An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... Circle • 7 . Equation of the Conic touching the Three Sides of the Tri- angle of Reference 39 • • 8 . Position of the Centre . Condition for a Parabola • 9 . Condition of Tangency ++ 20 ib . 40 42 • 10 . Equations of the Four Circles ...
... Circle • 7 . Equation of the Conic touching the Three Sides of the Tri- angle of Reference 39 • • 8 . Position of the Centre . Condition for a Parabola • 9 . Condition of Tangency ++ 20 ib . 40 42 • 10 . Equations of the Four Circles ...
Page ix
... external Point · 11 . Co - ordinates of the Centre 12 . Equation of the Asymptotes • 13. Condition for a Rectangular Hyperbola 14. Conditions for a Circle . 888 * 8 80 82 83 84 86 ARTS . 15 . 16 . 17 . 18 . CONTENTS . ix.
... external Point · 11 . Co - ordinates of the Centre 12 . Equation of the Asymptotes • 13. Condition for a Rectangular Hyperbola 14. Conditions for a Circle . 888 * 8 80 82 83 84 86 ARTS . 15 . 16 . 17 . 18 . CONTENTS . ix.
Page x
... Circles pass through the same two points at infinity All Conics , similar and similarly situated to each other , in ... Circle 92 • 20 . Locus of the intersection of two Tangents at right angles to one another . Directrix of a Parabola ...
... Circles pass through the same two points at infinity All Conics , similar and similarly situated to each other , in ... Circle 92 • 20 . Locus of the intersection of two Tangents at right angles to one another . Directrix of a Parabola ...
Page xi
... Circle ib . 118 23 . Reciprocation with respect to a Point 119 • 24 . The three circles described on the diagonals of a complete quadrilateral as diameters have a common radical axis ib . Foci of a quadrilateral ib . · • 25 ...
... Circle ib . 118 23 . Reciprocation with respect to a Point 119 • 24 . The three circles described on the diagonals of a complete quadrilateral as diameters have a common radical axis ib . Foci of a quadrilateral ib . · • 25 ...
Page xii
... circles : Projection of the foci and directrices of a Conic The anharmonic ratio of any pencil or range is unaltered by projection : • Any two lines , which make an angle A with each other , form with the lines joining the circular ...
... circles : Projection of the foci and directrices of a Conic The anharmonic ratio of any pencil or range is unaltered by projection : • Any two lines , which make an angle A with each other , form with the lines joining the circular ...
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Common terms and phrases
angular points anharmonic ratio asymptotes auxiliary conic b₁ b₂ C₁ centre Chap chord co-ordinates coefficients common tangents conic section determinant directrix find the equation fixed point fixed straight line follows four points given conic given point given straight line given triangle Hence investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides parabola Pascal's Theorem perpendicular point f points at infinity points of contact points of intersection PQRS prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree shewn similar and similarly sin POS tangents drawn term a,b,c theorem three points three straight lines triangle of reference ua² uf+w'g+v'h ux² V'ca va² Vb² vß² W'ab whence wy² λα