. The principles of projective geometry applied to the straight line and conic . Take any point G not on the base, and on OG, where 0 is the centre,take a point H such that OG. OH equals the constant of the involution,H and G being on the same or on opposite sides of 0 according as theconstant is positive or negative. If A be any point on the base, thecircle through AGH will meet the base in A the point conjugate to A,for OA . OA = OH. OG = the constant of the involution. When the constant of the involution is positive a tajigent OT canbe drawn to the circle and the double points L and M are a
. The principles of projective geometry applied to the straight line and conic . Take any point G not on the base, and on OG, where 0 is the centre,take a point H such that OG. OH equals the constant of the involution,H and G being on the same or on opposite sides of 0 according as theconstant is positive or negative. If A be any point on the base, thecircle through AGH will meet the base in A the point conjugate to A,for OA . OA = OH. OG = the constant of the involution. When the constant of the involution is positive a tajigent OT canbe drawn to the circle and the double points L and M are at distancesOT from 0. When the constant of the involution is negative, OG and OH canbe taken equally distant from 0 on the perpendicular through 0 to thebase and in this case every pair of conjugate points A and A subtenda right angle at G and H. The following illuistriites the difference between an involution with real doublepoints and one with imaginary double Let the double points if and L be real.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
