An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
From inside the book
Results 1-5 of 20
Page vii
... 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 ib . 25 • ARTS . PAGE 22 . The Bisectors of any Angle.
... 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 ib . 25 • ARTS . PAGE 22 . The Bisectors of any Angle.
Page viii
... Harmonic Pencil 25 · 23 . Anharmonic Ratio of a given Pencil 26 24 . Fourth Harmonic to Three given Straight Lines 27 · 25 . Harmonic Relation of Points and Lines 29 26 . ON INVOLUTION . Definitions 30 31 27-29 . Anharmonic Properties ...
... Harmonic Pencil 25 · 23 . Anharmonic Ratio of a given Pencil 26 24 . Fourth Harmonic to Three given Straight Lines 27 · 25 . Harmonic Relation of Points and Lines 29 26 . ON INVOLUTION . Definitions 30 31 27-29 . Anharmonic Properties ...
Page xi
... harmonic pencil , either pair will be its own polar reciprocal with respect to the other 116 Condition that two pairs of straight lines may form an har- . monic pencil ib . 118 • 119 24 , Foci of a quadrilateral 25 . 28 . 29 . 30 . The ...
... harmonic pencil , either pair will be its own polar reciprocal with respect to the other 116 Condition that two pairs of straight lines may form an har- . monic pencil ib . 118 • 119 24 , Foci of a quadrilateral 25 . 28 . 29 . 30 . The ...
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 barmonic range , and the straight ... harmonic pencil be cut by a transversal , the four points of section will form an harmonic range . And if four points ...
... harmonic pencil . A range , of which the anharmonic ratio is unity , is called an barmonic range , and the straight ... harmonic pencil be cut by a transversal , the four points of section will form an harmonic range . And if four points ...
Other editions - View all
Common terms and phrases
angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα