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But, because the Method of Infinitesimals is much in use, and is valued for its conciseness, I thought it was requisite to account explicitly for the… - Colin MacLaurin
" "But, because the Method of Infinitesimals is much in use, and is valued for its conciseness, I thought it was requisite to account explicitly for the truth, and perfect accuracy of the conclusions that are derived from it; the rather, that it does not seem to be a very proper reason that is assigned by Authors, when they determine what is called the Difference (but more accurately the ) of a Quantity, and tell us, That they reject certain Parts of the Element, because they become infinitely less than the other parts; not only because a proof of this nature may leave some doubt as to the accuracy of the conclusion, but because it may be demonstrated that those parts ought to be neglected by them at any rate, or that it would be an error to retain them.
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About Colin MacLaurin
Colin Maclaurin (February 1698 – 14 June 1746) M'Laurine, or MacLaurin, was a Scottish mathematician who made important contributions to geometry and algebra. He is also known for being a child prodigy and holding the record for being the youngest professor. The Maclaurin series, a special case of the Taylor series, is named after him.
Biography information from Wikiquote
Also Known As
Native Name:
Colin Maclaurin
•
Cailean MacLabhruinn
Alternative Names:
Colin M'laurine
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Additional quotes by Colin MacLaurin
If, upon the whole, the Evidence of this method be represented to the satisfaction of the Reader, some of the abstruse parts illustrated, or any improvements of this useful Art be proposed, I shall be under no great concern, though exceptions may be made to some modes of Expression, or to such Passages of this Treatise as are not essential to the principal design.
In the method of indivisibles, lines were conceived to be made up of points, surfaces of lines,and solids of surfaces; and such suppositions have been employed by several ingenious men for proving the old theorems, and discovering new ones, in a brief and easy manner. But as this doctrine was inconsistent with the strict principles of geometry, so it soon appeared that there was some danger of its leading them into false conclusions: therefore others, in the place of indivisible, substituted infinitely small divisible elements, of which they supposed all magnitudes to be formed; and thus endeavoured to retain, and improve, the advantages that were derived from the former method for the advancement of geometry.
The greatest part of the first Book was printed in 1737: but it could not have been so useful to the Reader without the second; and I... recommend... to peruse the first Chapters of the second Book, before the five last of the first; there being a few passages... that will be better understood by... [having] some knowledge of the principal Rules of the Method of Computation... in the second Book.
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