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 39
cle that shall be tangent to both sides of that angle. Solution.—Let P be the given point and ABC the given angle. Draw the bisectrix BO, of thegiven angle, and also the line BP;from any point Q, of BO, draw QRperpendicular to AB, and from Q,as a centre, and with a radius QR,draw the arc RS,… … PROPOSITIONS FROM LEGEKDRE. 33 The triangles BSQ and BPO have the angle at B common, andsince QS is parallel to OP, the angles BQS and BOP are equal, as arealso the angles BSQ and BPO; hence, the triangles are similar(Bk. IV, Prop, 18), and consequently, their corresponding sides areproportional.…
Geometry
Internet Archive · Library of Congress · Public Domain Mark 1.0. Free to use for anything.
