Advanced geometry for high schools : synthetic and analytical (1919)
McDougall, A. H. (Alexander Hiram), 1859-1946 · Toronto : Copp, Clark · leaf 17
. EA. By multiplication, and division by DO, OA and BC,AF . BD . CE = FB . DC . EA. (For another proof of this theorem see O.H. S.Geometry, § 122, Exercises 12 and 14.) (Historical Not*.—Giovanni Ceva, an Italian engineer, died in 1734 A.D.) 4 SYNTHETIC GEOMETRY 4. Converse of Cevas Theorem:—If, in… … Fia. 7. Fig. 8. Draw BE, CF and let them cut at O. Join AO andlet it cut BC at G. •/ AG, BE, CF are concurrent, .. AF . BG . CE = FB . GC . EA, (§ 3.) But AF. BD . CE - FB . DC . EA, by hypothesis. ,. .,. BG GC. .*., dividing, =r= = =—? , o> BD DC Dr, by alternation, ^ = ^. .*. G coincides with…
Geometry · Geometry, Analytic
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