An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Results 1-5 of 53
Page viii
... Centre . Condition for a Parabola 35 • 5 . Condition of Tangency . Every Parabola touches the Line at Infinity . 6 . Equation of the Circumscribing Circle ib . 323 37 7 . Equation of the Conic touching the Three Sides of the Tri- angle ...
... Centre . Condition for a Parabola 35 • 5 . Condition of Tangency . Every Parabola touches the Line at Infinity . 6 . Equation of the Circumscribing Circle ib . 323 37 7 . Equation of the Conic touching the Three Sides of the Tri- angle ...
Page ix
... the Conic from 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.
... the Conic from 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 xi
... line , and of the centre . Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle 140 11 . Self - conjugate Conic 141 PAGE ARTS . 12 . EXAMPLES Tangential rectangular Co - CONTENTS . xi.
... line , and of the centre . Condition for a Parabola 139 10 . Circular points at infinity ib . Conditions for a Circle 140 11 . Self - conjugate Conic 141 PAGE ARTS . 12 . EXAMPLES Tangential rectangular Co - CONTENTS . xi.
Page xiii
... CENTRE OF A SYSTEM OF CONICS WHICH SATISFY FOUR CONDITIONS . 11 . Four points given 12 . Three points and a tangent 13 . Two points and two tangents 14 . One point and three tangents • 15 . Four tangents . • 165 167 · 168 169 171 ...
... CENTRE OF A SYSTEM OF CONICS WHICH SATISFY FOUR CONDITIONS . 11 . Four points given 12 . Three points and a tangent 13 . Two points and two tangents 14 . One point and three tangents • 15 . Four tangents . • 165 167 · 168 169 171 ...
Page 4
... centres of the escribed circles ? 4. The co - ordinates of the centre of gravity are 2A 2A 3a 36 24 · 3c 5. Prove that a sin A + ẞ sin B + γ A sin C is equal to R where R is the radius of the circumscribing circle . 3. To find the ...
... centres of the escribed circles ? 4. The co - ordinates of the centre of gravity are 2A 2A 3a 36 24 · 3c 5. Prove that a sin A + ẞ sin B + γ A sin C is equal to R where R is the radius of the circumscribing circle . 3. To find the ...
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