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 36
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 , sup- pose these points to be B and C. Then 24 = - α1 = 0 , ẞ1 = = = b 2 Y1 = 0 , 2A = ; also ra . Hence ...
... determine . Since the values of l , m , n are independent of the positions of the points , the distance of which we wish to find , sup- pose these points to be B and C. Then 24 = - α1 = 0 , ẞ1 = = = b 2 Y1 = 0 , 2A = ; also ra . Hence ...
Page 8
... determined by the equations a cos AB 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 AB 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 . 17. 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 ...
... determined . 17. 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 ...
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 ...
Other editions - View all
Common terms and phrases
angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα