Newcomb, Simon, 1835-1909 · New York, H. Holt and company · leaf 119
em. If any perpendicular ho drawn to theceiitral line of tivo circles, the difference of the squares of thetangents from any one point of this perpendicular ivill be thesame as from every other point of it. Proof. Let PiV^ be any per-pend iculiir to the central lineof the circles C and 6, andP any… … R -r;R - r\ Hence, for the difference of the squares of the tangents, PT^ _ PT^ Z3 i^^ - R^ - (r^ - r). (1) From the right triangles PNG and PNC, we find, in thesame way, R^ - R = NC - NC; whence, from (1), PT^ _ prpn ^ jy-^2 _ j^fjn _ ^^.2 _ ^«) ^^j The second member of this equation has the same…
Geometry, Analytic
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