An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 4
... circle are R cos A , R cos B , R cos C , where R - 2A a cos A + b cos B + c cos C 3. The co - ordinates of the centre of the inscribe circle are each equal to 2A a + b + c ' What are the co - ordinates of the centres of the escribed circles ...
... circle are R cos A , R cos B , R cos C , where R - 2A a cos A + b cos B + c cos C 3. The co - ordinates of the centre of the inscribe circle are each equal to 2A a + b + c ' What are the co - ordinates of the centres of the escribed circles ...
Page 9
... circles . We shall hereafter prove that the points , in which the external bisectors of each angle respectively intersect the sides opposite to them , lie in the same straight line ; and also that the points in which the external ...
... circles . We shall hereafter prove that the points , in which the external bisectors of each angle respectively intersect the sides opposite to them , lie in the same straight line ; and also that the points in which the external ...
Page 22
... circle inscribed in the triangle ABC , with the middle point of the side BC , is parallel to the straight line joining A with the point of contact of the circle touching BC externally and AB , AC produced . 29 21 37 3 6. On the sides BC ...
... circle inscribed in the triangle ABC , with the middle point of the side BC , is parallel to the straight line joining A with the point of contact of the circle touching BC externally and AB , AC produced . 29 21 37 3 6. On the sides BC ...
Page 37
... circle , circumscribing the triangle of reference . This may be deduced from the consideration that the co - ordinates of the centre of the circumscribing circle are respectively proportional to cos A , cos B , cos C ( see p . 4 ) . Or ...
... circle , circumscribing the triangle of reference . This may be deduced from the consideration that the co - ordinates of the centre of the circumscribing circle are respectively proportional to cos A , cos B , cos C ( see p . 4 ) . Or ...
Page 38
... circle , then the angle EAC is equal to ABC , and FAB to_ACB ( Euc . III . 32 ) . Hence the equation of the tangent EAF must be are B sin B B γ + = sin C 0 , Fig . 15 . E B or + Y = 0 . Ъ C Similarly the equations of the other tangents ...
... circle , then the angle EAC is equal to ABC , and FAB to_ACB ( Euc . III . 32 ) . Hence the equation of the tangent EAF must be are B sin B B γ + = sin C 0 , Fig . 15 . E B or + Y = 0 . Ъ C Similarly the equations of the other tangents ...
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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