Examples of the Processes of the Differential and Integral CalculusJ. and J.J. Deighton, 1846 - 529 стор. |
З цієї книги
Результати 1-5 із 27
Сторінка 37
... quantities dp , dq , dr . Supposing we eliminate the last two we have da Mdp , M being a function of p , q , r . From this it follows that when dx = 0 , dp = 0. Hence supposing y to vary while a and ≈ are constant we have dy = Q1dq + ...
... quantities dp , dq , dr . Supposing we eliminate the last two we have da Mdp , M being a function of p , q , r . From this it follows that when dx = 0 , dp = 0. Hence supposing y to vary while a and ≈ are constant we have dy = Q1dq + ...
Сторінка 67
... quantities as before , b a " + ẞ " = ( ) { ca n + b b n ( n − 3 ) c2 a2 + & c . 1.2 b ? _b ? & c . } , b continued so long as there are positive powers of ( 12 ) Let u = m + e sin u . Expand u and sin u in terms of e . The expression ...
... quantities as before , b a " + ẞ " = ( ) { ca n + b b n ( n − 3 ) c2 a2 + & c . 1.2 b ? _b ? & c . } , b continued so long as there are positive powers of ( 12 ) Let u = m + e sin u . Expand u and sin u in terms of e . The expression ...
Сторінка 99
... quantities , the result will be equal to v = x ( x + 2 ) . dv 27 If ∞ = 0 ; v = 0 , = x + 2 = 2 , u = a minimum ; > dx 4 dv X = - 2 ; v = 0 , = α = - · 2 , u , a maximum . dx ( 9 ) ) ( 10 ) ( x − 1 ) 2 u = ( x + 1 ) 3 ° x = 5 gives u ...
... quantities , the result will be equal to v = x ( x + 2 ) . dv 27 If ∞ = 0 ; v = 0 , = x + 2 = 2 , u = a minimum ; > dx 4 dv X = - 2 ; v = 0 , = α = - · 2 , u , a maximum . dx ( 9 ) ) ( 10 ) ( x − 1 ) 2 u = ( x + 1 ) 3 ° x = 5 gives u ...
Сторінка 111
... quantities λ from the conditions that they make the terms involving da1 , dx2 , ... da , vanish , that is to say , if we determine them by the conditions M1 = 0 , M2 = 0 , ... M1 = 0 , + Mécanique Analytique , Vol . 1. p . 74 . the ...
... quantities λ from the conditions that they make the terms involving da1 , dx2 , ... da , vanish , that is to say , if we determine them by the conditions M1 = 0 , M2 = 0 , ... M1 = 0 , + Mécanique Analytique , Vol . 1. p . 74 . the ...
Сторінка 112
... quantities ~ and the r quantities à satisfy the n + r equations , M1 = 0 , M2 M2 = 0 ... M = 0 , L1 = 0 ... L , = 0 . As it is indifferent which of the variables we eliminate in order to determine A , ... A ,, the most general way of ...
... quantities ~ and the r quantities à satisfy the n + r equations , M1 = 0 , M2 M2 = 0 ... M = 0 , L1 = 0 ... L , = 0 . As it is indifferent which of the variables we eliminate in order to determine A , ... A ,, the most general way of ...
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a² b2 a²x² angle arbitrary constant asymptote becomes C₁ c²x² Cambridge circle co-ordinates condition Crelle's Journal curvature curve cycloid determine differential coefficients differential equation dx dx dx dy dx dy dx dx² dy dx dy dy dy dy dz dz dz eliminate ellipse equal Euler factor formula fraction function Geometry gives Hence hypocycloid infinite intersection John Bernoulli Let the equation lines of curvature locus logarithmic logarithmic spiral Multiply negative origin parabola perpendicular plane of reference radius SECT singular solution spiral Substituting subtangent surface tangent plane theorem triangle vanish whence x²)³