The Analyst: A Monthly Journal of Pure and Applied Mathematics, Volumes 3-4Pierson & Blair, 1876 |
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Page 14
... whence -- น u ' u ' y - = a - x " dx x x ' du ' = a dx x - - du'i y — u ' • ( 5 ) ( 6 ) This equation is true for every corresponding value of u , y and x ; but when x = x ' , y = u ' , and y น -- = - u ' u ' u ' · u ' u ' = 1 ; whence ...
... whence -- น u ' u ' y - = a - x " dx x x ' du ' = a dx x - - du'i y — u ' • ( 5 ) ( 6 ) This equation is true for every corresponding value of u , y and x ; but when x = x ' , y = u ' , and y น -- = - u ' u ' u ' · u ' u ' = 1 ; whence ...
Page 15
... whence , making xx ' , we get - น -- dy ' = ( ( x ) = x ( x2 ) dx - = P. NOTE ON THE CORRECTION OF AN ERROR IN THE THEORY OF POLY- CONIC PROJECTIONS , BY PROF . W. W. JOHNSON . IN the publications of the Coast Survey * it is erroneously ...
... whence , making xx ' , we get - น -- dy ' = ( ( x ) = x ( x2 ) dx - = P. NOTE ON THE CORRECTION OF AN ERROR IN THE THEORY OF POLY- CONIC PROJECTIONS , BY PROF . W. W. JOHNSON . IN the publications of the Coast Survey * it is erroneously ...
Page 27
... whence we easily obtain α r + rp ' ÷ p !! c + a 2 ° — · b ) = r ' ' ( a + b — c ) . - b a + b — с = b = الوب ا rr с jol + ppl ÷ p !! r + The triangle required is therefore similar to the one whose sides are r + ppp ! ÷ p !! , gol + gpp ...
... whence we easily obtain α r + rp ' ÷ p !! c + a 2 ° — · b ) = r ' ' ( a + b — c ) . - b a + b — с = b = الوب ا rr с jol + ppl ÷ p !! r + The triangle required is therefore similar to the one whose sides are r + ppp ! ÷ p !! , gol + gpp ...
Page 28
... whence 4y + 4x2- · 4ax + c2 . 462 -4d 2ac Substituting this value of cos 7 in ( 7 ) and ( 8 ) we obtain 4ab 8ax — 4y2 — 4x22 + 462 + 4d COS α = cos B 4a2 - 4y3 = Adding ( 2 ) and ( 3 ) we have 4y4x2 - c2 + 463 + 4d3 4ad b cos ad cos 8 + ...
... whence 4y + 4x2- · 4ax + c2 . 462 -4d 2ac Substituting this value of cos 7 in ( 7 ) and ( 8 ) we obtain 4ab 8ax — 4y2 — 4x22 + 462 + 4d COS α = cos B 4a2 - 4y3 = Adding ( 2 ) and ( 3 ) we have 4y4x2 - c2 + 463 + 4d3 4ad b cos ad cos 8 + ...
Page 36
... Whence it is obvious that La- place's Theorem will be found by simply changing in ( 8 ) , Ft into Ff't , and ft into ff't . That is , ( 16 ) Fx = Ff't + eff't dFf't + 1 d dt 1.2 dt ( fft . d . FS't ) + ... dt In the case of several ...
... Whence it is obvious that La- place's Theorem will be found by simply changing in ( 8 ) , Ft into Ff't , and ft into ff't . That is , ( 16 ) Fx = Ff't + eff't dFf't + 1 d dt 1.2 dt ( fft . d . FS't ) + ... dt In the case of several ...
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5th degree a₁ algebraic ANALYST angle ARTEMAS MARTIN assumed axis b₁ C₁ circular coefficients common logarithms constant curve denote determine differential distance E. B. SEITZ ellipse Elliptic Functions equal equation expression factor formula function given circle gives hence hyperbola integral intersection inverse Lagrange's Theorem locus logarithms method multiply observations orbital orbital force ORSON PRATT oxen parabola parallel perpendicular plane points at infinity position probable error quadrics quadrilateral radius ratio reduce represent result roots sides SOLUTION BY PROF SOLUTIONS of problems sphere square substitution surface tangent Taylor's Theorem Theorem tion triangle UNION SPRINGS unknown quantities values velocity whence zero