The Teaching of Geometry

by David Eugene Smith

[76] For a very full discussion of these four definitions see Heath's "Euclid," Vol. II, p. 116, and authorities there cited.

[77] These two and several which follow are from Stark, loc. cit.

[78] The author has a beautiful ivory specimen of the Sixteenth century.

[79] See, for example, G. B. Kaye, "The Source of Hindu Mathematics," in the Journal of the Royal Asiatic Society, July, 1910.

[80] An interesting Japanese proof of this general character may be seen in Y. Mikami, "Mathematical Papers from the Far East," p. 127, Leipzig, 1910.

[81] Special recognition of indebtedness to H. A. Naber's "Das Theorem des Pythagoras" (Haarlem, 1908), Heath's "Euclid," Gow's "History of Greek Mathematics," and Cantor's "Geschichte" is due in connection with the Pythagorean Theorem.

[82] The rule was so ill understood that Bhaskara (twelfth century) said that Brahmagupta was a "blundering devil" for giving it ("Lilavati," § 172).

[83] Bosanquet and Sayre, "The Babylonian Astronomy," Monthly Notices of the Royal Asiatic Society, Vol. XL, p. 108.

[84] This and the three illustrations following are from Kolb, loc. cit.

[85] This was in five colors of marble.