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By James Gow

James Gow's a quick historical past of Greek arithmetic (1884) supplied the 1st complete account of the topic on hand in English, and it this day continues to be a transparent and thorough advisor to early mathematics and geometry. starting with the origins of the numerical method and continuing in the course of the theorems of Pythagoras, Euclid, Archimedes and so forth, the quick heritage deals in-depth research and invaluable translations of person texts in addition to a wide ancient assessment of the improvement of arithmetic. elements I and II trouble Greek mathematics, together with the beginning of alphabetic numerals and the nomenclature for operations; half III constitutes a whole heritage of Greek geometry, from its earliest precursors in Egypt and Babylon via to the concepts of the Ionic, Sophistic, and educational colleges and their fans. specific recognition is given to Pythagorus, Euclid, Archimedes, and Ptolemy, yet a number of lesser-known thinkers obtain deserved realization in addition.

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38. 2 Thus Aristoxenus (apud Stob. Eel. Phys. I. 19. c. 2 ad initium) says that Pythagoras first raised a'/xffjUT/TiKi;'above the needs of merchants,' with which comp. Plato, Rep. 525 c. 3 Metaph. n . 2, 26. 4 Cf. Euclid vn. with Plato, Theaet. 147, 148, or Hep. 546 o. GREEK CALCULATION. Logisticd. 23 tively, the same subjectmatter in Plato's time, as afterwards and since he uses these terms casually, with no hint that they were novel, we may infer that the distinction between them dates from a very early time in the history of Greek science and philosophy1.

317—323. 8 It is doubtful whether the cipher was at first used by the Western Arabs among the. Gobar-signs. ' 3 This was Cantor's opinion, Math. Beitrage, p. , but in Vorlesungen, p. 610 and elsewhere he follows Woepcke (see next note). 38 GREEK CALCULATION. Logistica. signs from India or elsewhere and given them to the Italians on the one hand, the Arabs on the other1: and lastly whether the passage in Boethius is not a forgery2. It is sufficient here to repeat, what is admitted by all parties that there is no evidence in any Greek author that these apices were known to the Greeks : that there is also no evidence whatever that the Greeks ever used any written numerical signs with the abacus: that the MSS.

PAET II. GREEK ARITHMETIC. CHAPTER III. GREEK CALCULATION. Logistica. 17. C. 50). That it did so, however, is rendered pretty certain by many circumstances. It is probable, in the first place, that the Pythagoreans would have required some variety of terms to distinguish the exercises of schoolboys from their own researches into the genera and species of numbers8. In Aristotle3 a distinction, analogous to that between the kinds of arithmetic, is drawn between yecoBaiffia, the practical art of land-surveying, and the philosophical ryecofieTpia.

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