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 MODERN ...
... 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 MODERN ...
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 A = ẞ 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 A = ẞ 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 = γ , Fig . 8 . and let be its inclination to AD , the internal bisector of the angle 4 . Then sin ...
... 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 = γ , Fig . 8 . and let be its inclination to AD , the internal bisector of the angle 4 . Then sin ...
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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