An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page vii
... represented by an Equation of the First Degree • 4 • • 6 9 · 8 . 9 . Every Equation of the First Degree represents a Straight Line Point of Intersection of Two Straight Lines 11 12 10 . 11 . 12 . ✓ 13 . ✓ 14 . • · Equation of a ...
... represented by an Equation of the First Degree • 4 • • 6 9 · 8 . 9 . Every Equation of the First Degree represents a Straight Line Point of Intersection of Two Straight Lines 11 12 10 . 11 . 12 . ✓ 13 . ✓ 14 . • · Equation of a ...
Page viii
... represents a Conic Sec- tion • • 2 , 3. Equation of the Conic described about the Triangle of Refer- • · Condition for a Parabola ence · 34 4 . Position of the Centre . 35 5 . Condition of Tangency . Every Parabola touches the Line at ...
... represents a Conic Sec- tion • • 2 , 3. Equation of the Conic described about the Triangle of Refer- • · Condition for a Parabola ence · 34 4 . Position of the Centre . 35 5 . Condition of Tangency . Every Parabola touches the Line at ...
Page ix
... REPRESENTED BY THE GENERAL EQUATION OF THE 2 . SECOND DEGREE . To find the point in which a straight line , drawn in a given direction through a given point of the conic , meets the conic again • Equation of the Tangent at a given Point ...
... REPRESENTED BY THE GENERAL EQUATION OF THE 2 . SECOND DEGREE . To find the point in which a straight line , drawn in a given direction through a given point of the conic , meets the conic again • Equation of the Tangent at a given Point ...
Page xi
... represents a curve of the nth class · ib . 133 134 136 · 7 . Equation of a Conic , touching the three sides of the triangle of reference ib . 8 . Equation of circumscribed Conic 138 9 , Equation of the Pole of a given straight line ...
... represents a curve of the nth class · ib . 133 134 136 · 7 . Equation of a Conic , touching the three sides of the triangle of reference ib . 8 . Equation of circumscribed Conic 138 9 , Equation of the Pole of a given straight line ...
Page 3
... represented by az , and we shall therefore have as before — - aa + bB + cy = 2A . Thirdly , let P lie between AB , AC , produced backwards ( fig . 3 ) , so that ß , y are negative while a is positive . Twice Fig . 3 . B D the areas of ...
... represented by az , and we shall therefore have as before — - aa + bB + cy = 2A . Thirdly , let P lie between AB , AC , produced backwards ( fig . 3 ) , so that ß , y are negative while a is positive . Twice Fig . 3 . B D the areas of ...
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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