have a knowledge of what has already been done. This inventory will be the more artificial and useful, if it also contain things of every kind, which, according to common opinion, are impossible; as likewise such as seemed next to impossible, yet have been effected, the one to whet the human invention, and the other to direct it, so that from these optatives and potentials actives may the more readily be deduced.

The second thing is, that a calendar be made of such experiments as are most extensively useful, and that lead to the discovery of others. For example, the experiment of artificial freezing, by means of ice and bay salt, is of infinite extent, and discovers a secret method of condensation of great service to mankind; fire is ready at hand for rarefaction, but the means of condensation are wanted. And it would greatly shorten the way to discoveries, to have a particular catalogue of these leading experiments.

CHAPTER VI

The Great Appendix of Natural Philosophy both Speculative and Practical. Mathematics. Its Proper Position not among the Substantial Sciences, but in their Appendix. Mathematics divided into Pure and Mixed

T WAS well observed by Aristotle, that physics and mathematics produce practice, or mechanics;' there

IT

fore, as we have treated both the speculative and practical part of the doctrine of nature, we should also consider mathematics as an auxiliary science to both, which being revived into philosophy, comes in as a third part after physics and metaphysics. But upon due recollection, if we designed it as a substantial and principal science, it were more agreeable to method and the nature of the thing to make it a part of metaphysics. For quantity, the subject of mathematics applied to matter, is as the dose of nature,

1 Metaphysics, i. and xi.

3

and productive of numerous effects in natural things, and therefore ought to be reckoned among essential forms. And so much did the power of figures and numbers prevail with the ancients, that Democritus chiefly placed the principles of the variety of things in the figures of their atoms;' and Pythagoras asserted that the nature of things consisted of numbers. Thus much is true, that of natural forms, such as we understand them, quantity is the most abstracted and separable from matter; and for this reason it has been more carefully cultivated and examined into by mankind than any other forms, which are all of them more immersed in matter. For, as to the great disadvantage of the sciences, it is natural for men's minds to delight more in the open fields of generals, than in the inclosures of particulars, nothing is found more agreeable than mathematics, which fully gratifies this appetite of expatiating and ranging at large. But as we regard not only truth and order, but also the benefits and advantages of mankind, it seems best, since mathematics is of great use in physics, metaphysics, mechanics and magics, to make it an appendage or auxiliary to them all. And this we are in some measure obliged to do, from the fondness and towering notions of mathematicians, who would have their science preside over physics. It is a strange fatality, that mathematics and logic, which ought to be but handmaids to physics, should boast their certainty before it, and even exercise dominion against it. But the place and dig nity of this science is a secondary consideration with regard to the thing itself.

Mathematics is either pure or mixed. To the pure belong the sciences employed about quantity, wholly abstracted from matter and physical axioms. This has two partsgeometry and arithmetic; the one regarding continued, and the other discrete quantity. These two sciences have been cultivated with very great subtilty and application; but in plain geometry there has nothing considerable been added

? Laertius, Life of Democritus.

3 Lamblicus, Life of Pythagoras.

to the labors of Euclid, though he lived many ages since. The doctrine of solids has not been prosecuted and extended equal to its use and excellency, neither by the ancients nor the moderns; and in arithmetic there is still wanting a sufficient variety of short and commodious methods of calculation, especially with regard to progressions, whose use in physics is very considerable. Neither is algebra brought to perfection. As for the Pythagorical and mystical arithmetic, which began to be recovered from Proclus, and certain remains of Euclid, it is a speculative excursion, the mind having this misfortune, that when it proves unequal to solid and useful things, it spends itself upon such as are unprofitable.

5

Mixed mathematics has for its subject axioms and the

Be

In nature no two beings exist perfectly equal, and the same being cannot retain its qualities unchanged for an instant of time together. In the universe everything moves in a constant progression and series, and it probably was the presentiment of this truth that led the greatest mathematicians after Bacon's time to turn nearly all their attention to this department of mathematics. yond the analogy, however, there is nothing in these phenomena which has any relation with the reality of things; nor have any philosophers since Flud's day ever dealt with them except as pure conditional verities. With data sufficiently determinate, we may approach the solution of any question to which they refer; but if these facts are not given, the problem must remain unresolved. The mathematician may draw consequences; but it is not allowed him to form principles, and if he attempt to apply figures to any hypothesis not warranted by facts, he must be content with the fate of the Samian who constructed the world out of arithmetic, and has been rewarded by the derision of ages for his pains.

No part of learning has perhaps been more cultivated since this author wrote than mathematics, as every other science, or the body of philosophy itself, seems rendered mathematical. The doctrine of solids has been improved by several; the shorter ways of calculation here noted as deficient are in a great measure supplied by the invention of logarithms. Algebra has been so far improved and applied as to rival, or almost prejudice, the ancient geometry; add to this the new discoveries of the Method of Fluxions, the Method of Tangents, the Doctrine of Infinites, the Squaring of Curves, etc. For the general system of mathematical learning, see "Wolfii Elementa Matheseos Universæ," in two volumes 4to, printed at Halle in the year 1715; or for a more cursory view, Father Castel's "Mathématique Universelle," published in the year 1731; but for the history of mathematics, see Vossius "De Universæ Matheseos Natura et Constitutione"; the "Almagest" of Ricciolus; Morhof's "Polyhist. Mathemat."; and Wolfius's "Commentatio de Scriptis Mathematicis," at the end of the second volume of his "Elementa Matheseos Universe;" "Montucla's "Hist. Math. ;" and De la Croix's "Analysis of Infinites."-Ed.

5 He ought to have said from Iamblicus. Proclus was, like himself, totally ignorant even of the little mathematical learning extant in his day.—Ed.

parts of physics, and considers quantity so far as may be assisting to illustrate, demonstrate, and actuate those; for without the help of mathematics many parts of nature could neither be sufficiently comprehended, clearly demonstrated, nor dexterously fitted for use. And of this kind are perspective, music, astronomy, cosmography, architecture, and mechanics. In mixed mathematics we at present find no entire parts deficient, but foretell there will be many found hereafter, if men are not wanting to themselves; for if physics be daily improving, and drawing out new axioms, it will continually be wanting fresh assistances from mathematics; so that the parts of mixed mathematics must gradually grow more numerous.

We have now gone through the physical sciences, and marked out the waste ground in them. If, however, we have departed from the ancient and received opinions, and arrayed opponents against us, we have not affected contradiction, and therefore will not enter into the lists of contention. If we have spoken the truth,

"Non canimus surdis; respondent omnia sylvæ," "—

the voice of nature will cry it up, though the voice of man should cry it down; and as Alexander Borgia was wont to say of the expedition of the French against Naples, that they came with chalk in their hands to mark up their lodg ings, and not with weapons to fight, so we prefer that entry of truth which comes peaceably, when the minds of men capable of lodging so great a guest are signed as it were with chalk, than that which comes with pugnacity, and forces its way by contentions and controversies. Wherefore, having gone through the two parts of philosophy that relate to God and to Nature, we come to the third, which is man himself.

6 Virg. Eclogues, x. 8.

FOURTH BOOK

CHAPTER I

Division of the Knowledge of Man into Human and Civil Philosophy. Human Philosophy divided into the Doctrine of the Body and Soul. The Construction of one General Science, including the Nature and State of Man. The latter divided into the Doctrine of the Human Person and the Connection of the Soul with the Body. Division of the Doctrine of the Person of Man into that of his Miseries and Prerogatives. Division of the Relations between the Soul and the Body into the Doctrines of Indications and Impressions. Physiognomy and the Interpretation of Dreams assigned to the Doctrine of Indications. F ANY man, excellent king, shall assault or wound me. for any of these precepts, let him know that he infringes the code of military honor; for in addition to being under the gracious protection of your Majesty, I do not begin the fight, but am only one of those trumpeters of whom Homer speaks

Χαίρετε κήρυκες Διὸς ἄγγελοι, ἠδὲ καὶ ἀνδρῶν '

who pass inviolate even between enraged armies. Nor does our trumpet summon men to tear one another in frenzied combat, but rather to conclude a peace, that they who are now divided may direct their united forces against nature. herself; and by taking her high towers and dismantling her fortified holds, enlarge as far as God will permit the borders of man's dominion. We now come to the knowledge of ourselves, whither we are directed by the ancients, which merits a closer examination, since the knowledge of himself is to man the end and time of the sciences, of which nature only forms a portion. And here we must admonish. mankind, that all divisions of the sciences are to be under

1 Iliad, i. 334.

2

Plato's Alcibiades.