## A treatise on infinitesimal calculus, Volume 2 |

### From inside the book

Page xxiv

315 230 . Investigation of the surface - element in terms of r and p . . . 316 231 .

Quadrature of a surface between a curve , its evolute , and two bounding radii of

curvature . . . . . . . . 317 SECTION 3 . - Quadrature of Surfaces of

.

315 230 . Investigation of the surface - element in terms of r and p . . . 316 231 .

Quadrature of a surface between a curve , its evolute , and two bounding radii of

curvature . . . . . . . . 317 SECTION 3 . - Quadrature of Surfaces of

**Revolution**. 232.

Page xxv

Cubature of Solids of

when the axis of ac is the axis of

illustration 253 . Investigation of volume - element , when axis of y is that of

Cubature of Solids of

**Revolution**. 251 . Investigation of the volume - element ,when the axis of ac is the axis of

**revolution**. . . . . . . . . . . . . . 252 . Examples inillustration 253 . Investigation of volume - element , when axis of y is that of

**revolution**. Page 217

differential equation of the curve , if s is measured from the point where 0 = , 0 = 0

, s = a sec ale - ) ; so that when the curve reaches the pole and 6 = 7 , 8 = sec a ; ·

in which case $ = 0 ; whence it appears that the number of

differential equation of the curve , if s is measured from the point where 0 = , 0 = 0

, s = a sec ale - ) ; so that when the curve reaches the pole and 6 = 7 , 8 = sec a ; ·

in which case $ = 0 ; whence it appears that the number of

**revolutions**made by ... Page 316

... sb , sc , severally be the values of the radius vector after n - 1 , n , and n + 1

complete

the first

nth ...

... sb , sc , severally be the values of the radius vector after n - 1 , n , and n + 1

complete

**revolutions**, so that SA = 2 ( n - 1 ) ... therefore the area generated inthe first

**revolution**of the radius vector is 873 a ” ; and hence that generated in thenth ...

Page 317

To find the area contained between an epicycloid and its base - circle during one

the equation to the curve is ( a + 26 ) 2 p = ani therefore the area contained ...

To find the area contained between an epicycloid and its base - circle during one

**revolution**of the generating circle ; see fig . 42 , Vol . I . By ( 9 ) , Art . 268 , Vol . I ,the equation to the curve is ( a + 26 ) 2 p = ani therefore the area contained ...

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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