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By D'Ooge, Martin Luther; of Gerasa. Nicomachus; Robbins, Frank Egleston; Karpinski, Louis Charles
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I , pp. 212- 216. I Cr. Int,odUltiott, 11 . 24. 6 and Plato, Tif1UUus, 32 A. a Cl. Inlroduction , 11. 6. u's, 817 E, See Bumet, op. lil" pp. 224 ff. I Plato 's arithmetic includes also logistic. Other I'w(iences mentioned are those of weighing and measuring, 1'I'1'IIT"'~ and ptTp«;" besides those spoken of by Nicomachus. ; Gor,ias, 453 E; /lippias Minor, 361 8'. i PoliJu:us, 284 E; TMatltlus, 198 A 8'. c k '4 NICOMACHUS OF GERASA is omitted, but astronomy is distinguished, as by Nicomachus, as a science that treats of bodies in motion.
H~. Al; cf. Porphyry, Vita Pythagorico, 48; Simplicius, Physica, p. 50, B; Stobaeus, EcloglU I, Prooemium, 8-9 (vol. I, p. 21, cd. Wachsmuth-Hense). 1 from UNrY£RSlTY Of MICHIGAN 34 NICOMACHUS OF GERASA of the monad and one influenced a chapter of Theon of Smyrna, and, ' like Nicomachus, he probably discussed ten forms of proportions' Although little more is known of the scope and nature of the Pythagorean Lectures, it is at any rate clear that lvloderatus occupied himself with the themes of the a,s arithmetica and may well have produced an ars of his own.
2 Cl. Proclus, In Timaeum (Diehl) , vol. H, p. raJ 4, ol JlfWrtpclf. joyw, ~ Mo3tpA'TOtIJ o:al d TU'tJ 4AAOi ~TOi, lI'tp/: ~ """ '1pet... Td. v.. Lp' ~ ul 6 IIAtbw.. ,v, nt.. ¥-vxipo , O:'1A. This leads to the inferences, first, that Moderatus was actively interested in arithmetical subjects in much the same way as Nicomachus, and second , since their names are SO coupled, that he discussed, like Nicomachus, ten forms of proportion. 1 from UNrY£RSlTY Of MICHIGAN GREEK ARITHMETIC BEFORE NICOMACHUS 35 Aristotle, Eratosthenes, Plato and Philolaus, besides Pythagoras, to whom he refers in a general way.