An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page xii
... constant 144 23 , 24. Any system of Points in involution projects into a system in involution , and the foci of one system project into the foci of the other • • • . ib . 25 . A system of Conics , passing through four given points , cut ...
... constant 144 23 , 24. Any system of Points in involution projects into a system in involution , and the foci of one system project into the foci of the other • • • . ib . 25 . A system of Conics , passing through four given points , cut ...
Page 10
... constant . Let AQ = q , AR = r , then the areas of the triangles PAQ , PAR will be respectively represented by qß , try , and the area of QAR by qr bc A. Hence qB + my = 2gr A bc qr = ( aa + bB + cy ) . bc This is the equation of the ...
... constant . Let AQ = q , AR = r , then the areas of the triangles PAQ , PAR will be respectively represented by qß , try , and the area of QAR by qr bc A. Hence qB + my = 2gr A bc qr = ( aa + bB + cy ) . bc This is the equation of the ...
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
... constant , whatever point on the locus P may represent . This can only be true when that locus is a straight line . 9. To find the co - ordinates of the point of intersection of two given straight lines . Let the equations of the two ...
... constant , whatever point on the locus P may represent . This can only be true when that locus is a straight line . 9. To find the co - ordinates of the point of intersection of two given straight lines . Let the equations of the two ...
Page 13
... constant . For this equation is satis- fied when the equations of the given straight lines are both satisfied , and , being of the first degree , it represents a straight line . It is therefore the equation of a straight line passing ...
... constant . For this equation is satis- fied when the equations of the given straight lines are both satisfied , and , being of the first degree , it represents a straight line . It is therefore the equation of a straight line passing ...
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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