An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page x
... Directrix of a Parabola . 21 . To find the magnitudes of the axes of the Conic 35 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and an Hyperbola : 97 • EXAMPLES · 386 98 CHAPTER V. TRIANGULAR ...
... Directrix of a Parabola . 21 . To find the magnitudes of the axes of the Conic 35 93 94 22 . To find the area of the Conic . Criterion to distinguish be- tween an Ellipse and an Hyperbola : 97 • EXAMPLES · 386 98 CHAPTER V. TRIANGULAR ...
Page 47
... - angled at A , the form of the equation shews that A will be a focus of the conic , and BC the corresponding directrix . Suppose them to be PQ and RS . The intersection .CONDITION OF TANGENCY . 47 16 Condition of Tangency.
... - angled at A , the form of the equation shews that A will be a focus of the conic , and BC the corresponding directrix . Suppose them to be PQ and RS . The intersection .CONDITION OF TANGENCY . 47 16 Condition of Tangency.
Page 58
... directrix of the parabola , which touches the sides of the triangle of reference , and also the straight line la + mẞ + vy = 0 , is cos В a 008 4 ( -1 ) + 8 008 B ( -1 ) + YOO C ( 1-1 ) . cos 14. If the equation y cos ( la ) 1 + ( mß ) ...
... directrix of the parabola , which touches the sides of the triangle of reference , and also the straight line la + mẞ + vy = 0 , is cos В a 008 4 ( -1 ) + 8 008 B ( -1 ) + YOO C ( 1-1 ) . cos 14. If the equation y cos ( la ) 1 + ( mß ) ...
Page 94
... directrix , since that is the locus of the point of intersection of two tangents to a parabola at right angles to one another . The appearance of the line at infinity as a factor in the result in this case may be explained as follows ...
... directrix , since that is the locus of the point of intersection of two tangents to a parabola at right angles to one another . The appearance of the line at infinity as a factor in the result in this case may be explained as follows ...
Page 120
... any point S on its directrix , we obtain a rectangular hyperbola , passing through S. If a rectangular hyperbola be reciprocated with respect to any point Son its circumference , we obtain a parabola 120 TRILINEAR CO - ORDINATES .
... any point S on its directrix , we obtain a rectangular hyperbola , passing through S. If a rectangular hyperbola be reciprocated with respect to any point Son its circumference , we obtain a parabola 120 TRILINEAR CO - ORDINATES .
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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