Selected propositions in geometrical constructions and applications of algebra to geometry. Being a key to the appendix of Davies' Legendre (1875)
Legendre, A. M. (Adrien Marie), 1752-1833, Davies, Charles, 1798-1876 · New York, Chicago [etc.] A.S. Barnes & company · leaf 50
he principle demonstrated in the lastproposition^ deduce from it the truth that the square on the hypothenuseof a right-angled triangle is equal to the sum of the squares on theother two sides. Demonstration.-—Let ABC be a triangle right-angled at A, andlet BQ, AD, and AF be squares described on… … side GH = AE == AB; hence, it is equal to the triangle CAB inall its parts, that is, AH is equal to CB, * and the angle HAG is equal to the angleACB. Since the angle CAG is a rightangle, the sum of the angles HAG andCAT, or the sum of the angles ACB andCAT is equal to a right angle, and…
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-375-258.webp)
