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 Refer- 33333 ence 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 ...
... described about the Triangle of Refer- 33333 ence 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 ...
Page xi
... described on the diagonals of a complete quadrilateral as diameters have a common radical axis Orthocentre of a triangle · The director circles of all conics which touch four given straight lines have a common radical axis Polar ...
... described on the diagonals of a complete quadrilateral as diameters have a common radical axis Orthocentre of a triangle · The director circles of all conics which touch four given straight lines have a common radical axis Polar ...
Page 34
... described about the triangle of reference . 3. Let us now inquire how the line B γ + = 0 μ ע is related to this conic . If in the equation of the conic we put + = 0 , or , . μ ע 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 B γ + = 0 μ ע is related to this conic . If in the equation of the conic we put + = 0 , or , . μ ע 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 λẞy + 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 λẞy + μya + vaẞ = 0 , drawn ...
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Common terms and phrases
angular points asymptotes ax+bB+cy b₁ b₂ C₁ Cambridge centre Chap co-ordinates coefficients College common tangents conic section Crown 8vo determinant directrix Edition equation Fcap find the equation fixed point follows four points given conic given point given straight line Hence imaginary investigated Let the equation line at infinity line joining locus meets the conic nine-point circle numerous Illustrations obtain opposite sides Owens College pair parabola Pascal's Theorem perpendicular point f points of intersection pole Professor prove radical axis ratios rectangular hyperbola represented respect right angles second degree shewn similar and similarly sin POS tangents tangents drawn term a,b,c theorem three straight lines tion touches the line triangle of reference Ua² ux² V'ca v'f+u'g+wh va² values Vb² vß² W. K. CLIFFORD W'ab whence wy² λα