## A treatise on infinitesimal calculus, Volume 2 |

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Page xxviii

... limits are given by an equation of condition . . . . . . . . . . 446 313 . Simplification

when the element - function contains partial derived functions of only the first

order . . . . . . 447 314 . The calculus of variations

infinite ...

... limits are given by an equation of condition . . . . . . . . . . 446 313 . Simplification

when the element - function contains partial derived functions of only the first

order . . . . . . 447 314 . The calculus of variations

**considers**a function of aninfinite ...

Page 3

In the early part of the treatise I shall

shall assume the infinitesimal element to be of the form f ( x ) dx , and the superior

and inferior limits to be respectively & , and Xo ; so that Xn — X is the range of ...

In the early part of the treatise I shall

**consider**functions of one variable ; and Ishall assume the infinitesimal element to be of the form f ( x ) dx , and the superior

and inferior limits to be respectively & , and Xo ; so that Xn — X is the range of ...

Page 8

... whatever is the mode of partition , the value of the indefinite integral is the

same , as may thus be shewn : Whatever another mode is , we may

be a subdivision of the first , and thus its elements to be parts of the former

elements .

... whatever is the mode of partition , the value of the indefinite integral is the

same , as may thus be shewn : Whatever another mode is , we may

**consider**it tobe a subdivision of the first , and thus its elements to be parts of the former

elements .

Page 35

... which we have to

* + v – Isin mit ; 2 – cos 2 * - V = Isin 25 1 - cos n ! - CO n . . . . . . . . . . . . pa . . . . . . . .

. Combining the pairs of conjugate partial fractions according to equation 23 . ] ...

... which we have to

**consider**the function . Therefore the coefficient of - is ; { cos 2* + v – Isin mit ; 2 – cos 2 * - V = Isin 25 1 - cos n ! - CO n . . . . . . . . . . . . pa . . . . . . . .

. Combining the pairs of conjugate partial fractions according to equation 23 . ] ...

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### Common terms and phrases

according angle application approximate axis becomes Calculus called Chapter circle consequently consider constant contained continuous convergent coordinates corresponding curve definite integral denoted determined difference differential divergent divided dy dx effected element element-function ellipse employed equal equation equivalent evaluation evidently examples expressed finite formulæ fraction function Gamma-function geometrical give given greater Hence included increases infinite infinitesimal involute latter length less let us suppose limits means method multiple negative observed origin particular periodic plane positive possible preceding PRICE problem properties quantity radius range of integration refer replaced respectively result right-hand member similar substituting successive surface symbols taken theorem tion transformation values variables varies volume whole