An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... Tangent at a given Point Pole of a given Straight Line Condition of Tangency . Condition for a Parabola Co - ordinates of the Centre EXAMPLES 52 53 ib . 54 ib . • ib . 55 56 32 CHAPTER III . ELIMINATION BETWEEN LINEAR EQUATIONS . ARTS ...
... Tangent at a given Point Pole of a given Straight Line Condition of Tangency . Condition for a Parabola Co - ordinates of the Centre EXAMPLES 52 53 ib . 54 ib . • ib . 55 56 32 CHAPTER III . ELIMINATION BETWEEN LINEAR EQUATIONS . ARTS ...
Page ix
... Tangent at a given Point 74 3 . 75 4 , 5 . 6 . Condition that a given Straight Line may touch the Conic Condition for a ... Tangents drawn to the Conic from a given external Point · 11 . Co - ordinates of the Centre 12 . Equation of the ...
... Tangent at a given Point 74 3 . 75 4 , 5 . 6 . Condition that a given Straight Line may touch the Conic Condition for a ... Tangents drawn to the Conic from a given external Point · 11 . Co - ordinates of the Centre 12 . Equation of the ...
Page x
... Tangents at right angles to one another . Directrix of a Parabola . 21 . To find the magnitudes of the axes of the Conic 35 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and an Hyperbola : 97 ...
... Tangents at right angles to one another . Directrix of a Parabola . 21 . To find the magnitudes of the axes of the Conic 35 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and an Hyperbola : 97 ...
Page xi
... tangent in any curve is equal to the cor- responding angle in the Reciprocal Curve Co - ordinates of the foci of a Conic . Double application of the Method of Reciprocal Polars EXAMPLES • 121 ib . 123 125 · 126 128 ib . 2 . points • 3 ...
... tangent in any curve is equal to the cor- responding angle in the Reciprocal Curve Co - ordinates of the foci of a Conic . Double application of the Method of Reciprocal Polars EXAMPLES • 121 ib . 123 125 · 126 128 ib . 2 . points • 3 ...
Page xii
... Tangents , of Poles , and Polars ib . 15 . Any two conics may be projected into concentric curves 154 16 . Also into similar and similarly situated curves ib . 4 18 . 17. These projections may be effected in an infinite number of ways ...
... Tangents , of Poles , and Polars ib . 15 . Any two conics may be projected into concentric curves 154 16 . Also into similar and similarly situated curves ib . 4 18 . 17. These projections may be effected in an infinite number of ways ...
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Common terms and phrases
angular points anharmonic ratio asymptotes auxiliary conic b₁ b₂ C₁ centre Chap chord co-ordinates coefficients common tangents conic section determinant directrix find the equation fixed point fixed straight line follows four points given conic given point given straight line given triangle Hence investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides parabola Pascal's Theorem perpendicular point f points at infinity points of contact points of intersection PQRS prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree shewn similar and similarly sin POS tangents drawn term a,b,c theorem three points three straight lines triangle of reference ua² uf+w'g+v'h ux² V'ca va² Vb² vß² W'ab whence wy² λα