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 21
Page 2
... we get aa + bB + cy = 2A . Next , suppose P to lie between AB , AC produced , and on the side of BC remote from A ( fig . 2 ) . Then a will be Fig . 2 . B negative , while B , y are positive . Hence 2 MODERN GEOMETRY .
... we get aa + bB + cy = 2A . Next , suppose P to lie between AB , AC produced , and on the side of BC remote from A ( fig . 2 ) . Then a will be Fig . 2 . B negative , while B , y are positive . Hence 2 MODERN GEOMETRY .
Page 3
... produced backwards ( fig . 3 ) , so that B , y are negative while a is positive . Twice Fig . 3 . B the areas of PBC , PCA , PAB , are now represented by aa , bẞ , -cy respectively , so that we still have - aa + bB + cy = 2A . In all ...
... produced backwards ( fig . 3 ) , so that B , y are negative while a is positive . Twice Fig . 3 . B the areas of PBC , PCA , PAB , are now represented by aa , bẞ , -cy respectively , so that we still have - aa + bB + cy = 2A . In all ...
Page 22
... produced . 29 21 37 3 6. On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are taken , B , C1 ; С ̧ , A ̧ ; A ̧ , B .; such that the points of intersection of BC with BC . of CA with CA , and of AB with AB ...
... produced . 29 21 37 3 6. On the sides BC , CA , AB of the triangle ABC , respectively , pairs of points are taken , B , C1 ; С ̧ , A ̧ ; A ̧ , B .; such that the points of intersection of BC with BC . of CA with CA , and of AB with AB ...
Page 26
... produced to any point P ' , and let the angle P'OR be bisected by OS , then sin POQ = sin QOR , sin POS sin P'OS sin POQ . sin ROS sin POS . sin QOR Hence the truth of the proposition . = = sin ROS ; = 1 . 23. PROP . If ABC be the ...
... produced to any point P ' , and let the angle P'OR be bisected by OS , then sin POQ = sin QOR , sin POS sin P'OS sin POQ . sin ROS sin POS . sin QOR Hence the truth of the proposition . = = sin ROS ; = 1 . 23. PROP . If ABC be the ...
Page 28
... produce them to meet in E. Join AE , then AE shall be the fourth harmonic required . For , let ABC be the triangle of reference , and let the equation of AD be B - ky - 0 . Let the equation of B'C ' be λα + β -ly = 0 . Then that of ...
... produce them to meet in E. Join AE , then AE shall be the fourth harmonic required . For , let ABC be the triangle of reference , and let the equation of AD be B - ky - 0 . Let the equation of B'C ' be λα + β -ly = 0 . Then that of ...
Other editions - View all
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