An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
From inside the book
Results 6-10 of 25
Page 47
... locus of the equation ( L3M " — L'M2 ) ß2 + ( L3N " 2 – L'2N3 ) y2 = 0 passes through all the points P , Q , R , S ; and , since it may be resolved into linear factors , represents two straight lines . Suppose them to be PQ and RS . The ...
... locus of the equation ( L3M " — L'M2 ) ß2 + ( L3N " 2 – L'2N3 ) y2 = 0 passes through all the points P , Q , R , S ; and , since it may be resolved into linear factors , represents two straight lines . Suppose them to be PQ and RS . The ...
Page 76
... locus of the intersection of these tangents is the polar of the given point . We pro- ceed to find the equation of the polar of ( f , g , h ) . 91 Let f , g , h1 ; f , g , h , be the co - ordinates of the points in which any straight ...
... locus of the intersection of these tangents is the polar of the given point . We pro- ceed to find the equation of the polar of ( f , g , h ) . 91 Let f , g , h1 ; f , g , h , be the co - ordinates of the points in which any straight ...
Page 77
... locus of the point of intersection of the tangents drawn at the extremities of any chord passing through ( f , g , h ) , that is , it is the equation of the polar of ( f , g , h ) . It may also be written , do Y = 0 . do аф at B + dg dh ...
... locus of the point of intersection of the tangents drawn at the extremities of any chord passing through ( f , g , h ) , that is , it is the equation of the polar of ( f , g , h ) . It may also be written , do Y = 0 . do аф at B + dg dh ...
Page 87
... locus of the intersection of two tangents at right angles to one another Wg2 + Vh2 - 2 U'gh + Uh2 + Wf2 − 2 V ' hf + Vƒ2 + Ug2 — 2 W'fg + 2 ( U'ƒ2 + Ugh - V'fg - W'hf ) cos A +2 ( V'g3 + Vhf — W'gh – U'fg ) cos B +2 ( W'h2 + Wfg - U'hf ...
... locus of the intersection of two tangents at right angles to one another Wg2 + Vh2 - 2 U'gh + Uh2 + Wf2 − 2 V ' hf + Vƒ2 + Ug2 — 2 W'fg + 2 ( U'ƒ2 + Ugh - V'fg - W'hf ) cos A +2 ( V'g3 + Vhf — W'gh – U'fg ) cos B +2 ( W'h2 + Wfg - U'hf ...
Page 88
... locus of the point of intersection of two tangents to a parabola at right angles to one another . The appearance of the line at infinity as a factor in the result in this case may be explained as follows : Every para- bola touches the ...
... locus of the point of intersection of two tangents to a parabola at right angles to one another . The appearance of the line at infinity as a factor in the result in this case may be explained as follows : Every para- bola touches the ...
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