An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page ix
... EQUATION OF THE SECOND DEGREE . 2 . 3 . 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 . 74 75 4 , 5 . 6 ...
... EQUATION OF THE SECOND DEGREE . 2 . 3 . 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 . 74 75 4 , 5 . 6 ...
Page x
... Equation of the nine - point Circle 92 20 . Locus of the intersection of two Tangents at right angles to one another . Directrix of a Parabola 21 . To find the magnitudes of the axes of the Conic 355 93 94 22 . To find the area of the ...
... Equation of the nine - point Circle 92 20 . Locus of the intersection of two Tangents at right angles to one another . Directrix of a Parabola 21 . To find the magnitudes of the axes of the Conic 355 93 94 22 . To find the area of the ...
Page 4
... equation ß2 + hy + k2 = 0 is equivalent to the homogeneous equation 4A2ß2 + 2Ahy ( aa + bß + cy ) + k2 ( aa + bB + ... find the distance between two given points , in terms of their trilinear co - ordinates . 19 2 ' Let a ,, B1 , Y1 ; α ...
... equation ß2 + hy + k2 = 0 is equivalent to the homogeneous equation 4A2ß2 + 2Ahy ( aa + bß + cy ) + k2 ( aa + bB + ... find the distance between two given points , in terms of their trilinear co - ordinates . 19 2 ' Let a ,, B1 , Y1 ; α ...
Page 6
... equation of a straight line ; and first , we shall consider the cases of certain straight lines bearing important relations to the triangle of reference . To find the equation of the straight line drawn through one of the angular points ...
... equation of a straight line ; and first , we shall consider the cases of certain straight lines bearing important relations to the triangle of reference . To find the equation of the straight line drawn through one of the angular points ...
Page 8
... find the equation of the straight line drawn through one of the angular points of the triangle of reference , perpen- dicular to the opposite side . Making a construction similar to that in the last proposi- tion , it will be seen that ...
... find the equation of the straight line drawn through one of the angular points of the triangle of reference , perpen- dicular to the opposite side . Making a construction similar to that in the last proposi- tion , it will be seen that ...
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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