An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page ix
... through the same two points at infinity 86 16 . All Conics , similar and similarly situated to each other , intersect in the same two points in the line at infinity ib . ARTS . 17 . one another . Directrix of a CONTENTS . ix.
... through the same two points at infinity 86 16 . All Conics , similar and similarly situated to each other , intersect in the same two points in the line at infinity ib . ARTS . 17 . one another . Directrix of a CONTENTS . ix.
Page xi
... which the angles are of any magnitude Projection of Tangents , of Poles , and Polars 13 . 138 139 14 . Any two conics may be projected into concentric curves 140 ARTS . PAGE 15 . Also into similar and similarly CONTENTS . xi.
... which the angles are of any magnitude Projection of Tangents , of Poles , and Polars 13 . 138 139 14 . Any two conics may be projected into concentric curves 140 ARTS . PAGE 15 . Also into similar and similarly CONTENTS . xi.
Page 1
... similarly for B and 7. It thus appears that the trilinear co - ordinates of any point within the triangle of reference are all positive ; while no point has all its co - ordinates negative . 2. Between the trilinear co - ordinates of ...
... similarly for B and 7. It thus appears that the trilinear co - ordinates of any point within the triangle of reference are all positive ; while no point has all its co - ordinates negative . 2. Between the trilinear co - ordinates of ...
Page 6
... Similarly ab2c m 4A2 , abc2 n 442 Hence r2 : abc - - 42 ( α ( B1 - B2 ) ( Y1 - Y2 ) + b ( Y1 — Y2 ) ( α , — α ) { a - - + c ( α1 − α2 ) ( ẞ2 − B1 ) } . This is one form of the expression for r . It may also be proved in a similar ...
... Similarly ab2c m 4A2 , abc2 n 442 Hence r2 : abc - - 42 ( α ( B1 - B2 ) ( Y1 - Y2 ) + b ( Y1 — Y2 ) ( α , — α ) { a - - + c ( α1 − α2 ) ( ẞ2 − B1 ) } . This is one form of the expression for r . It may also be proved in a similar ...
Page 19
... Similarly , tan ( 6-4 ) - 2 = · v sin A μ + v cos A ' Hence , the inclinations of the given straight line to AB , AC , are determined . 17. To find the condition that two given straight lines may be perpendicular to one another . Let ...
... Similarly , tan ( 6-4 ) - 2 = · v sin A μ + v cos A ' Hence , the inclinations of the given straight line to AB , AC , are determined . 17. To find the condition that two given straight lines may be perpendicular to one another . Let ...
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Common terms and phrases
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα