An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page 118
... subtended at the centre of the auxiliary circle by the straight line joining their poles , or to its supplement . 22. From what has been said in Art . 15 , and the earlier articles of this chapter , it will appear that to find the polar ...
... subtended at the centre of the auxiliary circle by the straight line joining their poles , or to its supplement . 22. From what has been said in Art . 15 , and the earlier articles of this chapter , it will appear that to find the polar ...
Page 120
... subtends at S an angle the supplement of that between the asymptotes of the hyperbola . 27. From the last article it follows that , if a parabola be reciprocated with respect to any point S on its directrix , we obtain a rectangular ...
... subtends at S an angle the supplement of that between the asymptotes of the hyperbola . 27. From the last article it follows that , if a parabola be reciprocated with respect to any point S on its directrix , we obtain a rectangular ...
Page 121
... subtend a right angle at either focus of the quadrilateral formed by these four straight lines . " Or , in other words , " The director circles of all conics which touch four given straight lines , have a common radical axis , which is ...
... subtend a right angle at either focus of the quadrilateral formed by these four straight lines . " Or , in other words , " The director circles of all conics which touch four given straight lines , have a common radical axis , which is ...
Page 124
... subtends a constant angle at the focus . " This angle will be found , by reciprocating Euc . III . 20 , to be the complement of one - half of the angle subtended at the focus by the portion of the corresponding directrix intercepted ...
... subtends a constant angle at the focus . " This angle will be found , by reciprocating Euc . III . 20 , to be the complement of one - half of the angle subtended at the focus by the portion of the corresponding directrix intercepted ...
Page 130
... sub- tends a right angle at one of the points . 14. If a parabola be reciprocated with respect to any circle , the radius of curvature of the reciprocal conic , at the origin , varies inversely as the latus - rectum of the parabola . 15 ...
... sub- tends a right angle at one of the points . 14. If a parabola be reciprocated with respect to any circle , the radius of curvature of the reciprocal conic , at the origin , varies inversely as the latus - rectum of the parabola . 15 ...
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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