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
signif their boundaries are described in oppo-site senses. Accordmg to the distinc-tion which we have made, an area ispositive or negative according as itsboundary is described counter-clockwiseor clockwise, respectively. From this itfollows further that if the point P de-scribes a closed line on a… … hence = -OBC-OAB+OAC;ABC+CBA =0, CBA =-ABC. The same reasoning may be extended to the determination ofvolumes, which is left to the reader as an exercise. Ex. I. li A, B, C, D Sire four collinear points, prove that BC-AD+CA-BD + AB-CD = o. GENERAL CONSIDERATIONS. ^ 5 Ex. 2. For tlie same points…
Geometry, Projective · Geometry, Analytic
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