An introduction to projective geometry and its applications; an analytic and synthetic treatment (1905)
Emch, Arnold, b. 1871 · New York, J. Wiley & sons; London, Chapman & Hall, limited · leaf 68
is found (V) xf = x y, / = ky. These are the equations of affinity. Conversely, if a transforma-tion (VI) by COLLINE ATI ON. 55 is given, it may always be represented in the form (V), by puttingb = k and = — m. A characteristic property of this trans-formation is that closed curves are transformed… … Fig. of AB and AB, BC and BC, CA and CA by C^A,, Blt respect-ively. Now in Fig. 22 (1) aABC = a4CA+ aBAJO^ aCBxA„ (2) aABC=aAC1B1+ aBA.C^ aCB.A,; but as the corresponding triangles on the left side have equalbases and altitudes of constant ratio k, we have AACiB^k- AiCA; ABAxCx = k- aBA£x\ACB^^k-…
Geometry, Projective · Geometry, Analytic
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