An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... Centre . 35 5 . Condition of Tangency . Every Parabola touches the Line at Infinity 37 27 6 . Equation of the Circumscribing Circle • 7 . Equation of the Conic touching the Three Sides of the Tri- angle of Reference 39 • • 8 . Position ...
... Centre . 35 5 . Condition of Tangency . Every Parabola touches the Line at Infinity 37 27 6 . Equation of the Circumscribing Circle • 7 . Equation of the Conic touching the Three Sides of the Tri- angle of Reference 39 • • 8 . Position ...
Page ix
... external Point · 11 . Co - ordinates of the Centre 12 . Equation of the Asymptotes • 13. Condition for a Rectangular Hyperbola 14. Conditions for a Circle . 888 * 8 80 82 83 84 86 ARTS . 15 . 16 . 17 . 18 . CONTENTS . ix.
... external Point · 11 . Co - ordinates of the Centre 12 . Equation of the Asymptotes • 13. Condition for a Rectangular Hyperbola 14. Conditions for a Circle . 888 * 8 80 82 83 84 86 ARTS . 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 ARTS . 12 . EXAMPLES Tangential rectangular Co - ordinates 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 ARTS . 12 . EXAMPLES Tangential rectangular Co - ordinates 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 . 15 . One point and three tangents . 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 . 15 . One point and three tangents . 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 2A 9 3a ' 3b 3c 5. Prove that a sin A + ẞ sin B + y 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 2A 9 3a ' 3b 3c 5. Prove that a sin A + ẞ sin B + y sin C is equal to R where R is the radius of the circumscribing circle . 3. To find the ...
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Common terms and phrases
angular points anharmonic ratio asymptotes auxiliary conic b₁ b₂ C₁ centre Chap chord co-ordinates coefficients common tangents conic section determinant directrix find the equation fixed point fixed straight line follows four points given conic given point given straight line given triangle Hence investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides parabola Pascal's Theorem perpendicular point f points at infinity points of contact points of intersection PQRS prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree shewn similar and similarly sin POS tangents drawn term a,b,c theorem three points three straight lines triangle of reference ua² uf+w'g+v'h ux² V'ca va² Vb² vß² W'ab whence wy² λα