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 49
, ST be a chord of a circle,all angles subtended by this chordare equal, i.e., ZASC= Z.ATC,ZBSC= ZBTC, etc. Hence the pencils at S and T are projective.Connecting any point in space withall points of the circle, a cone isobtained. Cutting this cone by anyplane and passing planes through the vertex… … Fig. 12. 1 Introduced by Poncelet, loc. cit., p. 94. PENCILS AND RANGES. 37 therefore a curve of the second order; in this case a conic. It willbe seen later on that all curves of the second order are identicalwith all conies. To show how a circle may be described as an envelope, assumefirst the…
Geometry, Projective · Geometry, Analytic
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