An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 1
... point from its three sides will be called the trilinear co - ordinates of that point . We shall usually denote the angular points of the triangle of reference by the letters A , B , C , the lengths of the sides respectively opposite to ...
... point from its three sides will be called the trilinear co - ordinates of that point . We shall usually denote the angular points of the triangle of reference by the letters A , B , C , the lengths of the sides respectively opposite to ...
Page 6
... angular points of the triangle of reference , so as to bisect the opposite side . Let D be the middle point of the side BC , we have then to investigate the equation of the straight line AD . In AD take any point P , and let a 6 ...
... angular points of the triangle of reference , so as to bisect the opposite side . Let D be the middle point of the side BC , we have then to investigate the equation of the straight line AD . In AD take any point P , and let a 6 ...
Page 7
... point on the line AD , it therefore is the equation of that line . COR . It hence may be proved that the three straight lines , drawn through the angular points of a triangle to bisect the opposite sides , intersect in a point . For ...
... point on the line AD , it therefore is the equation of that line . COR . It hence may be proved that the three straight lines , drawn through the angular points of a triangle to bisect the opposite sides , intersect in a point . For ...
Page 8
... angular points of a triangle , perpen- dicular to the opposite sides , intersect in the point 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 ...
... angular points of a triangle , perpen- dicular to the opposite sides , intersect in the point 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 ...
Page 18
... angular points of the triangle of reference , to the sides which intersect in that point . Let the equation of the straight line AP be μβ = νγ , Fig . 8 . D and let the angle A. be its inclination to AD , the internal bisector of sin +0 ...
... angular points of the triangle of reference , to the sides which intersect in that point . Let the equation of the straight line AP be μβ = νγ , Fig . 8 . D and let the angle A. be its inclination to AD , the internal bisector of sin +0 ...
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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