 | Silvestre François Lacroix - 1816 - 762 lapas
...make a = versed sine, we have chord _ ^~^lc \'~¿ VJZ ' but the limit of v 2 - j is v <¿, since it may be made to differ from it by a quantity less than any assignable ; we may consequently conclude, that the limit of this ratio is •7=-» or 1 ; or in other... | |
 | Euclides - 1821 - 294 lapas
...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 - 1851 - 300 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... | |
 | Charles Davies, William Guy Peck - 1857 - 608 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... | |
 | Elias Loomis - 1859 - 320 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, *'+y'=R', the value of y increases... | |
 | John Merry Ross - 1877 - 625 lapas
...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 - 666 lapas
...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... | |
 | Charles Scott Venable - 1881 - 380 lapas
...limits A and B of the variables, differ by a quantity D. Then, as the variable which has A for a limit may be made to differ from it by a quantity less than -JD, and the second variable may be made to approach B to within less than £D, the variables would... | |
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... to the area of the circle than that of the first. 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.... 