An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page viii
... described about the Triangle of Reference · 34 4 . Position of the Centre . Condition for a Parabola 35 5 . Condition of Tangency . Every Parabola touches the Line at Infinity • 37 6 . Equation of the Circumscribing Circle ib . • 7 ...
... described about the Triangle of Reference · 34 4 . Position of the Centre . Condition for a Parabola 35 5 . Condition of Tangency . Every Parabola touches the Line at Infinity • 37 6 . Equation of the Circumscribing Circle ib . • 7 ...
Page 34
... described about the triangle of reference . 3. Let us now inquire how the line βγ + = 0 ע is related to this conic . β If in the equation of the conic we put + μ Y ע - 0 , or , which is the same thing , μy + vẞ = 0 , it reduces to λBy ...
... described about the triangle of reference . 3. Let us now inquire how the line βγ + = 0 ע is related to this conic . β If in the equation of the conic we put + μ Y ע - 0 , or , which is the same thing , μy + vẞ = 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 ...
Page 57
... described about the quadrangle . 6. If R be the radius of the circle described about the triangle of reference , p that of the circle with respect to which the triangle of reference is self - conjugate , prove that p + 4R * cos A cos B ...
... described about the quadrangle . 6. If R be the radius of the circle described about the triangle of reference , p that of the circle with respect to which the triangle of reference is self - conjugate , prove that p + 4R * cos A cos B ...
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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