An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 30
... ...... = = a constant k2 suppose . Then these points are said to form a system in involution . If K be a point such that OK2 = k2 , K is called a focus of the system . If 2 be positive , there will evidently be two 30 MODERN GEOMETRY .
... ...... = = a constant k2 suppose . Then these points are said to form a system in involution . If K be a point such that OK2 = k2 , K is called a focus of the system . If 2 be positive , there will evidently be two 30 MODERN GEOMETRY .
Page 31
... focus is conjugate to itself , and that the conjugate of the centre is at an infinite distance , and that a point and its conjugate will be on the same , or different sides of the centre , according as the foci are real or imaginary ...
... focus is conjugate to itself , and that the conjugate of the centre is at an infinite distance , and that a point and its conjugate will be on the same , or different sides of the centre , according as the foci are real or imaginary ...
Page 47
... of reference be right - angled at A , the form of the equation shews that A will be a focus of the conic , and BC the corresponding directrix . ( L2M " — L2M2 ) * B = ( CONDITION OF TANGENCY . 47 16 Condition of Tangency.
... of reference be right - angled at A , the form of the equation shews that A will be a focus of the conic , and BC the corresponding directrix . ( L2M " — L2M2 ) * B = ( CONDITION OF TANGENCY . 47 16 Condition of Tangency.
Page 57
... . Hence prove that the circle , which passes through the points of intersection of three tangents to a parabola , passes also through the focus . CHAPTER III . ON ELIMINATION BETWEEN LINEAR EQUATIONS . 1. EXAMPLES . 57.
... . Hence prove that the circle , which passes through the points of intersection of three tangents to a parabola , passes also through the focus . CHAPTER III . ON ELIMINATION BETWEEN LINEAR EQUATIONS . 1. EXAMPLES . 57.
Page 111
... focus , and of which the axis - minor is 2 2k2 ( p2 — c2 ) - & It will be an ellipse , parabola , or hyperbola , according as p is greater than , equal to , or less than c , that is , according as the centre of the auxiliary circle lies ...
... focus , and of which the axis - minor is 2 2k2 ( p2 — c2 ) - & It will be an ellipse , parabola , or hyperbola , according as p is greater than , equal to , or less than c , that is , according as the centre of the auxiliary circle lies ...
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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