An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 1
... positive , and that of the other as negative . We shall consider a , the distance of a point from the line BC , as positive if the point lie on the same side of that line as the point A does , negative if on the other side ; and ...
... positive , and that of the other as negative . We shall consider a , the distance of a point from the line BC , as positive if the point lie on the same side of that line as the point A does , negative if on the other side ; and ...
Page 2
... , we get ax + bB + cy = 2A . Next , suppose P to lie between AB , AC produced , and on the side of BC remote from A ( fig . 2 ) . Then a will be Fig . 2 . B negative , while ẞ , y are positive . Hence 2 TRILINEAR CO - ORDINATES .
... , we get ax + bB + cy = 2A . Next , suppose P to lie between AB , AC produced , and on the side of BC remote from A ( fig . 2 ) . Then a will be Fig . 2 . B negative , while ẞ , y are positive . Hence 2 TRILINEAR CO - ORDINATES .
Page 3
... positive . Hence , twice the area PBC will be represented by az , and we shall therefore have as before - aa + bB + cy = 2A . Thirdly , let P lie between AB , AC , produced backwards ( fig . 3 ) , so that B , y are negative while a is ...
... positive . Hence , twice the area PBC will be represented by az , and we shall therefore have as before - aa + bB + cy = 2A . Thirdly , let P lie between AB , AC , produced backwards ( fig . 3 ) , so that B , y are negative while a is ...
Page 30
... , k2 suppose . Then these points are said to form a system in involution . If K be a point such that OK = k2 , K is called a focus of the system . If 2 be positive , there will evidently be two 30 TRILINEAR CO - ORDINATES .
... , k2 suppose . Then these points are said to form a system in involution . If K be a point such that OK = k2 , K is called a focus of the system . If 2 be positive , there will evidently be two 30 TRILINEAR CO - ORDINATES .
Page 31
... positive , there will evidently be two such foci , one on each side of O , if negative ( and k therefore imagi- nary ) there will be no real foci . The point O is called the centre of the system . Two points , such as P , P ' , are said ...
... positive , there will evidently be two such foci , one on each side of O , if negative ( and k therefore imagi- nary ) there will be no real foci . The point O is called the centre of the system . Two points , such as P , P ' , are said ...
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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