An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 1
... EQUATION OF A STRAIGHT LINE . 1. In the system of co - ordinates ordinarily used , the position of a point in a plane is determined by means of its distances from two given straight lines . In the system of which we are about to treat ...
... EQUATION OF A STRAIGHT LINE . 1. In the system of co - ordinates ordinarily used , the position of a point in a plane is determined by means of its distances from two given straight lines . In the system of which we are about to treat ...
Page 3
... equation in a form homogeneous with respect to the trilinear co - ordinates of any point to which it relates . Any locus may be represented , as in the ordinary system , by means of a relation between two co- ordinates , B and y for ...
... equation in a form homogeneous with respect to the trilinear co - ordinates of any point to which it relates . Any locus may be represented , as in the ordinary system , by means of a relation between two co- ordinates , B and y for ...
Page 4
... equation B2 + hy + k2 = 0 is equivalent to the homogeneous equation 4A2ß2 + 2Ahy ( aa + bB + cy ) + k2 ( aa + bB + cy ) 2 = 0 . The following examples may familiarize the reader with this system of co - ordinates . 1. Prove that the co ...
... equation B2 + hy + k2 = 0 is equivalent to the homogeneous equation 4A2ß2 + 2Ahy ( aa + bB + cy ) + k2 ( aa + bB + cy ) 2 = 0 . The following examples may familiarize the reader with this system of co - ordinates . 1. Prove that the co ...
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 7
... equation of that line . COR . It hence may be proved that the three straight lines , drawn through the angular ... equations bB = cv , cy = aa , aa = bB , and , therefore , all pass through the point for which aa = bB = cy . In the next ...
... equation of that line . COR . It hence may be proved that the three straight lines , drawn through the angular ... equations bB = cv , cy = aa , aa = bB , and , therefore , all pass through the point for which aa = bB = cy . In the next ...
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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