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 6
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 + MI ) ( Ln + NI ) — 7MN = 0 , -- Lmn + Mnl + Nlm = = 0 , which may also be written . L M N + + = 0 . Τ m n ( ) ' It hence appears that the condition , that the line ( l , m , n ) ...
... considered as a quadratic in be equal , we have or ( Lm + MI ) ( Ln + NI ) — 7MN = 0 , -- Lmn + Mnl + Nlm = = 0 , which may also be written . L M N + + = 0 . Τ m n ( ) ' It hence appears that the condition , that the line ( l , m , n ) ...
Page 94
... considered as determined by the ratios of the areas of the tri- angles PBC , PCA , PAB , to the triangle of reference ABC . If these quantities be denoted by the letters x , y , z , they will be connected by the identical relation x + y ...
... considered as determined by the ratios of the areas of the tri- angles PBC , PCA , PAB , to the triangle of reference ABC . If these quantities be denoted by the letters x , y , z , they will be connected by the identical relation x + y ...
Page 119
... considered a point as deter- mined , 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 deter- mined , 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 120
... considered positive , and from C to B negative , it will readily be seen that 오 γ = a2 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 오 γ = a2 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
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα