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F I R S T E DI TI O N.
Isdom is certainly one of the main springs
of human happiness. And the more of ic each individual of a society acquires, the more happy, all things elfe alike, will that society be; for the wiser a man is, the better will he know how to preserve his own health, and pleasantly lengthen out his own life: he will better avoid the injuries of weather ; better provide food and cloathing; better avoid pain and sickness; better sooth, lesien, and command his own and other people's passions ; better observe the laws of his country; and, in short, better promote his own and neighbours happiness in all respects soever. Accordingly, since wisdom is so necessary to happiness, that learning, which is best adapted to promote and extend it, is undoubtedly the most valuable, and ought by all to be most encouraged, cultivated, and used. And therefore, since true wisdom very much consists in, and is ob. tained from, the knowledge of the comparative numbers and magnitudes of the qualities, powers, efficacies, matter, and motions of sensible objects, their various increase and decrease, &c. and as these may be acquired in a great measure from arithme, tic and geometry: these two sciences may truly be said to be the two great fountains from whence much of the wisdom and happiness of mankind flow: And therefore, if possible, they should be learned by every member of a society. No state ever did or scarcely could Aourish without them. They have always been in esteem and cultivated proportionably to the greatness and riches of a country, and as these have declined, so have those.
When learning flourish'd amongst the Romans, in the time of Cicero, mathematics were honoured and efteemed, and that by this great man himself; but afterwards, in worse ţimes, viz. the reign of Nero, &c. when gross ignorance' had seized the ftate, and learning became very weak and decrepid, the mathematics were neither understood nor in any repute, and some of the degenerate writers of those times, such as Tacitus, Suetonius, Gellius, seemed even not to know what mathematics or mathematicians were; they ranked mathematicians with conjurers and fortune-tellers. Nay it is said in Tacitus's Annals, that the senate passed a decree for banilhing mathematicians out of Italy.
As tyrants and arbitrary governours, immersed in pride, and stain'd with madness, are generally too stupid and brutal to be capable of understanding and esteeming these sciences, and their excellencies, and the major part of crafty Jesuits and other spiritual juglers, retailers of nonsense and spreaders of lies, have been always aspersing and lessening them, because, by their evidence, certainty, and use, they are so apt to dispose the mind to discover truth, and so much straîten, and clog up the paths and passages of fraud and implicit faith; fo on the other hand, all rational rulers, friends to liberty, and lovers of wisdom and mankind, deçesters of fallhood, and despisers of fraud, have ever embraced, and always encouraged these sciences; well knowing them to be the plentiful fountains of advantage to human affairs, from whence, in a great measure, spring the principal delights of life, securities of health, increase of fortune, and convenience of labour; which habituate the mind to a constant delight in study ; which strengthen and subject it to the government of right reason ; which wonderfully fortify it against all kind of imposition; and make it more easily, readily,
and powerfully encounter and overcome falshood, wherever it appears.
I have often thought, that the time of too many of the youth of this kingdom has long been, and now is misapplied, in learning Latin and Greek, efpecially the latter, and believe it would be of much more general advantage for greater numbers of them to be more employed in learning arithmetic, geometry, mechanics, and natural philosophy; as also rational systems of morality, politics, and good government : certainly some or all of these should be known, in a competent degree, more especially by all statesmen, lawyers, soldiers, failors, physicians, surgeons, artificers, &c. whereby they would all be better fitted for their several employments, know more of them, and execute them with much more ease, exactness and certainty. So that as Plato, che philosopher, wrote over the door of his academy, Let none enter in bere but thofe that understand Geometry, I would have it wrote over the door of every academy and public school in Britain, Let none-depart from hence unskilled in Matbema
tical science. It would require a volume to distinctly discuss, and fully lay out the beauties, excellencies, and uses of these sciences, as well as an abler hand than mine to do it; however, if any body is suspicious of the truth of these naked affertions or general posi. tions, and should call upon me for a particular proof, I shall at all times be both ready and willing to do it. Being firmly persuaded, that the truth of every one of them can be proved by such arguments, as cannot but be convincing to every rational man.
As use has a most powerful influence over the mind, as well as the body, there is one certain ad. vantage derived from the study of geometry efpecially, if it were no more, for which it always ought to be highly valued and held in the greatest esteem, viz. by constantly searching after and demonstrating geometrical truths. The mind of a geometrician is so much employ'd in, and used to truth, that it becomes, as it were, a part of his geometrical constitution: he ever loves it, and is constantly seeking it, in all sorts of subjects as well as those of geometry : he is so conversant in truth, that he naturally hates fallhood, tho' perhaps he fometimes is obliged, contrary to his inclination, to make use of it.--Hence, since it is demonstrable that the happiness and preservation of a society is aug mented by the greater quantity of veracity dispersed throughout the individuals of that society, for lying and deceit tend to destroy it ; who does not see the great use of the study of geometry in the promotion and maintenance of truth, and consequently its tendency to the preservation of society itself? Even the * author of a discourse, called The Analyst, printed in the year 1734. altho' he is so full of mistakes, and so much lessens and difparages fluxions and the mathematical students therein, and that chiefly because he does not understand them, has done justice to geometry, and spoken truly thereof. He says, “Geometry is an excellent .“ logic, and it must be own'd, that, when the dekfinitions are clear; when the postulata cannot “ be refused, nor the axioms denied; when from “ the distinct contemplation and comparison of “ figures, their properties are derived by a per" petual well-connected chain of consequences, che s objects being still kept in view, and the atten* tion ever fixed upon them, there is acquired