An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 22
... 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 , lie in a straight line ; BC , CB , intersect in L ; CA ,, AC , in M ; AB ,, BA , in N. Prove that AL , BM ...
... 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 , lie in a straight line ; BC , CB , intersect in L ; CA ,, AC , in M ; AB ,, BA , in N. Prove that AL , BM ...
Page 30
... taken that OP . OP ' = OQ . OQ ' OR . OR ' = ...... = = a constant k2 suppose . Then these points are said to form a system in involution . If K be a point such that OK2 = k2 , K is called a focus of the system . If 2 be positive ...
... taken that OP . OP ' = OQ . OQ ' OR . OR ' = ...... = = a constant k2 suppose . Then these points are said to form a system in involution . If K be a point such that OK2 = k2 , K is called a focus of the system . If 2 be positive ...
Page 39
... taken all negatively , or two positively and one negatively . For , if they be taken otherwise , the left - hand member of the equation of the conic will become a perfect square , as may be ascertained by sub- stitution , and the conic ...
... taken all negatively , or two positively and one negatively . For , if they be taken otherwise , the left - hand member of the equation of the conic will become a perfect square , as may be ascertained by sub- stitution , and the conic ...
Page 65
... taken from each line and from each column , and that the coefficients of one half of the terms are +1 , of the other 1. To determine the sign of any particular term we proceed as follows . Considering for simplicity the case of three ...
... taken from each line and from each column , and that the coefficients of one half of the terms are +1 , of the other 1. To determine the sign of any particular term we proceed as follows . Considering for simplicity the case of three ...
Page 98
... taken , is a circle . 2. The polar of the point of intersection of two given straight lines is the straight line which joins the poles of those straight lines . This will readily be seen to follow geometrically from the definitions of a ...
... taken , is a circle . 2. The polar of the point of intersection of two given straight lines is the straight line which joins the poles of those straight lines . This will readily be seen to follow geometrically from the definitions of a ...
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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