The Method of Fluxions And Infinite Series With Its Application to the Geometr
The Method of Fluxions And Infinite Series With Its Application to the Geometr
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Again, if we make A= 4^' -f- x*, and B 4^ -f- ax, by Subftitution we fliall have the Fraction . T5 -(- 48a*. V4 -f- i Zfi4, * -f- zqSjt . * * +1*9, .
nearer Approximation to the Root. And taking this Numerator for A, and the Denominator for B, we fliall approach nearer ftill. But this laft Approximation is fo near, that if we only take the firft five Terms of the Numerator, and divide them by the firft five Terms of the Denominator, (which, if rightly managed, will be no troublefome Operation, ...) we fliall have the fame five Terms of the Series, fo often found already.
And the Theorem will converge fo faft on this, and fuch like oc- -cafions, that if we here take the firft Approximation A = a, (ma- king B = i, ) we fliall have y = -^ ^ **, &c. = a ~x, &cc. . And if again we make this the fecond Approximation, or A a t*, (making B = i, ) we fliall have y = 4 a ax ~T -i * 4 5 1 z 4 if again we make this the third Approximation, or A=:a _ &c. (making 'B== J, ) we fliall have the Value of the D ti& ^ * *-** true Root to eight Terms at this Operation.
What to read after The Method of Fluxions And Infinite Series With Its Application to the Geometr?
You can find similar books in the "Read Also" column, or choose other free books by Isaac Newton to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Again, if we make A= 4^' -f- x*, and B 4^ -f- ax, by Subftitution we fliall have the Fraction . T5 -(- 48a*. V4 -f- i Zfi4, * -f- zqSjt . * * +1*9, .
nearer Approximation to the Root. And taking this Numerator for A, and the Denominator for B, we fliall approach nearer ftill. But this laft Approximation is fo near, that if we only take the firft five Terms of the Numerator, and divide them by the firft five Terms of the Denominator, (which, if rightly managed, will be no troublefome Operation, ...) we fliall have the fame five Terms of the Series, fo often found already.
And the Theorem will converge fo faft on this, and fuch like oc- -cafions, that if we here take the firft Approximation A = a, (ma- king B = i, ) we fliall have y = -^ ^ **, &c. = a ~x, &cc. . And if again we make this the fecond Approximation, or A a t*, (making B = i, ) we fliall have y = 4 a ax ~T -i * 4 5 1 z 4 if again we make this the third Approximation, or A=:a _ &c. (making 'B== J, ) we fliall have the Value of the D ti& ^ * *-** true Root to eight Terms at this Operation.
What to read after The Method of Fluxions And Infinite Series With Its Application to the Geometr?
You can find similar books in the "Read Also" column, or choose other free books by Isaac Newton to read onlineMoreLess
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