An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 17
... coincides , when the ratios 1 : mn continually approach to , and ultimately co- incide with , the ratios a : bc , is a straight line altogether at an infinite distance . This is often expressed by saying that the equation ax + bB + cy ...
... coincides , when the ratios 1 : mn continually approach to , and ultimately co- incide with , the ratios a : bc , is a straight line altogether at an infinite distance . This is often expressed by saying that the equation ax + bB + cy ...
Page 34
... coincide , since the line in question evidently passes through the point of intersection of B = 0 and y = 0. Hence the straight line and the conic meet one another in coincident points , that is , they touch one another at the point A ...
... coincide , since the line in question evidently passes through the point of intersection of B = 0 and y = 0. Hence the straight line and the conic meet one another in coincident points , that is , they touch one another at the point A ...
Page 48
... coincide with the intersections of the line joining each pair of points of intersection of the conics with the line join- ing the other pair . Hence also , if any number of conic sections be described about the same quadrangle * , and ...
... coincide with the intersections of the line joining each pair of points of intersection of the conics with the line join- ing the other pair . Hence also , if any number of conic sections be described about the same quadrangle * , and ...
Page 52
... coincides with the intersec- tion of the perpendiculars drawn from the angular points to the opposite sides . This is otherwise evident from geometri- cal considerations . 20. To find the equation of the conic which touches two sides of ...
... coincides with the intersec- tion of the perpendiculars drawn from the angular points to the opposite sides . This is otherwise evident from geometri- cal considerations . 20. To find the equation of the conic which touches two sides of ...
Page 70
... 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 Ex . 1 , Chap . II . Again , by supposing D to coincide with B , and E with C , we 70 ...
... 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 Ex . 1 , Chap . II . Again , by supposing D to coincide with B , and E with C , we 70 ...
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Common terms and phrases
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