An Introduction to Projective Geometry And Its Applications; An Analytic And Synthetic Treatment

Cover An Introduction to Projective Geometry And Its Applications; An Analytic And Synthetic Treatment
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Prove that in a circular cubic the oval and the ser- pentine appear under the same angle from any point of the curve.
Ex. 5. The extremities of two diameters AiA^ and A^A^ form a square. What is the locus of the points from which both diameters appear under the same angle?
§ 51. The Five Tjrpes of Cubics in the Steinerian Transfor- mation.^ I. Cubic with Oval and Serpentine.
This cubic is obtained when all four points of the funda- mental quadruple are either real or imaginary. As the case ^ Th
...is section has been published in The University of Colorado Studies, Vol. I., No. 4, Feb. 1904.
PROJECTIVE GEOMETRY.
with four real points has so far always been used to illustrate the general properties, we shall now assume an entirely imaginary quadruple determined by a coaxial system of circles with the limiting points P and Q, Fig. 87. On every ray g through an \^3 Fig. 87.
arbitrary fixed point B the circles of this system cut out an invo- lution of points whose double-points X and X' are two points of the cubic associated with the point B in the Steinerian transfor- mation belonging to the given imaginary quadruple.


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