The Elements of Euclid : viz. the first six books, together with the eleventh and twelfth : the errors, by which Theon, or others, have long ago vitiated these books, are corrected, and some of Euclid's demonstrations are restored : also, the book of Euclid's Data, in like manner corrected (1806)
Euclid, Simson, Robert, 1687-1768, Euclid. Elements. Book 11-12. English. 1806, Euclid. Data. English. 1806, Simson, Robert, 1687-1768. Notes, critical and geometrical. 1806, Simson, Robert, 1687-1768. Elements of plane and spherical trigonometry. 1806 · Philadelphia : Published by Mathew Cary, and sold by J. Conrad & Co., S.F. Bradford, Birch & Small, and Samuel Etheridge, printed by T. & G. Palmer ... · leaf 258
s thecircle ABCD is to any space less than the circle EFGH. In thesame manner jt may be demonstrated, that neither is the squareof FH to the square of BD, as the circle EFGH is to any spaceless than the circle ABCD. Nor is the square of BD to thesquare of FH, as the circle ABCD is to any space… … But as the space f T is to the circle ABCD, so is the circleEFGH to some space, which must be less «* than the circleABCD, because the space T is greater, by hypothesis, than thecircle EFGH. Therefore, as the square of FH is to the square t tot, as in the foregoing- note, at *, it was explained how…
Euclid's Elements · Mathematics, Greek · Geometry
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