An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 34
... meets the lines ẞ = 0 , y = 0 ; but these two points 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 ...
... meets the lines ẞ = 0 , y = 0 ; but these two points 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 ...
Page 40
... meet in O. Then O will be the centre of the conic ( see p . 32 ) . We have then to find the equations of BH , CI , which , by their in- tersection , determine 0 . B H Fig . 16 . Let f , g , h , be the co 40 MODERN GEOMETRY . 8 Position ...
... meet in O. Then O will be the centre of the conic ( see p . 32 ) . We have then to find the equations of BH , CI , which , by their in- tersection , determine 0 . B H Fig . 16 . Let f , g , h , be the co 40 MODERN GEOMETRY . 8 Position ...
Page 46
... meets the conic in two coincident points , and , therefore , touches it . Similarly La + Ny = 0 , La - MB - 0 , La + MB ... meet the conic in points situated in the line CA , it follows that CA is the chord of contact of tangents to the ...
... meets the conic in two coincident points , and , therefore , touches it . Similarly La + Ny = 0 , La - MB - 0 , La + MB ... meet the conic in points situated in the line CA , it follows that CA is the chord of contact of tangents to the ...
Page 48
... term quadrangle in preference to quadrilateral , considering a quadrangle as a figure primarily determined by four points , a quadrilateral by four indefinite straight lines . Where this meets the conic , we have L2 ( 48 MODERN GEOMETRY .
... term quadrangle in preference to quadrilateral , considering a quadrangle as a figure primarily determined by four points , a quadrilateral by four indefinite straight lines . Where this meets the conic , we have L2 ( 48 MODERN GEOMETRY .
Page 49
... meets the conic , we have L2 ( mß + ny ) 2 + 12 ( M2ß2 + N3y2 ) = 0 , and , making the two values of B : y equal , we get ( L3m2 + M2l2 ) ( L3n2 + N3l2 ) = L * m2n2 , whence or M2N ° 12 + N2L3m2 + L3M2n2 = 0 , 72 m2 na 2 L2 + M2 + No2 ...
... meets the conic , we have L2 ( mß + ny ) 2 + 12 ( M2ß2 + N3y2 ) = 0 , and , making the two values of B : y equal , we get ( L3m2 + M2l2 ) ( L3n2 + N3l2 ) = L * m2n2 , whence or M2N ° 12 + N2L3m2 + L3M2n2 = 0 , 72 m2 na 2 L2 + M2 + No2 ...
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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