It seems but just to trace and commemorate the inventors of the ingenious arts which furnish matter for discourses on these occasions; and not only the main inventors, but even those who first turned their thoughts upon the subject: for, though such men may not have produced any thing perfect, yet they may have suggested ideas to others of a less inventive, but of a more executive genius, and who, unprovided with those hints, would never have made any notable discovery. I must therefore observe, that the _Italians_ were the first who emerged out of those thick clouds of ignorance and barbarism which had so long overspread this quarter of the world. They profited by the unhappy fate of Constantinople; for by liberally receiving the learned emigrants on that distressful occasion, they were largely repaid by their arts and sciences, and still more abundantly by their language, whereby they were enabled to read and to translate those ancient manuscripts, which the Greeks had saved out of the wreck of their country. The art of printing, which was established soon after, was the means of quickly disseminating those treasures of knowledge, and concurred with the fall of the eastern empire to form an epoch for the advancement of learning, unparalleled in the annals of letters. The end of the 15th century, and the whole of the 16th, were chiefly employed by the Italians in the study and in the translation of the old Greek authors. The geometry of the ancient Greeks, as well as the arithmetic in numbers and species of the Arabians, were cultivated; but both remained, as it were, sciences by themselves, unassisting to, or at best but weak and reluctant auxiliaries to the philosophy of the schools: and indeed how could the abstracted doctrines of numbers and quantities be strained to co-operate with a system, in which neither the laws of motion, nor any but the superficial, and often delusive properties of matter, were to be met with? The genius of the Greeks, all acute and brilliant as it was, had never been properly directed to the interpretation of nature, and was indeed unfit (as Lord Bacon pronounced) for a study that made so slow and painful a progress, by re-iterated and varied experiments and observations. It was no wonder then, if the _mixed mathematics_, as they are called, descended to the moderns in a state no-wise corresponding to the elegance and certainty of those parts of the science which were elementary and pure; and that those mixed parts should have been found defective and erroneous, in proportion (if I may so express myself) to the physical considerations that were to be taken into the inquiry. The imperfection of the ancients, with regard to natural philosophy, was not perceived at that time; nay, at the period we are treating of, the learned were firmly persuaded of the contrary, and that all that was wanting to be known concerning the laws of nature, and the properties of matter, was to be taken either directly, or by deduction,