Principles of modern geometry, with numerious applications to plane and spherical figures; and an appendix, containing questions for exercise. Intended chiefly for the use of junior students (1862)
Mulcahy, John, 1810?-1853 · Dublin Hodges, Smith · leaf 18
; and,therefore, by similartriangles, AO : CL : :AO:KC. Hence KG= CL, and consequent-ly, KC= CL; whence it readily follows that AD : CD : :AB : BC; that is, the line AD is cut harmonically. A similar proof shews that if A be taken on the production ofAO, as for instance at A, a line such as AB is… … 8 TRANSVERSALS. speaking, however (considering a right line as infinite), thesewith the original constitute one and the same pencil. If BD coincide with KL, the point A is at an infinite dis-tance, and, therefore, since KL is bisected, in this case also wehave (Art. 3) the transversal AD cut…
Geometry -- Problems, exercises, etc · Geometry
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