Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 383
sitions into their correlatives. Theorem. If three fixed points not in the same straightline le given, the position of a line is completely determinedwhen the mutual ratios of its distances from these points aregiven. Proof. Let the three fixed points be A, B and C. Let it be given that the ratio… … C B be tlie perpendiculars from A and G upon the line L» Wethen have, by hypothesis, Aa : Cc :=^m : n. Hence, by simil?,r triangles. Ay \ Cy =. m: n. This last relation completely fixes the position of thepoint y (§ 279), which therefore remains the same for all lineswhich satisfy the given…
Geometry, Analytic
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