An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 4
... Prove that the co - ordinates of the middle point of the A line BC are 0 , C • 2. The co - ordinates of the centre of the circumscribed 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 ...
... Prove that the co - ordinates of the middle point of the A line BC are 0 , C • 2. The co - ordinates of the centre of the circumscribed 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 ...
Page 6
... proved in a similar manner that 2.2 = abc 4A2 { a cos △ ( α , — α ) 2 + b cos B ( ß ̧ — ß2 ) 2 - + c cos C ( Y1 — Y1⁄2 ) 3 } • 4. We next proceed to investigate the equation of a straight line ; and first , we shall consider the cases ...
... proved in a similar manner that 2.2 = abc 4A2 { a cos △ ( α , — α ) 2 + b cos B ( ß ̧ — ß2 ) 2 - + c cos C ( Y1 — Y1⁄2 ) 3 } • 4. We next proceed to investigate the equation of a straight line ; and first , we shall consider the cases ...
Page 7
... proved that the three straight lines , drawn through the angular points of a triangle to bisect the opposite sides , intersect in a point . For these straight lines will be represented by the equations bB = cv , cy = aa , aa = bB , and ...
... proved that the three straight lines , drawn through the angular points of a triangle to bisect the opposite sides , intersect in a point . For these straight lines will be represented by the equations bB = cv , cy = aa , aa = bB , and ...
Page 9
... 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 bisector of any one angle , and the ...
... 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 bisector of any one angle , and the ...
Page 16
... proved ( Art . 2 ) , aa + bB + cy = 2A . Hence the equa- tion ( 4 ) may be looked upon as an expression of the fact that two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot be simultaneously satisfied by any values of a , ß ...
... proved ( Art . 2 ) , aa + bB + cy = 2A . Hence the equa- tion ( 4 ) may be looked upon as an expression of the fact that two equations la + mB + ny = 0 , l'a + m'B + n'y = 0 , cannot be simultaneously satisfied by any values of a , ß ...
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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