The Fluxional Calculus: An Elementary Treatise ...Baldwin, Cradock and Joy, 1826 |
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Página 8
... root . Examples to the preceding rules . u = a + bx .. du bdx . u = x3 .. du = 3x2dx . 3 u = zx22 .. du = x2dx . u = 1 XC 1 - dx .. du = x2 - ndx u = n du = xn + 1 u = √2ax + x2 .. du ( a + x ) dx 2 = √2ax + x2 u = ( a2 + x2 ) 3 .. du ...
... root . Examples to the preceding rules . u = a + bx .. du bdx . u = x3 .. du = 3x2dx . 3 u = zx22 .. du = x2dx . u = 1 XC 1 - dx .. du = x2 - ndx u = n du = xn + 1 u = √2ax + x2 .. du ( a + x ) dx 2 = √2ax + x2 u = ( a2 + x2 ) 3 .. du ...
Página 38
... root . n - 1 Examples . 1 Sn . ( am + x1 ) n − 1m xm − 1 dx 1. ( am + xmn - 1 xm - 1 dx = 1 == mn ( am + xm ) " . • m n 2. f ( a + x ) 3 dx = ± ( a + x ) 1 . 8. J ( a + x y xdz = f ( a + 4. J ( a + x ) xdx = } ( a + c ) = . Or thus , ...
... root . n - 1 Examples . 1 Sn . ( am + x1 ) n − 1m xm − 1 dx 1. ( am + xmn - 1 xm - 1 dx = 1 == mn ( am + xm ) " . • m n 2. f ( a + x ) 3 dx = ± ( a + x ) 1 . 8. J ( a + x y xdz = f ( a + 4. J ( a + x ) xdx = } ( a + c ) = . Or thus , ...
Página 52
... root or the cube or any other root L of y be repeatedly extracted till y — 1 becomes a decimal with a great many zeros , the series converges , and we obtain an approximate value of Ly . I The process is not so tedious as it may appear ...
... root or the cube or any other root L of y be repeatedly extracted till y — 1 becomes a decimal with a great many zeros , the series converges , and we obtain an approximate value of Ly . I The process is not so tedious as it may appear ...
Página 53
... root be performed as in the preceding article , we shall obtain another approxi- mate value of Ly , and this is evidently less than the true value . If then we calculate both values corresponding to the same number n , we shall know to ...
... root be performed as in the preceding article , we shall obtain another approxi- mate value of Ly , and this is evidently less than the true value . If then we calculate both values corresponding to the same number n , we shall know to ...
Página 57
... root = the three cube roots.of it will appear that its square root = √1 ; - 1 , one of which is possible and = -1 ; its biquadratick roots are all im- possible , & c . & c . - Ex.1.2 / —a ./— b = 2 / avi / −12 / −1 = ÷ / ab ( √ — I ...
... root = the three cube roots.of it will appear that its square root = √1 ; - 1 , one of which is possible and = -1 ; its biquadratick roots are all im- possible , & c . & c . - Ex.1.2 / —a ./— b = 2 / avi / −12 / −1 = ÷ / ab ( √ — I ...
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Términos y frases comunes
absc abscissa assume asymptote axis bx² centre circle co-ordinates conjugate point consequently cos.x curvature curve cusp d³u differentiating draw dx dx dx dy dx² dxdy dy dx dy dy ellipse equal F(x+h finite fluent fluxional coefficients fluxional equations function given point hence hyperbola hyperbolick increment infinite inflexion integrated intersection latus rectum limit logarithms maxima and minima maximum minimum negative ordinate origin parabola parallel partial fluxions perpendicular polar equation positive radius ratio required equation right angles right line sin.x sine solid spiral substitution subtangent suppose supposition surface tangent plane Taylor's theorem vanish variables velocity vertex whence xn+1
Pasajes populares
Página 241 - Shew that the sum of the products of each body into the square of its velocity is a minimum, when the velocities are reciprocally proportional to the quantities of matter in the bodies.
Página 17 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Página 32 - Ultimae rationes illae quibuscum quantitates evanescunt, revera non sunt rationes quantitatum ultimarum, sed limites ad quos quantitatum sine limite decrescentium rationes semper appropinquant, & quas propius assequi possunt quam pro data quavis differentia, nunquam vero transgredi, neque prius attingere quam quantitates diminuuntur in infinitum.
Página 32 - By the philosophical use of words, I mean such an use of them as may serve to convey the precise notions of things, and to express, in general propositions, certain and undoubted truths which the mind may rest upon and be satisfied with, in its search after true knowledge.
Página 229 - ... positions in which it will rest in equilibrium. 13. A machine, driven by the impulse of a stream, produces the greatest effect when the wheel moves with one-third of the velocity of the water. 14. At a place whose latitude is 48°. 50'. 14", the meridian altitude of the spn's upper limb was observed to be 62°. 29'.
Página 32 - By their civil use, I mean such a communication of thoughts and ideas by words as may serve for the upholding common conversation and commerce about the ordinary affairs and conveniences of civil life, in the societies of men one amongst another.
Página 226 - A known weight (P) at the extremity of a rod which passes through two small rings fixed in the same vertical line, by its pressure puts a solid inclined plane in motion along an horizontal table; given the weight of the plane, find its elevation sothatthe velocity communicated to it in a given time may be a maximum.
Página 60 - The sines and cosines of multiple arcs may also be developed in terms of the powers of the sine and cosine of the simple arc, by help of a remarkable formula, known by the name of De Moivre's formula, which may be easily established, as follows.
Página 17 - The logarithms of the same number in different systems are to each other as the moduli of those systems. This is evident from the general logarithmic series. Thus the logarithm of 1 + x in a system whose modulus is m...
Página ii - Angli, nomine magis idoneo, quantitates fluentes vocant, et earum incrementa infinite parva seu evanescentia fluxiones nominant, ita ut fluxiones ipsis idem sint, quod nobis differentialia. Haec diversitas loquendi ita jam usu invaluit, ut conciliatio vix unquam sit expectanda : equidem Anglos in formulis loquendi lubenter imitarer, sed signa, quibus nos utimur, illorum signis longe anteferenda videntur.