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'yx + 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'yx + 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 a2 to be of a different sign from the other two , then writing , for convenience of future investigations , L3 , - M3 , - N2 for u , v , w ...
... coefficients of a2 , B2 , y2 , cannot be all of the same sign . Suppose the coefficient of a2 to be of a different sign from the other two , then writing , for convenience of future investigations , L3 , - M3 , - N2 for u , v , w ...
Page 47
... coefficients of p2 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 . Suppose them to be PQ and RS . The ...
... coefficients of p2 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 . Suppose them to be PQ and RS . The ...
Page 59
... expressed by omitting x , x , ... x , and writing the coefficients only in the order in which they appear in the given equations , thus , ... an bn b1 , b2 ... by 2 ( 59 ) ARTS CHAPTER III ELIMINATION BETWEEN LINEAR EQUATIONS.
... expressed by omitting x , x , ... x , and writing the coefficients only in the order in which they appear in the given equations , thus , ... an bn b1 , b2 ... by 2 ( 59 ) ARTS CHAPTER III ELIMINATION BETWEEN LINEAR EQUATIONS.
Page 62
... coefficients of x2 , x , x severally to zero . We shall then have ɑλ1 + b2λ1⁄2 + c2λ ̧ + d1⁄2λ a = 0 аžλï + b3λ1⁄2 + c3λ ̧ + d ̧λ ̧ = 0 α ̧λ1 + b ̧λ1⁄2 + ç ̧λ ̧ + dλ . = 0 which equations involve as a consequence ( A ' ) , ....... ( B ...
... coefficients of x2 , x , x severally to zero . We shall then have ɑλ1 + b2λ1⁄2 + c2λ ̧ + d1⁄2λ a = 0 аžλï + b3λ1⁄2 + c3λ ̧ + d ̧λ ̧ = 0 α ̧λ1 + b ̧λ1⁄2 + ç ̧λ ̧ + dλ . = 0 which equations involve as a consequence ( A ' ) , ....... ( B ...
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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