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 , L ' , - M2 , - N2 for u , v , w ...
... 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 , L ' , - M2 , - N2 for u , v , w ...
Page 47
... coefficients of 62 and y2 be equal , and the triangle of reference be right - angled at 4 , 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 62 and y2 be equal , and the triangle of reference be right - angled at 4 , 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 a1 , a2 b1 , b2 19 ... ... an ( 59 ) CHAPTER III ELIMIMATION 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 a1 , a2 b1 , b2 19 ... ... an ( 59 ) CHAPTER III ELIMIMATION BETWEEN LINEAR EQUATIONS.
Page 62
... coefficients of X , X , X severally to zero . We shall then have aλ1 + b2λ + c2 λ + d2 λ = 0 | аžλ1 + bλ1⁄2 + Cgλg + d2λ = 0 aλ + b1λ1⁄2 + çλ ̧ + d ̧λ1 = 0 , which equations involve as a consequence = 2 ( A ' ) , To determine the three ...
... coefficients of X , X , X severally to zero . We shall then have aλ1 + b2λ + c2 λ + d2 λ = 0 | аžλ1 + bλ1⁄2 + Cgλg + d2λ = 0 aλ + b1λ1⁄2 + çλ ̧ + d ̧λ1 = 0 , which equations involve as a consequence = 2 ( A ' ) , To determine the three ...
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Common terms and phrases
aa+bB+cy angular points anharmonic ratio asymptotes b₁ b₂ centre Chap chord coefficients common tangents condition of tangency conic section Crown 8vo curve determine directrix distance escribed circles Fcap find the equation fixed point foci focus four points given conic given point given straight line harmonic pencil Hence imaginary internal bisectors investigated Let the equation line at infinity line joining locus meets the conic nine-point circle obtain opposite sides pair parabola parallel Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact pole prove radical axis reciprocated with respect rectangular hyperbola represented right angles second degree sin POS tangents tangents drawn theorem three points three straight lines touches the line triangle of reference ua² V'ca values vß² W'ab whence wy² λα
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