An elementary treatise on modern pure geometry (1893)
Lachlan, Robert · London, New York, Macmillan and Co. · leaf 128
ations hold it may be provedthat the lines A A, BB, CC are concurrent; that is, the trianglesABC, ABC are in perspective. 179. When two triangles ABC, ABC are in perspective, theproduct of the ratios {AV : Ac), (Be: Ba), (Ca: Ch), is equal to unity, where a, b, c denote the sides of the… … But since A, Y, Z are colliDear, BJ£ CY AZ_GXAYBZ~- „ Ba Gb Ac , ^ m-AF-Bc = ^ ,, , . Ab Be Ca , that IS, ^-• D--r^ = l- Ac Ba Gb Conversely, when this relation holds, it follows that A, F, Zare collinear, and therefore that the triangles are in perspective. 180. Ex. 1. If any circle be drawn…
Geometry
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