nature of the thing and the clearness of order to place it as a branch of Metaphysic. For Quantity (which is the subject of Mathematic), when applied to matter, is as it were the dose of Nature, and is the cause of a number of effects in things natural; and therefore it must be reckoned as one of the Essential Forms of things. And so highly did the ancients esteem the power of figures and numbers, that Democritus ascribed to the figures of atoms the first principles of the variety of things; and Pythagoras asserted that the nature of things consisted of numbers. In the meantime it is true that of all natural forms (such as I understand them) Quantity is the most abstracted and separable from matter; which has likewise been the cause why it has been more carefully laboured and more acutely inquired into than any of the other forms, which are all more immersed in matter. For it being plainly the nature of the human mind, certainly to the extreme prejudice of knowledge, to delight in the open plains (as it were) of generalities rather than in the woods and inclosures of particulars, the mathematics of all other knowledge were the goodliest fields to satisfy that appetite for expatiation and meditation. But though this be true, regarding as I do not only truth and order but also the advantage and convenience of mankind, I have thought it better to designate Mathematics, seeing that they are of so much importance both in Physics and Metaphysics and Mechanics and Magic, as appendices and auxiliaries to them all. Which indeed I am in a manner compelled to do, by reason of the daintiness and pride of mathematicians, who will needs have this science almost domineer over Physic. For it has come to pass, I know not how, that Mathematic and Logic, which ought to be but the handmaids of Physic, nevertheless presume on the strength of the certainty which they possess to exercise dominion over it. But the place and dignity of this science is of less importance; let us now look to the thing itself. Mathematic is either Pure or Mixed. To Pure Mathematic belong those sciences which handle Quantity entirely severed from matter and from axioms of. natural philosophy. These are two, Geometry and Arithmetic; the one handling quantity continued, and the other dissevered. These two arts have been inquired into and handled with great wit and industry; and yet to the labours of Euclid in geometry no addition has been made by his successors worthy of so long an interval; nor has the doctrine of solids been sufficently examined and advanced either by ancients or moderns, in proportion to the use and excellency of the subject. And in arithmetic, neither have there been discovered formulas for the abridgment of computation sufficiently various and convenient, especially with regard to progressions, of which there is no slight use in Physics, nor has algebra been well perfected; and the mystic arithmetic of Pythagoras, which has been revived of late from Proclus and fragments of Euclid, is a kind of wandering speculation: for it is incidental to the human mind, that when it cannot master the solid, it wastes itself on the superfluous. Mixed Mathematic has for its subject some axioms and parts of natural philosophy, and considers quantity in so far as it assists to explain, demonstrate, and actuate these. For many parts of nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated to use with sufficient dexterity, with out the aid and intervention of Mathematic: of which sort are Perspective, Music, Astronomy, Cosmography, Architecture, Machinery, and some others. In Mixed Mathematics I do not find any entire parts now deficient, but I predict that hereafter there will be more kinds of them, if men be not idle. For as Physic advances farther and farther every day and develops new axioms, it will require fresh assistance from Mathematic in many things, and so the parts of Mixed Mathematics will be more numerous. And now I have passed through the doctrine concerning Nature, and marked the deficiencies thereof. Wherein if I have differed from the ancient and received doctrines, and thereby given a handle to contradiction; for my part, as I am far from wishing to dissent, so I purpose not to contend. If it be truth, Non canimus surdis, respondent omnia silvæ:1 the voice of nature will consent, whether the voice of man do or not. But as Alexander Borgia was wont to say of the expedition of the French to Naples, "that they came with chalk in their hands to mark up their lodgings, and not with weapons to break in; so I like better that entry of truth, which comes peaceably as with chalk to mark up those minds which are capable to lodge and harbour such a guest, than that which forces its way with pugnacity and contention. Having therefore gone through the two parts of philosophy respecting God and Nature, there remains the third, respecting Man. 1 Virg. Eclog. x. 8. :- To no deaf ears we sing, the echoing woods reply. |