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Newton, Caleb Smith, Dollond, Ramsden, &c. Drebell, a Dutchman, is said to have invented the microscope about 1621; but Fontana assumes the honour of the discovery, which he says took place in 1618. Torricellius invented the Barometer; and the Thermometer has been ascribed to different persons, as Galileo, Father Paul, Sanctorio, and Cornelius Drebell of Alkmaer. Antonio de Dominis first explained the phenomenon of the rainbow; as did Wellebrord Smellius the laws of refraction: Columbus first observed the variation of the magnetic needle; Edward Wright discovered the true method of dividing the meridian line, and of constructing the charts usually ascribed to Mercator. Napier was the first who published a system of Logarithms, viz. in 1614, which numbers were greatly improved by Briggs. Stevinus of Bruges was the inventor of Decimal Arithmetic, 1610. Harriot was the father of modern Algebra, 1631. Geometry and Analysis are indebted to Roberval, Cavalerius, Comiers, l'Hôpital, Leibnitz, Mercator, Pascal, Wren, Sauveur, Parent, Barrow, and Wallis, for several new, useful, and interesting theories. Gassendi, Kepler, Picard, Hevelius, Flamstead, Horrox, Recciolus, Hooke, Longomontanus, Kircher, Bayer, and Galileo, were eminent in Astronomy. Des Cartes excelled in Geometry and Algebra, and was the inventor of the Cartesian Philosophy, depending on the absurd theory of the vortices, the foundation of which existed only in the imagimation of the author. Sir Isaac Newton excelled in almost every branch of knowledge, and appears to have been the highly honoured instrument, designed by Providence to dispel the mists of error which had hitherto inveloped the human mind; his discoveries and improvements in Analysis are numerous and valuable; his Doctrine of Fluxions, in addition to its extensive application, is a masterpiece of ingenuity; he first established the true theory of Light and Colours in his excellent work on Optics: he confirmed the system of Copernicus; and by his discovery of the universality of the principle of gravitation, and his newly invented Analysis, he explained and demonstrated the laws by which that system is regulated. Bacon and Boyle were among the first who taught philosophers to reason from experiment and observation, and to emancipate the human mind from that slavery to Hypothesis, in which it had been triumphantly detained for several ages by the WOL. I.

schoolmen . During this century several Institutions for the joint purposes of cultivating, extending, and registering every part of science were formed in different parts of Europe, viz. at Soissons, Beaujolois, Nismes, Angers, Bologna, Florence, Naples, Verona, Brescia, and Padua. The Royal Society at London was founded in 1660; and the Academie des Sciences at Paris in 1666; the Observatory at Paris was built in 1672; that of Flamstead House, at Greenwich, in 1676. The recent discoveries and improvements by Vieta, Des Cartes, Harriot, Newton, Leibnitz, and others, opened a new and extensive field for the exercise of talent, in every department of science. The Newtonian Analysis has been applied with equal zeal and success to some of the most difficult and interesting problems in Mechanics, Astronomy, &c. the solution

* The learned men who flourished between the time of the Conquest and the revival of learning are usually denominated schoolmen, though some writers place them within narrower limits. The schoolmen had the vanity to pretend to account for every thing; they explained the Phenomena of Nature by Hypotheses, instead of facts deduced from experiment and observation; their hypotheses were always conjectural, and very frequently improbable and false, consequently their reasonings and conclusions must have been injurious to the progress of sound knowledge. They substituted hard and unintelligible words and phrases, for causes which they did not at all comprehend, in order to conceal their ignorance; and wished mankind to believe, that by referring to these they had explained the nature of things. Logical arguments were their grand resource, and the defence and support of favourite hypotheses, their chief employ. Their disputations were carried on with a view to obtain victory rather than for the discovery of truth. They infected every subject with their jargon; Law, Physic, Divinity, and Science abound with their sophisticated phraseology, consisting of little else than grave and pedantic displays of ostentatious trifling; especially the books on those subjects written about three centuries ago, which on this account the modern reader will be at considerable loss to understand. The logic of Aristotle, as the grand engine of the schoolmen, has met with indiscriminate censure from a great number of later writers; but I think without justice, as it is not the science, but its misapplication that deserves blame. Bacon, Boyle, Barrow, Locke, and other reformers of science have made great use of the Aristotlean logie in their discoveries, and the only difference is, that the reasonings of these were always founded on truth or (where that could not be obtained) strong probability, and had the discovery of truth for their object; while those of the schoolmen were too often founded on vague or improbable hypotheses, and terminated in procuring their authors undeserved renown, but made mankind neither wiser nor better.

of which had been hitherto sought for by other methods in Waln. The following are the names of some of those who since the commencement of the eighteenth century, have excelled in this and other branches, viz. Mad. Agnesi, D'Alembert, Atwood, De Billy, James, John, and Daniel Bernoulli, Bezout, Borda, Birch, Batten, Browne, Le Bas, Bossut, Barlow, Bonnycastle, Bridge, Cousin, Courtivron, Cotes, Colson, Clairaut, Cramer, Condorcet, Craig, C. and G. Cooke, Christie, Demoivre, Dalby, Dealtry, Dodson, Euler, Emerson, Fontaine, Facio, Fagnanus, Frend, Farish, La Grange, Guisnée, Glenie, Olinthus Gregory, L'Hôpital, La Hire, Hayes, Hornbuckle, Hermann, Hutton, Hustler, Hellings, Jacquier, Jones, Kirkby, Kelly, De Lagni, Landen, Littledale, Manfredi, Monmort, Maclaurin, Montucla, Maseres, Milner, Nicole, D'Omerique, Ozanam, Pemberton, Prestet, Pingré, Peacock, Riccati, Reyneau, Robertson, Rigaud, Sterling, Saunderson, Le Sieur, Saurin, Simson, T. Simpson, Sowerby, B. Taylor, M. Taylor, Turner, Viviani, Varignon, Vince, Waring Wolfius, Watson, Woodhouse, Wood, &c. Astronomy has been cultivated during the same space by many learned men, among which the following are some of the principal, viz. Adams, Bradley, Bouguer, Bailli, Bulkley, the Cassinis, La Caille, Ferguson, Halley, Harding, Herschel, Juan, Koenig, Reill, La Lande, Long, Lax, Maupertuis, Mayer, Maskelyme, Olbers, Pound, Smith, Wolloston, &c. Some of these, with many others, excelled in various branches of the Mathematics, besides those we have ascribed to them; to particularize their inventions, improvements, and excellencies, with just discrimination, would far exceed our prescribed limits; and fully to understand them, recourse must be had to a great variety of modern treatises on every branch of mathematical science. Thus we have endeavoured to shew, in a brief and general manner, the nature, great importance, and use of mathematical knowledge; and to point out a few of the leading facts in its history. The reader need not be informed, that by the improvements and discoveries in science, which have taken place during the three last centuries, and the application of mathematical and physical knowledge to Civil Polity, the Arts, Commerce, and Agriculture, the present generation enjoys advantages superior beyond comparison to those possessed by former ages. Our own country was, but a few centuries ago, an overgrown wilderness, a prey to the wildest superstition, and scarcely supplied the bare necessaries of life to its scanty and savage inhabitants. Now, the conveniences and luxuries of every kingdom in the world are poured in, and added to the produce of our own, constituting a rich abundance for the supply of every want, and the gratification of almost every wish; it follows then, that our obligations to Providence are proportionably greater than those of former ages. If the ox knows his owner, and the ass his master's crib, let us not, more stupid and ungrateful than they, while we live in the enjoyment of infinitely superior benefits, be less dutiful in our attachment, nor overlook the kind hand which supplies them. Possessing more ample means than our ancestors possessed, it is incumbent on us to improve our advantages, by the strict and faithful observance of every religious, moral, and social duty.

AN

E A SY IN T R O DU CTION

TO THE

MATHEMATICS, &c.

P A R T I. -
ARITHMETIC.

HISTORICAL INTRODUCTION.

Numerorum notitia cuicunque primis saltem literis eruditio necessaria est. QUINTILIAN.

ARITHMETIC ", or the science of Numbers, is justly considered as the basis of all the other mathematical sciences; and therefore a sufficient acquaintance with its principles and elementary rules ought to be acquired before any of the other branches are attempted. Arithmetic holds a distinguished rank among the mathematical sciences; it even surpasses them all in usefulness: its universal application to the common concerns of life renders it a part of knowledge not merely desirable, but necessary to every one who wishes to be serviceable to society, to manage his own private affairs well, and to guard against fraud and imposition. Nothing satisfactory can be offered respecting the origin and invention of Arithmetic; like almost every

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