An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 21
... become , and the greater , therefore , the distance from the point to the line ; which is in accordance with the remark made in Art . ( 14 ) . EXAMPLES . 1. Find the equation of the straight line joining the middle points of two sides ...
... become , and the greater , therefore , the distance from the point to the line ; which is in accordance with the remark made in Art . ( 14 ) . EXAMPLES . 1. Find the equation of the straight line joining the middle points of two sides ...
Page 39
... become a perfect square , as may be ascertained by sub- stitution , and the conic will degenerate into a straight line , or rather into two coincident straight lines . Taking then the double signs all negatively , and writing CONIC ...
... become a perfect square , as may be ascertained by sub- stitution , and the conic will degenerate into a straight line , or rather into two coincident straight lines . Taking then the double signs all negatively , and writing CONIC ...
Page 40
... becomes L3a2 + M2ß2 + N2y2 – 2MNßy – 2NLyα — 2LMɑß = 0 , which is equivalent to ± ( La ) 3 ± ( MB ) 3 ± ( Ny ) * = 0 . It may be remarked , that the condition that the point ( l , m , n ) should lie in the above conic , is the same as ...
... becomes L3a2 + M2ß2 + N2y2 – 2MNßy – 2NLyα — 2LMɑß = 0 , which is equivalent to ± ( La ) 3 ± ( MB ) 3 ± ( Ny ) * = 0 . It may be remarked , that the condition that the point ( l , m , n ) should lie in the above conic , is the same as ...
Page 43
... become the in- scribed circle . At the centre of this circle we have , as we know , a = ẞ = y . This gives , by the result of Art . 8 Equations of the Four Circles which touch the Three Sides the Triangle of Reference.
... become the in- scribed circle . At the centre of this circle we have , as we know , a = ẞ = y . This gives , by the result of Art . 8 Equations of the Four Circles which touch the Three Sides the Triangle of Reference.
Page 49
... becomes a2 72 + + L2 M2 N2 = = 0 . 18. To find the co - ordinates of the centre . Let B , B , be the points in which the conic is cut by CA , then , if B , B , be bisected in Q , the line BQ will pass through the centre . Now , let f ...
... becomes a2 72 + + L2 M2 N2 = = 0 . 18. To find the co - ordinates of the centre . Let B , B , be the points in which the conic is cut by CA , then , if B , B , be bisected in Q , the line BQ will pass through the centre . Now , let f ...
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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