An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page vii
... parallel to one another . Line at Infinity ib . 14 ib . 15 . Equation of a Straight Line , drawn through a given Point , parallel to a given Straight Line 17 16 . Inclination of a Straight Line to a side of the Triangle of Refer- ence ...
... parallel to one another . Line at Infinity ib . 14 ib . 15 . Equation of a Straight Line , drawn through a given Point , parallel to a given Straight Line 17 16 . Inclination of a Straight Line to a side of the Triangle of Refer- ence ...
Page 14
... two straight lines may be parallel to one another . Let the equations of the two straight lines be la + mß + ny = 0 ..................... . ...... l'a + m'B + n'y = 0 ............... .. ( 1 ) , . ( 2 ) . Let ( f , g , h ) ( a , B ...
... two straight lines may be parallel to one another . Let the equations of the two straight lines be la + mß + ny = 0 ..................... . ...... l'a + m'B + n'y = 0 ............... .. ( 1 ) , . ( 2 ) . Let ( f , g , h ) ( a , B ...
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 aa + bB + cy If + mg + nh = 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 aa + bB + cy If + mg + nh = af + bg + ch For this ...
Page 18
... parallel to ( l , m , n ) is la + mẞ + ny = k ( aa + b + 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 + mẞ + ny = k ( aa + b + 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 ) ẞ + ( n'a — l'c ) y = 0 . And these straight lines must be at right angles to one another . If 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 ) ẞ + ( n'a — l'c ) y = 0 . And these straight lines must be at right angles to one another . If 0 , ' be the respective ...
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Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²