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 22
Page vii
... 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.
... 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
... 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 of Points ...
... 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 of Points ...
Page x
... Pencil , formed by four intersect- ing straight lines , is the same as that of the range formed by their poles • · 113 15 . Any straight line drawn through a given point A is divided harmonically by any Conic Section and the polar of A ...
... Pencil , formed by four intersect- ing straight lines , is the same as that of the range formed by their poles • · 113 15 . Any straight line drawn through a given point A is divided harmonically by any Conic Section and the polar of A ...
Page xi
... 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 three ...
... 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 three ...
Page xii
... pencil or range is unaltered by projection . : : Any two lines , which make an angle A with each other , form with the lines joining the circular points at infinity to their point of intersection , a pencil of which the anharmonic ratio ...
... pencil or range is unaltered by projection . : : Any two lines , which make an angle A with each other , form with the lines joining the circular points at infinity to their point of intersection , a pencil of which the anharmonic ratio ...
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