. The principles of projective geometry applied to the straight line and conic . 48. Conjugate Points—Pole and Polar. Conjugate points with respect to twogiven straight lines are such that theirconnector is cut harmonically by thepair of lines. Thus, in the figure if {ABGD)=-\G and D are conjugates with respect toa and b. Conjugate lines with respect to twogiven points are such that they areharmonic conjugates of the lines joiningtheir point of intersection to the givenpoints. Thus, in the figure if {abed) = — 1a and h are conjugates with respect toC and Hence, it follows that if through a
. The principles of projective geometry applied to the straight line and conic . 48. Conjugate Points—Pole and Polar. Conjugate points with respect to twogiven straight lines are such that theirconnector is cut harmonically by thepair of lines. Thus, in the figure if {ABGD)=-\G and D are conjugates with respect toa and b. Conjugate lines with respect to twogiven points are such that they areharmonic conjugates of the lines joiningtheir point of intersection to the givenpoints. Thus, in the figure if {abed) = — 1a and h are conjugates with respect toC and Hence, it follows that if through anyfixed point D a variable transversal bedrawn to cut two given lines in A andB and a point C be taken on the linesuch that ABCD is harmonic (C beinga conjugate of /)), then the locus of C isa straight line c passing through thepoint of intersection of the given lines. Hence, it follows that if on anyfixed line h a variable point B is takenand lines c and d are drawn to thefixed points C and D and a line a istaken such that the pencil {ahcd) isharmonic (a being the conjugate of 6),then a always passes through a fixedpoint A, which is on the line joining Projective Forms Harmonic 85 The line c is called the polar of D with the given points. The point A is called respect to the given lines. the joo^e of b with respect to the pair of given points. This line is the locus of the con- This point is the envelope of the jugates of D. conjugates of b. The point D is called the pole of c The line b is called the polar of A with respect to the pair of lines. wi
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
