An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory of Projections |
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Page 34
... coefficients of the equation . First , suppose u , v , w , all = 0 . The equation then assumes the form u'ẞy + v'ya + w'aß = 0 , which we shall write λβγ + μγα + ναβ = 0 . Now , if in this equation we put a = 0 , it reduces itself to ...
... coefficients of the equation . First , suppose u , v , w , all = 0 . The equation then assumes the form u'ẞy + v'ya + w'aß = 0 , which we shall write λβγ + μγα + ναβ = 0 . Now , if in this equation we put a = 0 , it reduces itself to ...
Page 45
... coefficients of a2 , B2 , y2 , cannot be all of the same sign . Suppose the coefficient of a to be of a different sign from the other two , then writing , for convenience of future investigations , L2 , - M2 , - N2 for u , v , w respec ...
... coefficients of a2 , B2 , y2 , cannot be all of the same sign . Suppose the coefficient of a to be of a different sign from the other two , then writing , for convenience of future investigations , L2 , - M2 , - N2 for u , v , w respec ...
Page 47
... coefficients of B2 and y2 be equal , and the triangle of reference be right - angled at A , the form of the equation shews that A will be a focus of the conic , and BC the corresponding directrix . ( L2M " — L2M2 ) * B = ( CONDITION OF ...
... coefficients of B2 and y2 be equal , and the triangle of reference be right - angled at A , the form of the equation shews that A will be a focus of the conic , and BC the corresponding directrix . ( L2M " — L2M2 ) * B = ( CONDITION OF ...
Page 58
... the elimination may be expressed by omitting x ,, x , ... x , and writing the coefficients only in the order in which they appear in the given equations , thus a1 , as ... an b1 , b2 ... bn ( 58 ) ARTS PAGE 2 Definition of a Determinant.
... the elimination may be expressed by omitting x ,, x , ... x , and writing the coefficients only in the order in which they appear in the given equations , thus a1 , as ... an b1 , b2 ... bn ( 58 ) ARTS PAGE 2 Definition of a Determinant.
Page 61
... coefficients of x , x , x severally to zero . We shall then have 9 α2λ1 + b2λ1⁄2 + c2λ + d2λ4 : = ɑ3λ1 + b3λ1⁄2 + € 3λg + dgλ1 = 0 ¤ ̧λ1 + b1λ1⁄2 + çλ ̧ + d ̧λ = 0 ] which equations involve as a consequence . ( A ' ) , а1λ1 + b1λ1⁄2 + ...
... coefficients of x , x , x severally to zero . We shall then have 9 α2λ1 + b2λ1⁄2 + c2λ + d2λ4 : = ɑ3λ1 + b3λ1⁄2 + € 3λg + dgλ1 = 0 ¤ ̧λ1 + b1λ1⁄2 + çλ ̧ + d ̧λ = 0 ] which equations involve as a consequence . ( A ' ) , а1λ1 + b1λ1⁄2 + ...
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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