31/03/2017 · Kids learn about Isaac Newton's biography
Sir Isaac Newton Biography for Kids – Founder of Calculus
The part of the appendix which I have just described is practically the same as Newton's manuscript De Analysi per Equationes Numero Terminorum Infinitas, which wa subsequently printed in 1711. It is said that this was originally intended to form an appendix to Kinckhuysen's Algebra, which, as I have already said, he at one time intended to edit. The substance of it was communicated to Barrow, and by him to Collins, in letters of July 31 and August 12, 1669; and a summary of it was included in the letter of October 24, 1676, sent to Leibnitz.
My aim in life very short essay on dreams
but naturally the results are expressed as infinite series. He then proceeds to curves whose ordinate is given as an implicit function of the abscissa; and he gives a method by which y can be expressed as an infinite series in ascending powers of x, but the application of the rule to any curve demands in general such complicated numerical calculations as to render it of little value. He concludes this part by shewing that the rectification of a curve can be effected in a somewhat similar way. His process is equivalent to finding the integral with regard to x of (1 + y2)1/2 in the form of an infinite series. I should add that Newton indicates the importance of determining whether the series are convergent — an observation far in advance of his time—but he knew of no general test for the purpose; and in fact it was not until Gauss and Cauchy took up the question that the necessity of such limitations was commonly recognized.