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 21
ons above given are of great importance in thetheory of transversals. They are particular cases of moregeneral propositions, which shall be given in the sequel. These Lemmas being premised, we shall now explain theharmonic properties of a triangle. Let three right lines AA, BB, CC, be drawn (as in… … the figure so formed are cut harmonically, and, 2°, the pointsA, B, C, are in one right line. 1°. By the foregoing LemmasBA : AC : : BA : CA; that is,BA is cut harmonically. A similarproof applies to BC and AB. Again,if AA be joined, as BA is cut har-monically, so also is CA (Art. 7);and in like…
Geometry -- Problems, exercises, etc · Geometry
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