Advanced geometry for high schools : synthetic and analytical (1919)
McDougall, A. H. (Alexander Hiram), 1859-1946 · Toronto : Copp, Clark · leaf 57
n H. P. (b) By inversion, DB : AD = BC : AC.;. DB : DA = DC - DB : DA - DC. ••, by § 39, DB, DC, DA are in H. P. State and prove a converse to this theorem.Gfcli When a range of four points A, C, B, D is suchthat AC : CB = AD : DB, it is called a harmonic range. If any point P be joined to the four… … Fig. 44. V AACP||]ABCE,.. AP : EB = AC : CB. V AADPIHABDF,.. AP : BF = AD : DB. But, by hypothesis, AC :CB = AD : DB./. AP : EB = AP : BF.EB = BF. HARMONIC RANGES AND PENCILS 45 (43) By a proof similar to that of § 42, the followingconverse to the theorem of that article may be shownto be true. If,…
Geometry · Geometry, Analytic
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