| Silvestre François Lacroix - Calculus - 1816 - 720 pages
...its sine : if we make x = versed sine, we have chord sine but the limit of V 2 - x is ^"57 since it **may be made to differ from it by a quantity less than any** assignable 5 we may consequently conclude, that the limit of this ratio is -ri, or 1 5 or in other... | |
| Euclides - 1821
...the radii. Pf 1 7. The area of the circumscribed polygon = -jj- .-. since the area of a circle can **be made to differ from it by a quantity less than any** assignable, the area- of the circle = «• ?•*. ON PORISMSSomething still remains to be said on... | |
| Elias Loomis - Calculus - 1851 - 278 pages
...inscribe another polygon having twice the number of sides, the area of the second will come nearer **to the area of the circle than that of the first....quantity. Hence the circle is said to be the limit of** all its inscribed polygons. So, also, in the equation of a circle, z°+y'=R', the value of y increases... | |
| Charles Davies, William Guy Peck - Mathematics - 1855 - 592 pages
...inscribed in a circle, and the number of sides be increased, the area of the inscribed polygon approaches **that of the circle, and may be made to differ from it by** less than any assignable quantity ; finally, when the number of sides becomes infinite, we may regard... | |
| john m. ross - 1877
...series, which in the former case, however far taken, never reach a cer236 tain finite value, though they **may be made to differ from it by a quantity less than any** given quantity, and which in the latter case may be made of greater value than any given quantity by... | |
| Globe encyclopaedia - 1878
...never reaches the value 2, but it continually approaches it, and by taking a sufficient number of terms **may be made to differ from it by a quantity less than** the smallest assignable but finite quantity ; 2 is the L. of the series. Similarly, the area of a polygon... | |
| |