An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 8
... Hence PG.AC cos B PH.AB cos C ; B cos B = Y cos C. This will be the equation of the straight line , drawn through A , at right angles to BC . COR . It may hence be shewn that the three straight lines drawn through the angular points of ...
... Hence PG.AC cos B PH.AB cos C ; B cos B = Y cos C. This will be the equation of the straight line , drawn through A , at right angles to BC . COR . It may hence be shewn that the three straight lines drawn through the angular points of ...
Page 9
... Hence , if QK = B , QL = -7 . We have therefore B + 7 = 0 as the equation of the line AQ , which externally bisects the angle A. From the form of these equations we see , ( 1 ) , That the three internal bisectors of the angles of a ...
... Hence , if QK = B , QL = -7 . We have therefore B + 7 = 0 as the equation of the line AQ , which externally bisects the angle A. From the form of these equations we see , ( 1 ) , That the three internal bisectors of the angles of a ...
Page 10
... Hence qB + my = 2gr A bc qr = ( aa + bB + cy ) . bc This is the equation of the straight line QR , and , since it involves the two arbitrary quantities q , r , it is in the most general form of the equation of the first degree between ...
... Hence qB + my = 2gr A bc qr = ( aa + bB + cy ) . bc This is the equation of the straight line QR , and , since it involves the two arbitrary quantities q , r , it is in the most general form of the equation of the first degree between ...
Page 11
... ( y − h ) = 0 , aa + bB + cy = 2A , af + bg + ch = 2A ; - - :: a ( a − ƒ ) + b ( B − g ) + c ( y − h ) = 0 ; a - f B - g bn - cm = cl -an y - h = am - bl Hence , the ratio of Pm to Pn is constant EQUATION OF THE FIRST DEGREE . 11.
... ( y − h ) = 0 , aa + bB + cy = 2A , af + bg + ch = 2A ; - - :: a ( a − ƒ ) + b ( B − g ) + c ( y − h ) = 0 ; a - f B - g bn - cm = cl -an y - h = am - bl Hence , the ratio of Pm to Pn is constant EQUATION OF THE FIRST DEGREE . 11.
Page 12
The Method of Reciprocal Polars, and the Theory of Projections Norman Macleod Ferrers. Hence , the ratio of Pm to Pn is constant , whatever point on the locus P may represent . This can only be true when that locus is a straight line . 9 ...
The Method of Reciprocal Polars, and the Theory of Projections Norman Macleod Ferrers. Hence , the ratio of Pm to Pn is constant , whatever point on the locus P may represent . This can only be true when that locus is a straight line . 9 ...
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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