An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page viii
... Circle ib . 323 37 7 . Equation of the Conic touching the Three Sides of the Tri- angle of Reference . 39 · 8 . Position of the Centre . Condition for a Parabola 40 9 . Condition of Tangency 42 10 . Equations of the Four Circles which ...
... Circle ib . 323 37 7 . Equation of the Conic touching the Three Sides of the Tri- angle of Reference . 39 · 8 . Position of the Centre . Condition for a Parabola 40 9 . Condition of Tangency 42 10 . Equations of the Four Circles which ...
Page ix
... a given external Point 80 11 . Co - ordinates of the Centre . 82 • 12 . Equation of the Asymptotes 83 13. Condition for a Rectangular Hyperbola 14. Conditions for a Circle 84 86 ARTS . PAGE 15 . 16 . 17 . 18 CONTENTS . ix.
... a given external Point 80 11 . Co - ordinates of the Centre . 82 • 12 . Equation of the Asymptotes 83 13. Condition for a Rectangular Hyperbola 14. Conditions for a Circle 84 86 ARTS . PAGE 15 . 16 . 17 . 18 CONTENTS . ix.
Page x
... Circles pass through the same two points at infinity All Conics , similar and similarly situated to each other , in ... Circle 92 20 . Locus of the intersection of two Tangents at right angles to one another . Directrix of a Parabola 21 ...
... Circles pass through the same two points at infinity All Conics , similar and similarly situated to each other , in ... Circle 92 20 . Locus of the intersection of two Tangents at right angles to one another . Directrix of a Parabola 21 ...
Page xi
... Circle 118 23 . Reciprocation with respect to a Point 119 24 . The three circles described on the diagonals of a complete quadrilateral as diameters have a common radical axis ib . Foci of a quadrilateral ib . 25 . Orthocentre of a ...
... Circle 118 23 . Reciprocation with respect to a Point 119 24 . The three circles described on the diagonals of a complete quadrilateral as diameters have a common radical axis ib . Foci of a quadrilateral ib . 25 . Orthocentre of a ...
Page xii
... circles 155 20 . Projection of the foci and directrices of a Conic ib . 21 . The anharmonic ratio of any pencil or range is unaltered by projection 156 • 22 . Any two lines , which make an angle A with each other , form with the lines ...
... circles 155 20 . Projection of the foci and directrices of a Conic ib . 21 . The anharmonic ratio of any pencil or range is unaltered by projection 156 • 22 . Any two lines , which make an angle A with each other , form with the lines ...
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Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²