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 40
, at its extremity;hence, the circle whose radius is OA, is tangent to both sides of thegiven angle; it is therefore the required circle. Prop. XLVII.—Show that the middle points of the sides of anyquadrilateral are the vertices of an inscribed parallelogram. Demonstration.—Let ABCD be any… … 34 KEY. Hence, from Bk. IV, Prop. 16, PQ is parallel to DB. In like mannerit may be shown that RS is parallel to DB: hence, PQ and SR areparallel to each other. The lines QR and PS are parallel to AC, forsimilar reasons; hence, they are parallel to each other, and conse-quently, the figure PQRS is…
Geometry
Internet Archive · Library of Congress · Public Domain Mark 1.0. Free to use for anything.
![An illustration from Works. Popular edition.] 2 series (1886)](https://img.insideoutlibrary.com/img/200/bl-bl_003191336_9-300-1.webp)
