Eratosthenes led the way for Nicomachus. Theon reports See pp. lIsff. I See pp. I12 ff. • See on IntrodlKlion, I. 3- 4; 3. I; 4. 2,3; 14. 2; 23.

15]; Heath, History, vo!. I, p. QC. I. Euclkl, Stclio Canonis, c. 16, p. 161 (Von }an), 1" PwlttNU; Harmonica, p. menU da VorsoMatiier, vol. P, pp. 334-335. c k • 22 NICOMACHUS OF GERASA states what is the peculiar characteristic of each; this is precisely the procedure of Nicomachus in the Introduction. ' Either in the same work or in another, Archytas seems to have written upon certain of the fundamental conceptions of arithmetic; for it is reported that he and Philolaus used the terms' monad' and 'one' indiscriminately, and that he believed the monad to partake of the nature of both odd and even,' and we may note also the passage which Nicomachus quotes in the Introduction, I.

N. t, and on I. 4. • See p. 72, CL Heath, History, vol. n. pp. 238-2-44. • Expositio Rerum Matitematicamm ad ugNfdum Pl4Ionem Utili"m, eel . E. HiDer, Leipzig, 1878 (whose paging is cited). See also J. yrne, Paris, 1892. 1 from UNrY£RSlTY Of MICHIGAN GREEK ARITHMETIC BEFORE NICOMACHUS 37 made some reference to Moderatus of Gades' The book is interesting as an illustration of the methods then in vogue of helping Platonic students in their tasks, and inasmuch as there is evidence that Nicomachus took account of such writings, a comparison of the two authors, even though not wholly conclusive, cannot but be enlightening.

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Introduction to Arithmetic by D'Ooge, Martin Luther; of Gerasa. Nicomachus; Robbins, Frank Egleston; Karpinski, Louis Charles

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