An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory Projections |
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Page viii
... described about the Triangle of Refer- 33 • ence 34 · · 4 . Position of the Centre . Condition for a Parabola 35 • 5 . Condition of Tangency . Every Parabola touches the Line at Infinity . 6 . Equation of the Circumscribing Circle ib ...
... described about the Triangle of Refer- 33 • ence 34 · · 4 . Position of the Centre . Condition for a Parabola 35 • 5 . Condition of Tangency . Every Parabola touches the Line at Infinity . 6 . Equation of the Circumscribing Circle ib ...
Page xi
... described on the diagonals of a complete quadrilateral as diameters have a common radical axis ib . Foci of a quadrilateral ib . 25 . Orthocentre of a triangle . ib . 28 . The director circles of all conics which touch four given ...
... described on the diagonals of a complete quadrilateral as diameters have a common radical axis ib . Foci of a quadrilateral ib . 25 . Orthocentre of a triangle . ib . 28 . The director circles of all conics which touch four given ...
Page 34
... described about the triangle of reference . 3. Let us now inquire how the line B. Y + = 0 μ ע is related to this conic . B If in the equation of the conic we put + = 0 , or , μ V which is the same thing , uy + v8 = 0 , it reduces to λBy ...
... described about the triangle of reference . 3. Let us now inquire how the line B. Y + = 0 μ ע is related to this conic . B If in the equation of the conic we put + = 0 , or , μ V which is the same thing , uy + v8 = 0 , it reduces to λBy ...
Page 48
... described about the same quadrangle * , and the diagonals of that quadrangle intersect in A , while the sides produced intersect in B and C , then A , B , C form , with respect to each of the circumscribing conics , a conjugate triad ...
... described about the same quadrangle * , and the diagonals of that quadrangle intersect in A , while the sides produced intersect in B and C , then A , B , C form , with respect to each of the circumscribing conics , a conjugate triad ...
Page 56
... described about a conic ; prove that the straight lines , joining each angular point with the point of contact of the opposite side , intersect in a point . 3 . Find the equations of the normals to the conic Aẞy + μya + vaẞ = 0 , drawn ...
... described about a conic ; prove that the straight lines , joining each angular point with the point of contact of the opposite side , intersect in a point . 3 . Find the equations of the normals to the conic Aẞy + μya + vaẞ = 0 , drawn ...
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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