An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page vii
... 20 EXAMPLES · 21 19 . ANHARMONIC RATIO . Definitions • 23 20 . The Anharmonic Ratio of a Pencil is equal to that of the range 21 . in which it is cut by any Transversal Definition of an Harmonic Pencil 228585 ib . ARTS . 22 . 23 . 24 . 25 .
... 20 EXAMPLES · 21 19 . ANHARMONIC RATIO . Definitions • 23 20 . The Anharmonic Ratio of a Pencil is equal to that of the range 21 . in which it is cut by any Transversal Definition of an Harmonic Pencil 228585 ib . ARTS . 22 . 23 . 24 . 25 .
Page viii
... Harmonic Pencil · Anharmonic Ratio of a given Pencil Fourth Harmonic to Three given Straight Lines Harmonic Relation of Points and Lines ON INVOLUTION . Definitions Anharmonic Properties of Points and Lines in Involution CHAPTER II ...
... Harmonic Pencil · Anharmonic Ratio of a given Pencil Fourth Harmonic to Three given Straight Lines Harmonic Relation of Points and Lines ON INVOLUTION . Definitions Anharmonic Properties of Points and Lines in Involution CHAPTER II ...
Page 23
... harmonic and anharmonic section , as a familiarity with this conception is useful in the higher geometrical investiga- tions . DEF . 1. If OP , OQ , OR , OS be four straight lines in- tersecting in a point , the ratio sin POQ . sin ROS ...
... harmonic and anharmonic section , as a familiarity with this conception is useful in the higher geometrical investiga- tions . DEF . 1. If OP , OQ , OR , OS be four straight lines in- tersecting in a point , the ratio sin POQ . sin ROS ...
Page 25
... harmonic pencil . A range , of which the anharmonic ratio is unity , is called an harmonic range , and the straight line , on which the range lies , is said to be divided harmonically . From what has been said above , it will be seen ...
... harmonic pencil . A range , of which the anharmonic ratio is unity , is called an harmonic range , and the straight line , on which the range lies , is said to be divided harmonically . From what has been said above , it will be seen ...
Page 27
... harmonic pencil . 24. Hence we deduce a geometrical construction for the determination of the fourth harmonic to three given inter- secting straight lines . Let AB , AD , AC be three given intersecting straight lines , and let it be ...
... harmonic pencil . 24. Hence we deduce a geometrical construction for the determination of the fourth harmonic to three given inter- secting straight lines . Let AB , AD , AC be three given intersecting straight lines , and let it be ...
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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