## A treatise on infinitesimal calculus, Volume 2 |

### From inside the book

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Page xix

given by the forms of definite integrals 147 117 . Bernoulli ' s series for

s series ...

**Approximation**by means of known integrals . . . . . . 116 .**Approximate**valuesgiven by the forms of definite integrals 147 117 . Bernoulli ' s series for

**approximate**value . . . . . . . . . 150 118 .**Approximate**value deduced from Taylor 's series ...

Page 90

( n - 3 ) ( n - 1 ) and therefore if n is a very large number , we have the following

. ' an equivalent for a which was first discovered by Dr . Wallis , and will be of ...

( n - 3 ) ( n - 1 ) and therefore if n is a very large number , we have the following

**approximate**value of TT , 2 . 2 . 4 . 4 . 6 . 6 . . . . . . . ( 15 ) * * 1 . 3 . 3 . 5 . 5 . 7 . . . . .. ' an equivalent for a which was first discovered by Dr . Wallis , and will be of ...

Page 139

... by any of the methods explained in the preceding sections , yet there are many

methods by which an

limits also can be determined within which the error of

... by any of the methods explained in the preceding sections , yet there are many

methods by which an

**approximate**value of it can frequently be found ; and thelimits also can be determined within which the error of

**approximation**lies . Page 141

A small value of n will be sufficient for a first

of considerable practical use . ... s dx · I have chosen one , the value of which is

known , that the

A small value of n will be sufficient for a first

**approximation**, and this is frequentlyof considerable practical use . ... s dx · I have chosen one , the value of which is

known , that the

**approximate**results may be compared with the true result . Page 142

If however the number of parts into which the range is divided is finite , and the

sum of the elementfunctions corresponding to these is calculated , that sum will

be only an

...

If however the number of parts into which the range is divided is finite , and the

sum of the elementfunctions corresponding to these is calculated , that sum will

be only an

**approximate**expression for the value of the area . For suppose mn , in...

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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 formulę 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