An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page xiii
... constant PAGE 158 • 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 · A system of Conics , passing through four given points , cut any straight line ...
... constant PAGE 158 • 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 · A system of Conics , passing through four given points , cut any straight line ...
Page 10
... constant . Let AQ = q , AR = r , then the areas of the triangles PAQ , PAR will be respectively represented by 198 , ry , and the area of QAR by A. qr bc Hence 2qr qB + ry = bc = qr ( aa + bB + cy ) . 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 198 , ry , and the area of QAR by A. qr bc Hence 2qr qB + ry = bc = qr ( aa + bB + cy ) . This is the equation of the ...
Page 11
... − h ) = 0 . aa + bB + cy = 2A , af + bg + ch = 2A ; :: a ( a − ƒ ) + b ( B − g ) + c ( y− h ) = 0 ; . : a - f bn - cm = B - g cl- -an = 7 - h am - bl ' Hence , the ratio of Pm to Pn is constant EQUATION OF THE FIRST DEGREE . 11.
... − h ) = 0 . aa + bB + cy = 2A , af + bg + ch = 2A ; :: a ( a − ƒ ) + b ( B − g ) + c ( y− h ) = 0 ; . : a - f bn - cm = B - g cl- -an = 7 - 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 . that locus is a straight line . This can only be true when 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 . that locus is a straight line . This can only be true when 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
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²