An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page vii
... passing through Two given Points ib . Equation of a Straight Line passing through the Point of Inter- section of Two Given Straight Lines • 13 12 . 13 . 14 . • 15 . Condition that Three Points may lie in the same Straight Line ib ...
... passing through Two given Points ib . Equation of a Straight Line passing through the Point of Inter- section of Two Given Straight Lines • 13 12 . 13 . 14 . • 15 . Condition that Three Points may lie in the same Straight Line ib ...
Page xii
... passing through four given points , cut any straight line in a system of points in involution • 26. Orthogonal Projection 145 ib . ON THE DETERMINATION OF A CONIC FROM FIVE GIVEN GEOMETRI- CAL CONDITIONS . 28 . If five points be given ...
... passing through four given points , cut any straight line in a system of points in involution • 26. Orthogonal Projection 145 ib . ON THE DETERMINATION OF A CONIC FROM FIVE GIVEN GEOMETRI- CAL CONDITIONS . 28 . If five points be given ...
Page 1
... passing through the same point . The triangle formed by these three straight lines is called the triangle of reference , its sides , lines of reference , and the distances of a point from its three sides will be called the trilinear co ...
... passing through the same point . The triangle formed by these three straight lines is called the triangle of reference , its sides , lines of reference , and the distances of a point from its three sides will be called the trilinear co ...
Page 12
... passing through two given points . Let f , g , h ; f ' , g ' , h ' , be the co - ordinates of the two given points , and suppose the equation of the required straight line to be La + MB + Ny = 0 . We must then have Lf + Mg + Nh = 0 ...
... passing through two given points . Let f , g , h ; f ' , g ' , h ' , be the co - ordinates of the two given points , and suppose the equation of the required straight line to be La + MB + Ny = 0 . We must then have Lf + Mg + Nh = 0 ...
Page 13
... passing through their point of intersection , may be represented by an equation of the form la + mB + ny = k ( l'a + m'ß + n'y ) , where k is an arbitrary constant . For this equation is satis- fied when the equations of the given ...
... passing through their point of intersection , may be represented by an equation of the form la + mB + ny = k ( l'a + m'ß + n'y ) , where k is an arbitrary constant . For this equation is satis- fied when the equations of the given ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα