# The Fluxional Calculus: An Elementary Treatise ...

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### Contenido

 Explanation of Terms Page 1 Circular functions 21 Infinitesimals 30 On Integration 36 On finding the first fluxions of 105 On the different orders of fluxions 121 Eulers theorem 186 Maxima and minima functions of 207
 Lines and surfaces 250 Points in space 293 Tangents normals asymptotes 297 the rectifica 327 Spirals 373 involutes and evolutes 392 Singular points of curves 419 Orders of inflexion 443

### 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.