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" By continuing to double the number of sides, the area of the polygon will approach nearer and nearer to that of the circle, and- may be made to differ from it by a quantity less than any finite quantity. "
Principles of the Differential and Integral Calculus: Familiarly Illustrated ... - 2. lappuse
autors: William Ritchie - 1836 - 174 lapas
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An Elementary Treatise on the Differential and Integral Calculus

Silvestre François Lacroix - 1816 - 720 lapas
...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...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

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...
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Elements of Analytical Geometry and of the Differential and Integral Calculus

Elias Loomis - 1851 - 278 lapas
...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...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - 1855 - 592 lapas
...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...
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the globe encyclopaedia of universal information

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...
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The Globe encyclopaedia of universal information, ed. by J.M. Ross, 4. sējums

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...
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