An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 6
... side . Let D be the middle point of the side BC , we have then to investigate the equation of the straight line AD . In AD take any point P , and let a 6 MODERN GEOMETRY . 4—6 Investigation of Equations of certain Straight Lines.
... side . Let D be the middle point of the side BC , we have then to investigate the equation of the straight line AD . In AD take any point P , and let a 6 MODERN GEOMETRY . 4—6 Investigation of Equations of certain Straight Lines.
Page 7
... sides , intersect in a point . For these straight lines will be represented by the equations bB = cv , cy = aa , aa = bB , and , therefore , all pass through the point for which aa = bB = cy . In the next three propositions the reader ...
... sides , intersect in a point . For these straight lines will be represented by the equations bB = cv , cy = aa , aa = bB , and , therefore , all pass through the point for which aa = bB = cy . In the next three propositions the reader ...
Page 8
... side . Making a construction similar to that in the last proposi- tion , it will be seen that we have here DE . AC DF ... sides , intersect in the point determined by the equations a cos A = ẞ cos B = y cos C. 6. To find the equations of ...
... side . Making a construction similar to that in the last proposi- tion , it will be seen that we have here DE . AC DF ... sides , intersect in the point determined by the equations a cos A = ẞ cos B = y cos C. 6. To find the equations of ...
Page 9
... side of AC , Q and C will lie on opposite sides of AB , and vice versa . Hence , if QK = B , QL = -7 . We have therefore B + 7 = 0 as the equation of the line AQ , which externally bisects the angle A. From the form of these equations ...
... side of AC , Q and C will lie on opposite sides of AB , and vice versa . Hence , if QK = B , QL = -7 . We have therefore B + 7 = 0 as the equation of the line AQ , which externally bisects the angle A. From the form of these equations ...
Page 18
... sides which intersect in that point . Let the equation of the straight line AP be μβ = γ , Fig . 8 . and let be its inclination to AD , the internal bisector of the angle 4 . Then sin + 812 2 sin ( e ) tan 0 whence A tan- = = μ - V μ + ...
... sides which intersect in that point . Let the equation of the straight line AP be μβ = γ , Fig . 8 . and let be its inclination to AD , the internal bisector of the angle 4 . Then sin + 812 2 sin ( e ) tan 0 whence A tan- = = μ - V μ + ...
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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