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 84
ken as bases, and in a similar manner it may beproved for any other pair of the three diagonals AO, BC, BC. 2°. The middle points of the three diagonals of a completequadrilateral are in oneright line. Let IFGM, IEGL,FEML be the componentquadrilaterals, and IG,FM, LE the three diago-nals of the… … M 74 ADDITIONAL EXAMPLES ON TRANSVERSALS. 11) BL is cut harmonically) the points A, D, F are in one rightline. Now let X, Y, Z be the middle points of LE, FM, IG, andwe have (Art. 3) BX : EX : : EX : AX ; therefore (conversionand alternation) BE : AE : : BX : EX, whence, BE2 : AE2 : : BX2 : EX2 : :…
Geometry -- Problems, exercises, etc · Geometry
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