I mean useless with reference to sensible and gross Uses; for otherwise they shall not be so. An Object upon which alone you cast your Eyes is the clearer and brighter, when the neighbouring Objects, which however you do not look upon, are also enlighten'd; because it hath the Benefit of the Rays, which are reflected from them. Thus those Discoveries, which are palpably useful, and deserve our chiefest Attention, are in some measure enlighten'd by those, which may be call'd useless. For all Truths make one another more lucid.
It is always useful to have right Notions, even of useless Subjects. And tho' we cou'd reap no benefit by the Knowledge of Numbers and Sines, yet it wou'd still be the only certain Knowledge granted to our Natural Light, and they wou'd serve to give our Reason the first Habit of and Inclination to Truth. They wou'd teach us to operate upon Truths; to take the Thread of them, which is generally very fine and almost imperceptible; and to follow it as far as it reaches: In a word, they wou'd make Truth so familiar, that we might on other Occasions know it at first sight, and almost by Instinct.
A Geometrical Genius is not so confin'd to Geometry, but that it may be capable of learning other Sciences. A Tract of Morality, Politicks, or Criticism, and even a Piece of Oratory, supposing the Author qualify'd otherwise for those Performances, shall be the better for being compos'd by a Geometrician. That Order, Perspicuity, Precision and Exactness, which some time since are found in good Books, may originally proceed from that Geometrical Genius, which is now more common than ever, and in some manner is communicated by one Relation to another, nay even to those that do not understand Geometry. Sometimes a Great Man draws all his Cotemporaries after him; and he who hath the justest Claim to the Glory of having settled a new Art of Arguing, was an Excellent Geometrician.
Lastly, whatever raises us to Great and Noble Reflexions, tho' they be purely Speculative, afford a Spiritual and Philosophical Utility. The Wants of the Mind are perhaps as many as those of the Body. She desires to extend her Knowledge: All that can be known, is necessary to her, and there can be no better Proof than this, that she is design'd for Truth. Nothing perhaps can redound more to her Glory, than the Pleasure that is felt sometimes, in spight of ones self, in the dry and crabbed Questions of Algebra.
But without running counter to the common Notions, and recurring to Advantages which may seem too far fetch'd and refin'd, it may fairly be own'd, that the Mathematicks and Natural Philosophy have some things which are only subservient to Curiosity; and so have those Sciences which are most generally acknowledg'd to be useful, as History, &c.
History doth not in every Part of it supply us with Examples of Vertue and Rules for our Behaviour. For besides these, therein you have a View of the perpetual Revolutions of Human Affairs, of the Beginning and Fall of Empires, of Manners, Customs, and Opinions which continually succeed one another; and in a word, of all that rapid, tho' insensible, Motion that carries all before it, and incessantly alters the Face of the Earth.
Had we a mind to oppose Curiosity to Curiosity, we shou'd find that instead of the Motion, which agitates Nations, and gives birth to, and destroys States; Natural Philosophy considers that Great and Universal Motion, which hath put the whole Frame of Nature in Order, and suspended the Cœlestial Bodies in several Spheres, and which illuminates and extinguishes some Stars; and by following always unalterable Laws, diversifies its effects ad infinitum. If the surprising difference of Manners and Opinions of Mankind is so entertaining; there is too a great deal of Pleasure to study the prodigious diversity of the Structure of the different Species of Animals, with reference to their different Functions, to the Elements they live in, to the Climates they inhabit, and the Aliments they are to take, &c. The most curious strokes of History shall hardly be more curious than the Phosphorus, the cold Liquors which being mixt together, break out into a flame; Silver Trees, the almost Magical Operations of the Load-Stone, and a vast number of Secrets, which Art hath discover'd by a near and diligent Scrutiny of Nature.
Lastly, Natural Philosophy doth as much as it is possible unravel the Footsteps of that Infinite Intellect and Wisdom, who hath made all things: Whereas the Object of History are the disorderly Effects of the Passion, and of Humane Caprices; and so odd a Series of Events, that some formerly fancy'd that a Blind and Senseless Deity had the Direction of them.
We must not look upon the Sublime Reflexions which Natural Philosophy leads us to make concerning the Author of the Universe, as meer Curiosities. For this stupendous Work, which appears always more wonderful the more we know it, gives us such exalted Notions of its Maker, that they fill our Minds with Admiration and Respect. But above all, Astronomy and Anatomy are the two Sciences which more palpably lay before us two grand Attributes of our Creator; one his Immensity by the distance, Magnitude and Number of Cœlestial Bodies; the other his Infinite Knowledge by the Mechanism of Animals. True Natural Philosophy is a kind of Theology.
The different views of Humane Understanding are almost infinite; and Nature is really so. So that we may every day expect some Discoveries, either in Mathematicks or Natural Philosophy, which shall be of a new sort of Utility or Curiosity. Make a Collection of all the different Advantages which the Mathematicks afforded a Hundred Years ago, and you'll find nothing to be compar'd to the Perspective Glasses they have furnish'd since that time, and which are a new Organ to the Sight, and cou'd not be expected from Art. How surpriz'd had the Ancients been, if they had been told that their Posterity, by the help of some Instruments, shou'd one day see a vast number of Objects which they did not see; a Heaven that was unknown to them; and Plants and Animals they did not even suspect it was possible to exist. Naturalists had already a great many curious Experiments; but within about half a Century, the Air-Pump hath produced a prodigious quantity of them wholly new, and which by shewing Bodies in a Space void of Air, shews them as transported in a World different from ours, where they undergo Alterations whereof we had no Notion. The Excellency of Geometrical Methods, which are every day invented and improv'd, may perhaps at last exhaust Geometry; that is, The Art of making Geometrical Discoveries, and that is all: Whereas Natural Philosophy, which contemplates an Object of an unlimited Variety, and Fæcundity, shall always find room for new Observations, and opportunities to increase its vast Stock, and shall have the Advantage of never being a compleat Science.