An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
From inside the book
Results 1-5 of 24
Page vii
... parallel to one another . Line at Infinity Equation of a Straight Line , drawn through a given Point , parallel to a given Straight Line 14 16 · · • 17 16 . Inclination of a Straight Line to a side of the Triangle of Reference 18 17 ...
... parallel to one another . Line at Infinity Equation of a Straight Line , drawn through a given Point , parallel to a given Straight Line 14 16 · · • 17 16 . Inclination of a Straight Line to a side of the Triangle of Reference 18 17 ...
Page 14
... parallel to one another . Let the equations of the two straight lines be lx + mB + ny = 0 ..... l'a + m'B + n'y 0 .............. - ... ..... . ( 1 ) , ( 2 ) . Let ( f , g , h ) ( a , B , y ) be the co - ordinates of any two points in ...
... parallel to one another . Let the equations of the two straight lines be lx + mB + ny = 0 ..... l'a + m'B + n'y 0 .............. - ... ..... . ( 1 ) , ( 2 ) . Let ( f , g , h ) ( a , B , y ) be the co - ordinates of any two points in ...
Page 17
... parallel to a given straight line . Let ( l , m , n ) be the given straight line , ( f , g , h ) the given point , then the equation of the required straight line will be la + mB + ny If + mg + nh = aa + bB + cy af + bg + ch ' For this ...
... parallel to a given straight line . Let ( l , m , n ) be the given straight line , ( f , g , h ) the given point , then the equation of the required straight line will be la + mB + ny If + mg + nh = aa + bB + cy af + bg + ch ' For this ...
Page 18
... parallel to ( l , m , n ) is la + mB + ny = k ( aa + bB + cy ) , where k is an arbitrary constant . 16. To find the inclinations of a straight line , drawn through one of the angular points of the triangle of reference , to the sides ...
... parallel to ( l , m , n ) is la + mB + ny = k ( aa + bB + cy ) , where k is an arbitrary constant . 16. To find the inclinations of a straight line , drawn through one of the angular points of the triangle of reference , to the sides ...
Page 19
... parallel to them . These will be represented by the equations ( ma — lb ) B + ( na — lc ) y = 0 , - ( m'a — l'b ) B + ( n'a— l'c ) y = 0 . And these straight lines must be perpendicular to each other . If 0 , 0 ' be the respective ...
... parallel to them . These will be represented by the equations ( ma — lb ) B + ( na — lc ) y = 0 , - ( m'a — l'b ) B + ( n'a— l'c ) y = 0 . And these straight lines must be perpendicular to each other . If 0 , 0 ' be the respective ...
Other editions - View all
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