An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page viii
... Parabola 35 • 5 . Condition of Tangency . Every Parabola touches the Line at Infinity . 6 . Equation of the Circumscribing Circle ib . 323 37 7 . Equation of the Conic touching the Three Sides of the Tri- angle of Reference . 39 · 8 ...
... Parabola 35 • 5 . Condition of Tangency . Every Parabola touches the Line at Infinity . 6 . Equation of the Circumscribing Circle ib . 323 37 7 . Equation of the Conic touching the Three Sides of the Tri- angle of Reference . 39 · 8 ...
Page ix
... Parabola . 76 78 · 7 . Condition that the Conic may break up into Two Straight Lines ib . 8 . Equation of the Polar of a given Point · ib . 9 . Co - ordinates of the Pole of a given Straight Line 79 10 . • Equation of the pair of ...
... Parabola . 76 78 · 7 . Condition that the Conic may break up into Two Straight Lines ib . 8 . Equation of the Polar of a given Point · ib . 9 . Co - ordinates of the Pole of a given Straight Line 79 10 . • Equation of the pair of ...
Page x
... Parabola 21 . To find the magnitudes of the axes of the Conic 355 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and an Hyperbola EXAMPLES . 388 96 98 CHAPTER V. TRIANGULAR CO - ORDINATES . 1 ...
... Parabola 21 . To find the magnitudes of the axes of the Conic 355 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and an Hyperbola EXAMPLES . 388 96 98 CHAPTER V. TRIANGULAR CO - ORDINATES . 1 ...
Page xi
... line , and of the centre . Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle 140 11 . Self - conjugate Conic 141 PAGE ARTS . 12 . EXAMPLES Tangential rectangular Co - CONTENTS . xi.
... line , and of the centre . Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle 140 11 . Self - conjugate Conic 141 PAGE ARTS . 12 . EXAMPLES Tangential rectangular Co - CONTENTS . xi.
Page 35
... as to bisect their chord of contact passes also through the centre , O will be the centre of the conic . Now , at the point E , we have α 3-2 CENTRE OF THE CONIC . 35 4 Position of the Centre Condition for a Parabola.
... as to bisect their chord of contact passes also through the centre , O will be the centre of the conic . Now , at the point E , we have α 3-2 CENTRE OF THE CONIC . 35 4 Position of the Centre Condition for a Parabola.
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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