An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 9
... Hence , if QK = B , QL = — y . 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 = — y . 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 2qr qB + ry = A bc = qr • 27 ( ax + 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 ...
... Hence 2qr qB + ry = A bc = qr • 27 ( ax + 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 ...
Page 11
... ( y − h ) = 0 . ax + 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 . ax + 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 ...
Page 15
... Hence , the required condition of parallelism is bn - cm cl- an am - bl = = bn ' - cm ' cl ' - an ' am ' - bl ( 3 ) . These two equations are equivalent to one only , since they may be written in the form n с m b a m b α ### n m - n m b ...
... Hence , the required condition of parallelism is bn - cm cl- an am - bl = = bn ' - cm ' cl ' - an ' am ' - bl ( 3 ) . These two equations are equivalent to one only , since they may be written in the form n с m b a m b α ### n m - n m b ...
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angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα