CHAP. IX. MATHEMATICS-DR. BARROW, SIR ISAAC NEWTON, MR. WHISTON, AND OTHERS. MATHEMATICS, by the ancients, was called by eminence the learning, and diva mathesis, the divine mathematics; yet not till a late period did Cambridge University cultivate it, with much devotion or success a: but having, at length, found the true avenue to it's temple, they have approached to it's most intimate recesses. Though there were doubtless (before the time of Dr. Barrow) men of much mathematical knowledge at Cambridge (of whom notice will incidentally be taken in the proper place), yet the mathematical age properly commences with him: his Præ-lectiones Mathematicæ, being the book that preceded in Whiston goes on: et pudeat nobis non immerito; his præsertim temporibus, quibus scientiæ mathematicæ florent alias ubiq., et excoluntur; quibusq. veram Physicam a Mathesi dependere unice, sit adeo certum et exploratum. Quinimo illud vel maxime fuit opprobrio, quod jam tum mathemata nobis academicis minimæ fuerunt curæ, cum Ducem et Professorem ipsum Newtonum, Geometrarum hujus Ævi, ne quid amplius jam dicam, facilè Principem, habuerimus. Prælec. Astron. Hab. Cantab. Anteloquium. 1707. course of due mathematical investigation. He was born in 1630, and was appointed Master of Trinity College by Charles II. Other eminent mathematicians were nearly contemporary with him, such as Dr. Smith, and Mr. Cotes, of Trinity College, and Mr. Whiston, of Clare Hall, and others. But they may all be considered as the precursors, or the genuine succesors, of Sir Isaac Newton. Newton was of Trinity College, was born at Woolsthorpe, in Lincolnshire, in 1642, and lived to a good old age, though all his discoveries were made and completed in the earlier period of his life. He died in 1727. His great work, Naturalis Philosophia Principia Mathematica, was first printed in 1687. It was the same light which beamed on Bacon, which guided Newton to his discoveries: what the former considered as desiderata, the latter supplied. Prior to their time, the mode of philosophizing consisted in assigning to each species of things their specific, and occult qualities, from which all the operations of bodies, by some unknown, mysterious order, proceeded: this was the philosophy of the peripatetics, and having been implicitly adopted by the schoolmen, has been since called the Scholastic Philosophy: they affirmed that each effect of bodies flowed from its individual nature; but whence the several natures proceeded, they did not shew; they were defective in observation and experiment, dwelling rather on the names of things, than on the things themselves. According, therefore, to the Newtonians, whose words I borrow, they had invented a philosophical language, but could not be said to have taught philosophy a. Newtoni Principia Philosophiæ Naturalis. Præf. a R. Cotes. Some, indeed, according to the statement of the Newtonians, had, emerging somewhat from this obscurity of mere words, maintained that all matter was of the same kind; and that all the variety of forms, which we see in bodies, arises from the most simple affections of their component parts: but to those affections they assigned other modes than what, it appears, has been assigned to them by nature, indulging themselves in a liberty, which however plausible to the imagination, was not founded in reality; they conceived certain unknown figures and magnitudes, positions and motions of parts, together with certain occult fluids, which, by entering the pores of the bodies, agitated them with great subtlety and force: here, too, it was insisted, they had no authority, from observation or experiment, their theory being all founded on conjecture: the Newtonians, on advancing these objections, had in view the doctrine of atoms and vortices of Descartes and his followers. The accuracy of many of their mechanical laws and deductions were admitted; but their speculations were considered as mere hypotheses, fabulam, said the Newtonians, elegantem forte et venustam, fabulam tamen concinnare dicendum esse. Thus was Newton led on to that third way of philoso phizing, called experimental: he assumed no principle that was not sanctioned by phenomena, and from the most simple principles he aimed to arrive at general causes, and original laws: hypotheses he laid down not as systems to be believed, but as questions to be tried; and he proceeded by a twofold method, which he called analytic, and synthetic he deduced the more simple powers and laws of forces from certain select phenomena; this he called analysis; and then proceeding from those single phenomena to more general and comprehensive forms, he established synthesis. Not that this way of proceeding by analysis and synthesis are novelties, they are noticed by Aristotle. But these are the rules followed by Sir Isaac Newton, in his way of philosophizing, and by these he established a theory, which was said to explain and illustrate the system of the universe. According to this theory, then, it was maintained, that all bodies had a tendency to gravitate, mutually, and to some centre; that they had a twofold force, one urging them to move forward, in a straight line, the other downward, to a center; the two forces combined forming a curve: thus he accounted for the motion of the heavenly bodies, and all proceeded on mathematical demonstrations, accompanied with the calculations of algebra. The other branches of philosophy, as well as astronomy, were, in like manner, brought to the test of experience, and subjected to mathematics and algebra. Such was the philosophy of Newton. The science which had been laid down by this great man in the profoundest speculations, was opened in a more popular manner by others, particularly by Whiston, as already observed, in the public schools.--What has been said above upon this subject, has been delivered nearly in the Newtonian's own words; and it is not necessary to proceed farther: suffice it that this philosophy, made up, as we have said, of mathematics and algebra, constitutes now the principal discipline, and prime glory, of the University of Cambridge. Thus have I attempted to lay before the readers a short account of the literature of Cambridge. I have, |