An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 1
... sides respectively opposite to them by a , b , c , and the dis- tances of any point from BC , CA , AB respectively by the letters a , ẞ , y . When two points lie on opposite sides of a line of re- ference , the distance of one of these ...
... sides respectively opposite to them by a , b , c , and the dis- tances of any point from BC , CA , AB respectively by the letters a , ẞ , y . When two points lie on opposite sides of a line of re- ference , the distance of one of these ...
Page 7
... opposite 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 ...
... opposite 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 ...
Page 8
... opposite side . Making a construction similar to that in the last proposi- tion , it will be seen that we have here ... sides , intersect in the point determined by the equations a cos A = ẞ cos B = y cos C. 6. To find the equations of ...
... opposite side . Making a construction similar to that in the last proposi- tion , it will be seen that we have here ... 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
... sides opposite to them , lie in the same straight line ; and also that the points in which the external bisector of any one angle , and the internal bisectors of the other two angles , intersect the sides respectively opposite to them ...
... sides opposite to them , lie in the same straight line ; and also that the points in which the external bisector of any one angle , and the internal bisectors of the other two angles , intersect the sides respectively opposite to them ...
Page 30
... sides opposite to them , lie in the same straight line ; and that the points in which the external bisector of any one angle and the internal bisectors of the other two angles , intersect the sides respectively opposite to them , lie in ...
... sides opposite to them , lie in the same straight line ; and that the points in which the external bisector of any one angle and the internal bisectors of the other two angles , intersect the sides respectively opposite to them , lie in ...
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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