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 36
he four angles of anyquadrilateral intersect in four points, all of which lie on the circum-ference of the same circle. Demonstration—Let ABCD be any quadrilateral, and let AR,BR, CP and DP, be the bisectricesof its four angles. Draw PR. The angle PSR, or its equal ASD,is equal to one-half the sum… … 30 KEY. sum of the four angles of the given quadrilateral, that is, to two rightangles. Consequently, from the converse of Prop. 18, Bk. Ill, Cor. 4,the quadrilateral SPQR can be inscribed in a circle, which was to beproved. Prop. XLII.—If two circles touch each other externally, and iftwo common…
Geometry
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