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
y, m y = ky. These are the equations of afhnity. Conversely, if a transforma-tion 0!/ =x+ay, y ^hy (VI) COLLIN RATION. 55 is given, it may always be represented in the form (V), by putting b = k and -— = —w. A characteristic property of this trans-a formation is that closed curves are transformed… … Fig. 22. of AB and AB, BC and BC, CA and CA by C^,A,, B„ respect-ively. Now in Fig. 22 (i) aABC= aAC,B,+ aBA,C,+ aCB.A,, (2) aABC=aAC,B,+ aBA,C,+ aCB.A,; but as the corresponding triangles on the left side have equalbases and altitudes of constant ratio k, we have AAC,B, = k- aAC^B,; ABA^C, = k-…
Geometry, Projective · Geometry, Analytic
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