By James Gow

James Gow's a brief historical past of Greek arithmetic (1884) supplied the 1st complete account of the topic to be had in English, and it at the present time is still a transparent and thorough consultant to early mathematics and geometry. starting with the origins of the numerical approach and continuing during the theorems of Pythagoras, Euclid, Archimedes etc, the fast heritage deals in-depth research and helpful translations of person texts in addition to a vast historic review of the improvement of arithmetic. elements I and II situation Greek mathematics, together with the beginning of alphabetic numerals and the nomenclature for operations; half III constitutes an entire heritage of Greek geometry, from its earliest precursors in Egypt and Babylon via to the suggestions of the Ionic, Sophistic, and educational colleges and their fans. specific realization is given to Pythagorus, Euclid, Archimedes, and Ptolemy, yet a bunch of lesser-known thinkers obtain deserved recognition to boot.

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I. p. 477, also by N. Caussinus in his Eloquentia Sacra et Humana, Bk. ix. ch. 8, pp. 565—568 (Paris, 1636), and elsewhere. See Boediger's article in Jahresb. der Deutsch. Morgenldnd. Gesellscli. for 1845, pp. 111—129. Boediger, who has been followed by many writers, supposed that Nicolaus Smyrnaeus was of the 7th or 8th century, but Dr Gtinther (Vermischte Untersueh. zur Geseh. der Math. 1876) has lately discovered him to be a contemporary of Manuel Moschopulus, a much later writer. GRKEK CALCULATION1.

THE preceding pages contain probably all the meagre facts from which it is still possible to discern how the Greeks came by their arithmetical nomenclature, both for whole numbers and for fractions. The subsequent progress of calculation, that is to say, the further use of the elementary processes, depends on many conditions which cannot well be satisfied without a neat and comprehensive visible symbolism. This boon the Greeks never possessed. Yet even without it a retentive memory and a clear logical faculty would suffice for the discovery of many important rules, such for instance as that, in a proportion, the product of the means is equal to the product of the extremes.

GREEK CALCULATION. Logistica. 35 the 10 spaces at one part of the board contained stones representing values from a talent to an obol, in the order TFXF'HF1 A Phi: and the 5 spaces at the other part of the board contained: stones representing values from an obol to a chalcus, in the order |, C, T, X. The transverse line would serve to distinguish two sums which were to be added together or subtracted one from the other: or again, as in the Roman system, the numbers compounded with p might have been placed above this line.

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