An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 4
... Let P , Q be the two given points . Join PQ , and draw PM , QM ' perpen- Again , since - aa1 + bß1 + cy1 = 4 MODERN GEOMETRY . Identical relation between the Trilinear Co-ordinates of a Point Distance between two given Points.
... Let P , Q be the two given points . Join PQ , and draw PM , QM ' perpen- Again , since - aa1 + bß1 + cy1 = 4 MODERN GEOMETRY . Identical relation between the Trilinear Co-ordinates of a Point Distance between two given Points.
Page 6
... relations to the triangle of reference . To find the equation of the straight line drawn through one of the angular points of the triangle of reference , so as to bisect the opposite side . Let D be the middle point of the side BC , we ...
... relations to the triangle of reference . To find the equation of the straight line drawn through one of the angular points of the triangle of reference , so as to bisect the opposite side . Let D be the middle point of the side BC , we ...
Page 7
... relation between the co - ordinates of any point on the line AD , it therefore is the equation of that line . COR . It hence may be proved that the three straight lines , drawn through the angular points of a triangle to bisect the ...
... relation between the co - ordinates of any point on the line AD , it therefore is the equation of that line . COR . It hence may be proved that the three straight lines , drawn through the angular points of a triangle to bisect the ...
Page 9
... the first degree . Let be any point on the straight line AC , R on AB , and P any point on the straight line QR , then we have to investigate the relation between the co - ordinates ( a EQUATION OF A STRAIGHT LINE . 9 *』་
... the first degree . Let be any point on the straight line AC , R on AB , and P any point on the straight line QR , then we have to investigate the relation between the co - ordinates ( a EQUATION OF A STRAIGHT LINE . 9 *』་
Page 10
... relation between the co - ordinates ( a , B , y ) of the point P. Fig . 6 . B The property of the straight line , which we shall make the basis of our investigation , is , that it is the locus of a point which moves in such a manner ...
... relation between the co - ordinates ( a , B , y ) of the point P. Fig . 6 . B The property of the straight line , which we shall make the basis of our investigation , is , that it is the locus of a point which moves in such a manner ...
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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