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 37
be the centres of two circleswhich are tangent to each other at thepoint Q. Draw the secants BC and DE, ter-minating in the concave arcs BD andEC; draw also BD and EC, and at Qdraw TS tangent to both circles. The angle SQE is equal to QCE(Bk. Ill, Prop. 21 and 18); in like manner the angle TQD is… … Prop. XLIII.—Let an equilateral triangle be inscribed in a circle,and let two of the subtended arcs be bisected by a chord: then showthat the sides of the triangle divide the chord into three equal parts. Demonstration.—Let ABC be an equilateral triangle inscribed ina circle ASBCP, and let P and S…
Geometry
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