An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page ix
... 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 Curve again Equation of the Tangent at a given Point 3 . 4 , 5 . Condition that a ...
... 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 Curve again Equation of the Tangent at a given Point 3 . 4 , 5 . Condition that a ...
Page x
... find the magnitudes of the axes of the Conic 89 19 . To find the area of the Conic . Criterion to distinguish ... Equation of the Polar Reciprocal of one Conic with regard to another ΙΟΙ · IO . Instances of Transformation · 12 ...
... find the magnitudes of the axes of the Conic 89 19 . To find the area of the Conic . Criterion to distinguish ... Equation of the Polar Reciprocal of one Conic with regard to another ΙΟΙ · IO . Instances of Transformation · 12 ...
Page 4
... equation B2 + hy + k2 = 0 is equivalent to the homogeneous equation 4A2ß2 + 2Ahy ( aa + bB + cy ) + k2 ( aa + bB + ... find the distance between two given points , in terms of their trilinear co - ordinates . Let a1 , B11 ; a2 , B2 , Ya ...
... equation B2 + hy + k2 = 0 is equivalent to the homogeneous equation 4A2ß2 + 2Ahy ( aa + bB + cy ) + k2 ( aa + bB + ... find the distance between two given points , in terms of their trilinear co - ordinates . Let a1 , B11 ; a2 , B2 , Ya ...
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
a₁ aa+bB+cy Algebra angular points anharmonic ratio Arithmetic asymptotes auxiliary conic b₁ c₁ CAMBRIDGE CLASS BOOKS centre Chap chord cloth co-ordinates coefficients College common tangents condition conic passing conic section conics intersect Crown 8vo curve determine directrix ellipse find the equation fixed point focus four points given conic given point given straight line Hence hyperbola imaginary investigated line at infinity line joining locus meets the conic obtain pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact PQRS projection prove reciprocal polars represented respect right angles second degree Second Edition Similarly sin POS system of conics tangents tangents drawn theorem three points three straight lines touches the line Treatise triangle of reference U'bc ua² V'ca Vb² vß² W'ab wy² λα