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 18
Page viii
... Chord of a Conic is divided harmonically by the Conic , any Point , and its Polar • Equation of a Line joining Two given Points Equation of the Tangent at a given Point Pole of a given Straight Line . 51 F 52 53 ib . 54 • ib . • • 26 ...
... Chord of a Conic is divided harmonically by the Conic , any Point , and its Polar • Equation of a Line joining Two given Points Equation of the Tangent at a given Point Pole of a given Straight Line . 51 F 52 53 ib . 54 • ib . • • 26 ...
Page xii
... chords are real ; if not , one pair only is real Invariants of two Conics • 146 • 147 150 • ON PROJECTIONS . 9 . Definition of Projections 10 . 13 . 152 ib . • Projection to infinity Any quadrilateral may be projected , in an infinite ...
... chords are real ; if not , one pair only is real Invariants of two Conics • 146 • 147 150 • ON PROJECTIONS . 9 . Definition of Projections 10 . 13 . 152 ib . • Projection to infinity Any quadrilateral may be projected , in an infinite ...
Page 35
... the intersection of two tangents so as to bisect their chord of contact passes also through the centre , O will be the centre of the conic . Now , at the point E , we have α 3-2 . CENTRE OF THE CONIC . 35 4 Position of the Centre.
... the intersection of two tangents so as to bisect their chord of contact passes also through the centre , O will be the centre of the conic . Now , at the point E , we have α 3-2 . CENTRE OF THE CONIC . 35 4 Position of the Centre.
Page 46
... chord of contact of tangents to the conic drawn through B , or that CA is the polar of B , and B the pole of CA with respect to the conic . Similarly , C , AB , stand to one another in the relation of pole and polar . Again , since the ...
... chord of contact of tangents to the conic drawn through B , or that CA is the polar of B , and B the pole of CA with respect to the conic . Similarly , C , AB , stand to one another in the relation of pole and polar . Again , since the ...
Page 53
... chord of a conic is divided harmonically by the conic itself , any point on the chord , and the polar of the point with respect to the conic . 22. We may observe , that the two straight lines repre- sented by the equations 1 la = ωβ ...
... chord of a conic is divided harmonically by the conic itself , any point on the chord , and the polar of the point with respect to the conic . 22. We may observe , that the two straight lines repre- sented by the equations 1 la = ωβ ...
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