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 ib . • 54 25 . 26 . 27 . Pole of a given Straight Line Condition of Tangency . Condition for a Parabola Co - ordinates of the Centre ib . ib . • 55 EXAMPLES 56 CONTENTS . ix ARTS . 2 . CHAPTER III . viii CONTENTS .
... Tangent at a given Point ib . • 54 25 . 26 . 27 . Pole of a given Straight Line Condition of Tangency . Condition for a Parabola Co - ordinates of the Centre ib . ib . • 55 EXAMPLES 56 CONTENTS . ix ARTS . 2 . CHAPTER III . viii CONTENTS .
Page ix
... Tangent at a given Point 72 74 75 · 77 ib . ib . 78 79 81 • 82 • 83 85 4 , 5 . 6 . Condition that a given Straight Line ... Tangents , drawn to the Conic from a Co - ordinates of the Centre 13 . 14 . 23+ 12 . Equation of the Asymptotes ...
... Tangent at a given Point 72 74 75 · 77 ib . ib . 78 79 81 • 82 • 83 85 4 , 5 . 6 . Condition that a given Straight Line ... Tangents , drawn to the Conic from a Co - ordinates of the Centre 13 . 14 . 23+ 12 . Equation of the Asymptotes ...
Page x
... Tangents at right angles to one another . Directrix of a Parabola 21 . To find the magnitudes of the axes of the Conic 22 . To find the area of the Conic . Criterion to distinguish between an Ellipse and an Hyperbola · • 96 EXAMPLES ...
... Tangents at right angles to one another . Directrix of a Parabola 21 . To find the magnitudes of the axes of the Conic 22 . To find the area of the Conic . Criterion to distinguish between an Ellipse and an Hyperbola · • 96 EXAMPLES ...
Page xi
... tangent in any curve is equal to the corresponding angle in the Reciprocal Curve Co - ordinates of the foci of a Conic 122 124 33 . 125 34 . Double application of the Method of Reciprocal Polars EXAMPLES • 127 ib . 119 120 ib . CHAPTER ...
... tangent in any curve is equal to the corresponding angle in the Reciprocal Curve Co - ordinates of the foci of a Conic 122 124 33 . 125 34 . Double application of the Method of Reciprocal Polars EXAMPLES • 127 ib . 119 120 ib . CHAPTER ...
Page xii
... Tangents , of Poles , and Polars 151 ib . 78 . 14 . 15. Any two conics may be projected into concentric curves 16. Also into similar and similarly situated curves • • 17 . 18 . • 152 152 19 . Projection of the foci and directrices of a ...
... Tangents , of Poles , and Polars 151 ib . 78 . 14 . 15. Any two conics may be projected into concentric curves 16. Also into similar and similarly situated curves • • 17 . 18 . • 152 152 19 . Projection of the foci and directrices of a ...
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Common terms and phrases
aa+bB+cy angular points anharmonic ratio asymptotes b₁ b₂ centre Chap chord coefficients common tangents condition of tangency conic section Crown 8vo curve determine directrix distance escribed circles Fcap find the equation fixed point foci focus four points given conic given point given straight line harmonic pencil Hence imaginary internal bisectors investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides pair parabola parallel Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact pole prove radical axis reciprocated with respect rectangular hyperbola represented right angles second degree sin POS tangents tangents drawn theorem three points three straight lines touches the line triangle of reference ua² V'ca values vß² W'ab whence wy² λα
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