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 53
46 KEY. be F; draw the diameter BFG, and on the radius FB, as a diameter,describe a second circle cutting AC, in Dand R; draw BE, DF and EG. The angles BDF and BEG, being in-scribed in semicircles, are right angles,and consequently, the triangles BDF andBEG are similar; hence, BD ±= DE. From Prop.… … Prop. LXIV.—Show that the sum of the squares of the diagonalsof any quadrilateral is equal to the sum of the squares of the foursides of the quadrilateral, increased by four times the square of thedistance between the middle points of the diagonals. Demonstration.—Let ABCD be any quadrilateral, AC…
Geometry
Internet Archive · Library of Congress · Public Domain Mark 1.0. Free to use for anything.
![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-299-194.webp)
