. The principles of projective geometry applied to the straight line and conic . CB lies on this line. This result also follows from theproperties of Harmonic Perspective whenS is the centre and .s the axis ofPerspective. Let a, b, c, ... and a, b, c, ... be theranges, in which aa, bb, cc, ... lie on afixed line s. Consider the triangles abcand abc. They are in perspective withs for axis of perspective. Thereforeab. ba, be. cb intersect in a point Swhich lies on o the connector of thevertices. If aa, bb are regarded as two pairsof fixed corresponding rays, which deter-mine the pencils, the poi
. The principles of projective geometry applied to the straight line and conic . CB lies on this line. This result also follows from theproperties of Harmonic Perspective whenS is the centre and .s the axis ofPerspective. Let a, b, c, ... and a, b, c, ... be theranges, in which aa, bb, cc, ... lie on afixed line s. Consider the triangles abcand abc. They are in perspective withs for axis of perspective. Thereforeab. ba, be. cb intersect in a point Swhich lies on o the connector of thevertices. If aa, bb are regarded as two pairsof fixed corresponding rays, which deter-mine the pencils, the point *S is fixedand the variable line be. eb passesthrough this point. This result also follows from theproperties of Harmonic Perspective whens is the axis and *S the centre of Per-spective. Projective Forms Anharmonic 61 35. Projective ranges and pencils. Construction of corresponding elements of projective forms*. Given three pairs of corre-sponding points A and A, B andB, C and C on two bases s and s,to construct the projective rangesdetermined by these Given three pairs of corre-sponding rays a and a, b and b,c and c passing through two ver-tices S and S, to construct theprojective pencils determined bythese corresponding rays.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
