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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1884 Excerpt:...sides containing the right angle, or else the' problem about application of an area." The texts have irepl Tou xuplov rrjs irapaporjs, for which Bretschneider (p. 79, n.) proposes, evidently rightly, irepl Tts Tou xptov irapapoXijs. The text is sometimes translated "on the area of the parabola," which involves a gross anachronism. 2 Plutarch, Quaest. Conv. vin. 2, c. 4. 3 According to Iamblichus (Vita Pyth. c. 18, s. 88) Hippasus was drowned for divulging the knowledge of "the sphere with the twelve pentagons" (i.e. the inscribed ordinate dodecahedron) "for he took the glory as discoverer, whereas everything belonged to Him efocu Si iravra ixdvov) for so they call Pythagoras." 4 See Chasles, p. 477, sqq. This Pythagoraefigura was used through the middle ages, and was regarded even by Paracelsus as a symbol of health. It is the drudenfuss of Goethe's Faust, sc. iii. 6 The oldest authority for this is Vitruvius, ix. pref. 5, 6, 7. It is attested also by Plutarch (supra, n. 1). Diog. L. vin. 11. / / (10) Pythagoras used to say that of all solids the sphere was the most beautiful; of all plane figures, the circle. (Diog. Laert..viII. 19.) (11) The Pythagoreans are siid to have solved the quadrature of the circle. (Iamblichus quoted by Simplicius in Ar. Phys. 185, a, 16. Ed. Brandis, p. 327, b.) (12) The Pythagoreans, as has been already stated (supra p. 70) were largely occupied with the study of proportion, doubtless not in arithmetic only but in geometry1. (13) From the Pythagorean use of 'gnomon' as a designation of those numbers, which, when added to a square number, make a square total, it is evident that the Pythagoreans were accustomed to consider and use the gnomon in geometry/ 92. It will be seen at once that all this...