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15. but FIG. 2. FIG. 3. Prop. 17. but It is worth while to show how these results are proved. Prop. 13. (1) In Fig. 2 it is clear that The triangles LON, CLN being similar, therefore Hence therefore [If be developed as a continued fraction, we easily obtain , which is in fact ] (2) But therefore Again and therefore, ex aequali, (3) Since the same cone comprehends the sun and the moon, the triangle BUV (Fig. 1) and the triangle BLN (Fig. 2) are similar, and But therefore, a fortiori, And But therefore, ex aequali, Prop.

Eutocius (fl. about A. D. 500) only wrote commentaries on these works and on the plane Equilibriums, and he does not seem even to have been acquainted with the Quadrature of the parabola or the work On Spirals, although these have survived. Isidorus of Miletus revised the commentaries of Eutocius on the Measurement of a Circle and the two Books On the Sphere and Cylinder, and it would seem to have been in the school of Isidorus that these treatises were turned fro their original Doric into the ordinary language, with alterations designed to make them more intelligible to elementary pupils.

Solution of the of Archimedes, On Spirals, Prop. 8, by means of conics Book V. Preface on the sagacity of Bees Section (1). Isoperimetry after Zenodorus Section (2). Comparison of volumes of solids having their surfaces equal. Case of sphere Section (3). Digression on semi-regular solids of Archimedes Section (4). Propositions on the lines of Archimedes, On the Sphere and Cylinder Section (5). Of regular solids with surfaces equal, that is greater which has more faces Book VI Problem arising out of Euclid’s Optics Book VII.

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