An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Results 1-5 of 8
Page 1
... considered as 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 ...
... considered as 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 ...
Page 43
... considered as a quadratic in be equal , we have or ( Lm + Ml ) ( Ln + NI ) — 1aMN = 0 , Lmn + Mnl + Nlm = 0 , which may also be written M N L + + ī m n = = 0 . It hence appears that the condition , that the line ( l , m , n ) should ...
... considered as a quadratic in be equal , we have or ( Lm + Ml ) ( Ln + NI ) — 1aMN = 0 , Lmn + Mnl + Nlm = 0 , which may also be written M N L + + ī m n = = 0 . It hence appears that the condition , that the line ( l , m , n ) should ...
Page 75
... considered as a quadratic in 8 , determine the two points where the line meets the conic . Now , since ( f , g , h ) is , by supposition , a point on the conic , it follows that ( f , g , h ) must be itself = 0. Hence , one of the two ...
... considered as a quadratic in 8 , determine the two points where the line meets the conic . Now , since ( f , g , h ) is , by supposition , a point on the conic , it follows that ( f , g , h ) must be itself = 0. Hence , one of the two ...
Page 131
... considered a point as de- termined , directly or indirectly , by means of its distances from three given straight lines ; and we have regarded a curve as the aggregation of all points , the co - ordinates of which satisfy a certain ...
... considered a point as de- termined , directly or indirectly , by means of its distances from three given straight lines ; and we have regarded a curve as the aggregation of all points , the co - ordinates of which satisfy a certain ...
Page 132
... considered positive , and from C to B negative , it will readily be seen that 9 а1 = az Since this is a relation between the co - ordinates of any line passing through the point D , it may be considered as the equation of the point D ...
... considered positive , and from C to B negative , it will readily be seen that 9 а1 = az Since this is a relation between the co - ordinates of any line passing through the point D , it may be considered as the equation of the point D ...
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Common terms and phrases
angular points anharmonic ratio asymptotes auxiliary conic b₁ b₂ C₁ centre Chap chord co-ordinates coefficients common tangents conic section determinant directrix find the equation fixed point fixed straight line follows four points given conic given point given straight line given triangle Hence investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides parabola Pascal's Theorem perpendicular point f points at infinity points of contact points of intersection PQRS prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree shewn similar and similarly sin POS tangents drawn term a,b,c theorem three points three straight lines triangle of reference ua² uf+w'g+v'h ux² V'ca va² Vb² vß² W'ab whence wy² λα