An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page 1
... determined by means of its distances from two given straight lines . In the system of which we are about to treat , the position of a point in a plane will be determined by the ratios of its distances from three given straight lines in ...
... determined by means of its distances from two given straight lines . In the system of which we are about to treat , the position of a point in a plane will be determined by the ratios of its distances from three given straight lines in ...
Page 6
... determine . Since the values of l , m , n are independent of the positions of the points , the distance of which we wish to find , suppose these points to be B and C. Then α1 = 0 , B1 = 24 b , 1 = 0 , 2A = ; C α2 = 0 , B2 = 0 , Y2 2 2A ...
... determine . Since the values of l , m , n are independent of the positions of the points , the distance of which we wish to find , suppose these points to be B and C. Then α1 = 0 , B1 = 24 b , 1 = 0 , 2A = ; C α2 = 0 , B2 = 0 , Y2 2 2A ...
Page 8
... determined by the equations a cos A = ẞ cos B : = Y cos C. 6. To find the equations of the internal and external bisectors of an angle of the triangle of reference . For the internal bisector of the angle A , we shall have , making the ...
... determined by the equations a cos A = ẞ cos B : = Y cos C. 6. To find the equations of the internal and external bisectors of an angle of the triangle of reference . For the internal bisector of the angle A , we shall have , making the ...
Page 19
... determined . To find the condition that two given straight lines may be perpendicular to one another . Let ( l , m , n ) , ( l ' , m ' , n ' ) be the two given straight lines . Through A draw two straight lines parallel to them . These ...
... determined . To find the condition that two given straight lines may be perpendicular to one another . Let ( l , m , n ) , ( l ' , m ' , n ' ) be the two given straight lines . Through A draw two straight lines parallel to them . These ...
Page 31
... determined if two pair of conjugate points be given ; as may be seen as follows . Let p , p , q , q ' be the ... determines the centre . 27. PROP . The anharmonic ratio of four points is equal to that of their four conjugates . For , if ...
... determined if two pair of conjugate points be given ; as may be seen as follows . Let p , p , q , q ' be the ... determines the centre . 27. PROP . The anharmonic ratio of four points is equal to that of their four conjugates . For , if ...
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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