An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page 30
... 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 k2 be positive , there will evidently be two 30 TRILINEAR CO - ORDINATES .
... 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 k2 be positive , there will evidently be two 30 TRILINEAR CO - ORDINATES .
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 . Suppose them to be PQ and RS . The intersection CONDITION OF TANGENCY . 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 . Suppose them to be PQ and RS . The intersection CONDITION OF TANGENCY . 47.
Page 57
... a conic about a triangle . Hence prove that the circle , which passes through the points of intersection of three tangents to a parabola , passes also through the focus . 11. Prove that the equation of the line passing through EXAMPLES .
... a conic about a triangle . Hence prove that the circle , which passes through the points of intersection of three tangents to a parabola , passes also through the focus . 11. Prove that the equation of the line passing through EXAMPLES .
Page 120
... focus . 26. If any conic be reciprocated with respect to an ex- ternal point S , the angle between the asymptotes of the re- ciprocal hyperbola will be the supplement of that between the tangents drawn from S to the conic . ( See Art ...
... focus . 26. If any conic be reciprocated with respect to an ex- ternal point S , the angle between the asymptotes of the re- ciprocal hyperbola will be the supplement of that between the tangents drawn from S to the conic . ( See Art ...
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Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²