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" "There were some, however, who disliked the... use of infinites and infinitesimals in geometry. Of this number was Sir Isaac Newton (whose caution was almost as distinguishing a part of his character as his invention), especially after he saw that this liberty was growing to so great a height. In demonstrating the grounds of the method of fluxion, he avoided them, establishing it in a way more agreeable to the strictness of geometry.
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.
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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.
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He considered magnitudes as generated by a or motion, and showed how the velocities of the generating motions were to be compared together. There was nothing in this doctrine but what seemed to be natural and agreeable to the antient geometry. But what he has given us on this subject being very short, his conciseness maybe supposed to have given some occasion to the objections which have been raised against his method.