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 78
a 9. 3. PROP. X. THEOR. ONE circumference of a circle cannot cut anotherin more than two points. If it be possible, let the circumfe-rence FAB cut the circumferenceDEF in more than two points, viz.in B, G, F; take the centre K of thecircle ABC, and join KB, KG, KF:and because within the circle… … OF EUCLID. 77 the centre of the circle DEF: but K is also the centre of the Book III.circle ABC; therefore the same point is the centre of two cir ^ .r-mjcles that cut one another, which is impossible. Therefore one b5. 3.circumference of a circle cannot cut another in more than twopoints. Q. E. D.…
Euclid's Elements · Mathematics, Greek · Geometry
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![An illustration from Nicolai Copernici Torinensis De reuolutionibus orbium coelestium, libri VI : Habes in hoc opere iam recens nato, & aedito, studiose lector, motus stellarum, tam fixarum, quàm erraticarum, cum ex ueteribus, tum etiam ex recentibus obseruationibus restitutos: & nouis insuper ac admirabilibus hypothesibus ornatos. Habes etiam tabulas expeditissimas, ex quibus eosdem ad quoduis tempus quàm facillime caculare poteris. Igitur eme, lege, fruere. [Line in Greek] (1543)](https://img.insideoutlibrary.com/img/200/ia-nicolaicopernici00cope-297-191.webp)
