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 17
=-OAC. Two areas have therefore to be considered as of opposite signif their boundaries are described in oppo-site senses. According to the distinc-tion which we have made, an area ispositive or negative according as itsboundary is described counter-clockwiseor clockwise, respectively. From this… … Fig. 2. where OCA is negative. On the other hand CBA=OCB+ OBA + OAC = -OBC-OAB+OAC; hence ABC+CBA=o, CBA = - ABC. The same reasoning may be extended to the determination ofvolumes, which is left to the reader as an exercise. Ex. 1. If A, B, C, D are four collinear points, prove that BC-AD+CA BD +…
Geometry, Projective · Geometry, Analytic
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