Osgood, William F. (William Fogg), 1864-1943, Graustein, William Caspar, 1888-1941, joint author · New York, The Macmillan company · leaf 177
the criticism that conceivablywe might have a-a = 0, b-b = 0, and then the equation u — v = 0 would not represent a straightline. But in that case the circles would be concentric, and we have demanded that they cut each other. Example 2. We can now proyethe following theorem : Given threecircles,… … iv = a2 + if + ax + by -f c = 0. CERTAIN GENERAL METHODS 171 Then the equations of the three common chords can be writtenin the form: u — v = 0, v — w = 0, w — u — 0. Let Ux = V — W, Vx = W — U, Wx = U — V. We observe that the equation, (8) Ux 4- Vx 4- Wx = 0 or — wx = ux + v1} holds identically…
Geometry, Analytic
Internet Archive · Library of Congress · Public Domain Mark 1.0. Free to use for anything.
