. The principles of projective geometry applied to the straight line and conic . Let ABGD be the quadrangle,and E, F, G its diagonal pointstriangle. Let GE meet DA andGB in E and E. Let abed be the quadrilateral,and e, f, g its diagonal the lines joining ge to da. andcb be e and e. Projective Forms Hmmonic 83 Then projecting from E,{FECB) = {FEDA).Projecting from G, {FECB) = {FEAD).Therefore (FEDA) = (FEAD).Therefore A and D are harmonicconjugates of F and E. Given a range of three points toconstruct graphically the harmonicconjugate of any one ivith respectto the other tiuo. Then
. The principles of projective geometry applied to the straight line and conic . Let ABGD be the quadrangle,and E, F, G its diagonal pointstriangle. Let GE meet DA andGB in E and E. Let abed be the quadrilateral,and e, f, g its diagonal the lines joining ge to da. andcb be e and e. Projective Forms Hmmonic 83 Then projecting from E,{FECB) = {FEDA).Projecting from G, {FECB) = {FEAD).Therefore (FEDA) = (FEAD).Therefore A and D are harmonicconjugates of F and E. Given a range of three points toconstruct graphically the harmonicconjugate of any one ivith respectto the other tiuo. Then taking sections on e, {fech) = (feda).Taking sections on g,(fecb)==(fead).Therefore (feda) = (fead).Therefore a and d are harmonicconjugates of/and e. Given a pencil of three rays toconstruct graphically the harmonicconjugate of any one luith respect tothe other two.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
