. The principles of projective geometry applied to the straight line and conic . ars from A on BC, from B on CA, and from C on AB are alsoconcurrent. 80 Principles of Projective Geometry /3, /3, y, y arc equal. In the figure, the angles marked n, the Sine form of Cevas Theorem,the condition that the perpendicularsthrough J5(7 should be concurrent issin a sin /3 sin y _sin a sin 0 sin yThis is also the condition that theperpendiculars through ABC shouldbe concurrent. (15) The triangle PQR is inscribedin the triangle ABC and is in per-spective with it: and the triangleXYZ is circumscribed a
. The principles of projective geometry applied to the straight line and conic . ars from A on BC, from B on CA, and from C on AB are alsoconcurrent. 80 Principles of Projective Geometry /3, /3, y, y arc equal. In the figure, the angles marked n, the Sine form of Cevas Theorem,the condition that the perpendicularsthrough J5(7 should be concurrent issin a sin /3 sin y _sin a sin 0 sin yThis is also the condition that theperpendiculars through ABC shouldbe concurrent. (15) The triangle PQR is inscribedin the triangle ABC and is in per-spective with it: and the triangleXYZ is circumscribed about thetriangle ABC and is in perspectivewith it. Show that the triangles PQR,XYZ axe in perspective. Use Sine form of Cevas Theorem. (16) ABC is a triangle and 0 a point within it. Through ABC and within the triangle lines are drawn makingwith AB, BC, CA angles equal respectively to OAC, DBA, OCB ; prove that theselines meet at a point whose distances from the sides of the triangle are inverselyproportional to the corrasponding distances of Sine form of Cevas CHAPTER YII HARMONIC FORMS :—HARMONIC PROPERTY OF THE QUADRANGLEAND QUADRILATERAL. HARMONIC PERSPECTIVE. 45. Harmonic Ranges and Pencils. If two harmonic rouges of fourpoints have a self-correspondingpoint at the point of intersection ofthe bases, then the ranges have twocentres of perspective. If two harmonic pencils of fourrays have a self-corresponding rayin the line joining their vertices,then the pencils have tiuo axes ofperspective.
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometryprojective
