An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page ix
... Pascal's Theorem EXAMPLES CHAPTER IV . ON THE CONIC REPRESENTED BY THE GENERAL EQUATION OF THE 2 . SECOND DEGREE . To find the point in which a straight line , drawn in a given direction through a given point of the conic , meets the ...
... Pascal's Theorem EXAMPLES CHAPTER IV . ON THE CONIC REPRESENTED BY THE GENERAL EQUATION OF THE 2 . SECOND DEGREE . To find the point in which a straight line , drawn in a given direction through a given point of the conic , meets the ...
Page 69
... PASCAL'S THEOREM . From the analytical result stated in Art . 6 of the present chapter , that the value of a determinant is not altered by changing its lines into columns and its columns into lines , we obtain a proof of Pascal's theorem ...
... PASCAL'S THEOREM . From the analytical result stated in Art . 6 of the present chapter , that the value of a determinant is not altered by changing its lines into columns and its columns into lines , we obtain a proof of Pascal's theorem ...
Page 70
... Pascal's Theorem many interesting conse- quences may be deduced . Thus , if the point F coincide with A , D with B , E with C , then AF , BD , CE become the tangents at A , B , C , respectively , and we obtain the theorem enunciated in ...
... Pascal's Theorem many interesting conse- quences may be deduced . Thus , if the point F coincide with A , D with B , E with C , then AF , BD , CE become the tangents at A , B , C , respectively , and we obtain the theorem enunciated in ...
Page 71
... theorem : " If the opposite sides of a quadrilateral , in- scribed in a conic , be produced to meet , and likewise the pairs of tangents at opposite angles of the quadrilateral , the four ... PASCAL'S THEOREM . 71 Pascal's Theorem EXAMPLES.
... theorem : " If the opposite sides of a quadrilateral , in- scribed in a conic , be produced to meet , and likewise the pairs of tangents at opposite angles of the quadrilateral , the four ... PASCAL'S THEOREM . 71 Pascal's Theorem EXAMPLES.
Page 73
... y , z ; and y ย + = OC + α + λ also that x b + λ y c + λ ย c + y 1+ 2 + + ( a + a ) 2 1 · ( b + a ) 2 † ( c + a ) 2 ( y - a ) ( a - B ) ( a + a ) ( b + a ) ( c + a ) * · · = y c + a - 1 , 1 , 1 , b + y PASCAL'S THEOREM . 73.
... y , z ; and y ย + = OC + α + λ also that x b + λ y c + λ ย c + y 1+ 2 + + ( a + a ) 2 1 · ( b + a ) 2 † ( c + a ) 2 ( y - a ) ( a - B ) ( a + a ) ( b + a ) ( c + a ) * · · = y c + a - 1 , 1 , 1 , b + y PASCAL'S THEOREM . 73.
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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