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

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Another fragment of Arcbytas, dealing with the proportions, is likewise notable for its scientific accuracy of expression. This is quoted by Porphyry' as follows: "Archytas, in explaining the means, wrote the following: 'There are in music three means; the first is the arithmetical mean, the second is the geometrical, and the third is the subcontrary mean which is called harmonica!. The mean is arithmetical when the three terms are in proportion according to the following excess: the quantity by which the first exceeds the second is the same precisely as that by which the second exceeds the third.

Bilschrif' fur iigyptisclu Sprache. vol. XXXVIII, pp. 135-140, and vol. XL, pp. 65-66. 1 from UNrY£RSlTY Of MICHIGAN SOURCES OF GREEK MATHEMATICS IS sion to Greece from Babylon, but no Babylonian record confirming the statement has yet been found. The squares and cubes of numbers also received particular attention in Babylon, and tables of squares and cubes have been found. In Egypt the relation 3' + 4' = 5' appears to have been used in the laying out of right angles by means of a stretched rope.

168 B j Parmu,idrs, 140 C, '50 D, 151 JI. ICharmidrs, 168 Bj PhMdo, 105 Ai Mtn

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