An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page v
... Second Degree . I have introduced a short Chapter on Determinants . The great utility of these expressions in investigations connected with curves of the second degree will , I hope , be a sufficient excuse for the employment of a notation.
... Second Degree . I have introduced a short Chapter on Determinants . The great utility of these expressions in investigations connected with curves of the second degree will , I hope , be a sufficient excuse for the employment of a notation.
Page viii
... SECOND DEGREE . PAGE 2 UN NUN 25 26 27 29 30 ib . I. Every Equation of the Second Degree represents a Conic Section · 33 2 , 3 . Equation of the Conic described about the Triangle of Reference · 34 4 . Position of the Centre . Condition ...
... SECOND DEGREE . PAGE 2 UN NUN 25 26 27 29 30 ib . I. Every Equation of the Second Degree represents a Conic Section · 33 2 , 3 . Equation of the Conic described about the Triangle of Reference · 34 4 . Position of the Centre . Condition ...
Page ix
... SECOND DEGREE . To find the Point in which a Straight Line , drawn in a given direction through a given Point of the ... another . Directrix of a CONTENTS . ix.
... SECOND DEGREE . To find the Point in which a Straight Line , drawn in a given direction through a given Point of the ... another . Directrix of a CONTENTS . ix.
Page 4
... second degree * . 27 V1 * This , if not self - evident , may be proved as follows : Let P , Q be the two given points . Join PQ , and draw PM , QM ' perpen- Again , since - aa1 + bß1 + cy1 = 4 MODERN GEOMETRY . Identical relation ...
... second degree * . 27 V1 * This , if not self - evident , may be proved as follows : Let P , Q be the two given points . Join PQ , and draw PM , QM ' perpen- Again , since - aa1 + bß1 + cy1 = 4 MODERN GEOMETRY . Identical relation ...
Page 5
... second degree . where l , m , n are certain functions of DISTANCE BETWEEN TWO POINTS . 5.
... second degree . where l , m , n are certain functions of DISTANCE BETWEEN TWO POINTS . 5.
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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