## A treatise on infinitesimal calculus, Volume 2 |

### From inside the book

Results 1-5 of 22

Page xxiv

Quadrature of Surfaces of

319 233. The area of a surface, when the generating plane curve revolves about

the axis of y 321 234. The area of a surface of

Quadrature of Surfaces of

**Revolution**. 232. Investigation of the surface-element319 233. The area of a surface, when the generating plane curve revolves about

the axis of y 321 234. The area of a surface of

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