An Elementary Treatise on Trilinear Co-ordinates: The Method of Reciprocal Polars, and the Theory 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'By + 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'By + 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 , B " , 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 , M , N for u , v , w respectively ...
... coefficients of a2 , B " , 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 , M , N for u , v , w respectively ...
Page 47
... coefficients of 62 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 62 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
... eliminated between them , and the result of the elimination may be expressed by omitting a , ... x , and writing the coefficients only in the order in which they appear in the given equations , thus x2 a1 , a2 an b1 , b2 ... bn = ( 59 )
... eliminated between them , and the result of the elimination may be expressed by omitting a , ... x , and writing the coefficients only in the order in which they appear in the given equations , thus x2 a1 , a2 an b1 , b2 ... bn = ( 59 )
Page 62
... coefficients of x2 , x , x severally to zero . We shall then have ɑ „ λ ̧ + b2λ1⁄2 + С2λ ̧ + d2λ ̧ = 0 ) 2 а ̧λ1 + b ̧λ + câλ3 + d2λ4 2 - 0 a1λ1 + b1λ + cλ ̧ + d2λ = 0 ) 3 which equations involve as a consequence ...... ( A ' ) , а1λ ̧ ...
... coefficients of x2 , x , x severally to zero . We shall then have ɑ „ λ ̧ + b2λ1⁄2 + С2λ ̧ + d2λ ̧ = 0 ) 2 а ̧λ1 + b ̧λ + câλ3 + d2λ4 2 - 0 a1λ1 + b1λ + cλ ̧ + d2λ = 0 ) 3 which equations involve as a consequence ...... ( A ' ) , а1λ ̧ ...
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An Elementary Treatise on Trilinear Coordinates, the Method of Reciprocal ... Norman Macleod Ferrers No preview available - 2015 |
Common terms and phrases
aa+bB+cy angular points asymptotes auxiliary conic b₁ Brianchon's Theorem C₁ centre Chap chord co-ordinates coefficients common tangents conic passing conic section determinant directrix find the equation fixed point fixed straight line focus follows four points given conic given point given straight line Hence imaginary internal bisectors investigated Let the equation line at infinity locus meets the conic nine-point circle obtain opposite sides pair parabola Pascal's Theorem perpendicular point f point of intersection points at infinity points of contact polar reciprocal projection prove radical axis reciprocal curve reciprocated with respect rectangular hyperbola represented right angles second degree similar and similarly system of conics tangents drawn theorem three points three straight lines triangle of reference ua² uf+w'g+v'h Vb² vß² W'ab Wc² whence wy²