## A Treatise on Infinitesimal Calculus: Differential calculus. 1857 |

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Results 1-5 of 52

Page xv

The relation between y and its

has been successively increased n times 115 69. 70. Modification of the

preceding, when * is equicrescent . . 116 71. Taylor's Series 119 72. Limits of

Taylor's ...

The relation between y and its

**equivalent**/ (x), of the equation y = f (x). when xhas been successively increased n times 115 69. 70. Modification of the

preceding, when * is equicrescent . . 116 71. Taylor's Series 119 72. Limits of

Taylor's ...

Page xvi

Transformation of expressions involving partial derived - functions into their

preceding principles .... 182 CHAPTER IV. CERTAIN RELATIONS BETWEEN ...

Transformation of expressions involving partial derived - functions into their

**equivalents**in terms of other variables 180 107, 108. Examples illustrative of thepreceding principles .... 182 CHAPTER IV. CERTAIN RELATIONS BETWEEN ...

Page 10

Thus 2x3 = 6, and 6 is an abstract number of the same kind as 2 and 3 ; that is,

twice thrice is

is twice. The same is also true of the operations of Involution and Evolution.

Thus 2x3 = 6, and 6 is an abstract number of the same kind as 2 and 3 ; that is,

twice thrice is

**equivalent**to six times; 8-h4=2, that is, one-fourth part of eight timesis twice. The same is also true of the operations of Involution and Evolution.

Page 42

e^ — l = dx; replacing therefore e^ — 1 by its

and omitting dx when added to the finite quantity x, we have . exdx ~ {e' + l}2" If

therefore ex ex /(*) = ITTT' A*) = e* + l' J v ' {e'+l}2 Ex. 4. To differentiate coax sin

2x.

e^ — l = dx; replacing therefore e^ — 1 by its

**equivalent**in the above equation,and omitting dx when added to the finite quantity x, we have . exdx ~ {e' + l}2" If

therefore ex ex /(*) = ITTT' A*) = e* + l' J v ' {e'+l}2 Ex. 4. To differentiate coax sin

2x.

Page 45

Let the reader therefore be careful as to the meaning of the symbol it : it is a

number, and a number only. By some authors it has been used as

two right angles or 180°: such an use is incorrect as to form ; and although

commonly ...

Let the reader therefore be careful as to the meaning of the symbol it : it is a

number, and a number only. By some authors it has been used as

**equivalent**totwo right angles or 180°: such an use is incorrect as to form ; and although

commonly ...

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### Common terms and phrases

algebraic curves algebraical angle asymptote axis becomes Calculus change of sign changes sign circle coefficients conic constant coordinates corresponding critical values curvature cycloid decreases determine direction double point drawn dy _ elimination ellipse epitrochoid equa equal equicrescent equivalent explicit function expression factors finite quantity geometrical given point Hence homogeneous homogeneous function hyperbola hypocycloid hypotrochoid imaginary increases infinitesimal Infinitesimal Calculus infinity involving l)th let us suppose logarithmic maxima and minima maximum or minimum minimum value negative normal nth degree number of points observed ordinate parabola parallel partial derived-functions pass perpendicular plane curve plane of reference point of inflexion points of intersection polar positive properties radius real roots right-hand member roots of f(x shewn Similarly singular value straight line substituting symbol tangent Theorem tion Tractory triangle vanish whence Witch of Agnesi zero

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