An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 7
... point on the line AD , it therefore is the equation of that line . COR . It hence may be proved that the three straight lines , drawn through the angular points of a triangle to bisect the opposite sides , intersect in a point . For ...
... point on the line AD , it therefore is the equation of that line . COR . It hence may be proved that the three straight lines , drawn through the angular points of a triangle to bisect the opposite sides , intersect in a point . For ...
Page 8
... three straight lines drawn through the angular points of a triangle , perpen- dicular to the opposite sides , intersect in the point determined by the equations a cos A = ẞ cos B = y cos C. 6. To find the equations of the internal and ...
... three straight lines drawn through the angular points of a triangle , perpen- dicular to the opposite sides , intersect in the point determined by the equations a cos A = ẞ cos B = y cos C. 6. To find the equations of the internal and ...
Page 9
... three internal bisectors of the angles of a triangle intersect in a point ; ( 2 ) , That the internal bisector of any one angle , and the external bisectors of the other two , also intersect in a point . These points may be shewn to be ...
... three internal bisectors of the angles of a triangle intersect in a point ; ( 2 ) , That the internal bisector of any one angle , and the external bisectors of the other two , also intersect in a point . These points may be shewn to be ...
Page 13
... point of intersection . 12. To find the condition that three points may lie in the same straight line . 29 Let α1 , B1 , Y1 ; α , B2 , Y2 ; as , B. , Y. , be the co - ordinates of the three given points , then , if these points lie in ...
... point of intersection . 12. To find the condition that three points may lie in the same straight line . 29 Let α1 , B1 , Y1 ; α , B2 , Y2 ; as , B. , Y. , be the co - ordinates of the three given points , then , if these points lie in ...
Page 14
... three straight lines should intersect in a point , and that three points should lie in a straight line , is worthy of notice . Its full geometrical mean- ing will be seen hereafter . We shall sometimes , in future investigations , speak ...
... three straight lines should intersect in a point , and that three points should lie in a straight line , is worthy of notice . Its full geometrical mean- ing will be seen hereafter . We shall sometimes , in future investigations , speak ...
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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