are in common opinion reputed impossible in every kind, noting, in connexion with each, what thing is extant which comes nearest in degree to that impossibility; that by the one human invention may be stimulated, and by the other it may to a certain extent be directed; and that by these optatives and potentials active discoveries may the more readily be deduced. The second is, that there be also made a calendar of those experiments which are of most general use, and lead the way to the invention of others. For example, the experiment of the artificial freezing of water by the mixture of ice and bay salt bears on an infinite number of things; for it reveals a secret method of condensation, than which nothing is more serviceable to man. For rarefactions we have fire at hand, but for the means of condensation we are in difficulty. Now it would greatly tend to abridge the work of invention if Polychrests of this kind were set down in a proper catalogue.

CHAP. VI.

Of the great Appendix of Natural Philosophy, both Speculative and Operative, namely Mathematic; and that it ought rather to be placed among Appendices than among Substantive Sciences. Division of Mathematic into Pure and Mixed.

ARISTOTLE has well remarked that Physic and Mathematic produce Practice or Mechanic'; wherefore as we have already treated of the speculative and operative part of natural philosophy, it remains to speak of Mathematic, which is a science auxiliary to both. Now this in the common philosophy is annexed as a third part to Physic and Metaphysic; but for my part, being now engaged in reviewing and rehandling these things, if I meant to set it down as a substantive and principal science, I should think it more agreeable both to the 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 Arist. Præf. ad Quæst. Mechan. B B

VOL. IV.

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 sufficiently 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

Γ

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, without 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 : '

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.

372

OF

THE ADVANCEMENT OF LEARNING.

BOOK IV.

CHAPTER I.

Division of the doctrine concerning Man into Philosophy of Humanity and Philosophy Civil. Division of the Philosophy of Humanity into doctrine concerning the Body of Man and doctrine concerning the Soul of Man. Constitution of one general doctrine concerning the Nature or the State of Man. Division of the doctrine concerning the State of Man into doctrine concerning the Person of Man, and doctrine concerning the League of Mind and Body. Division of the doctrine concerning the Person of Man into doctrine concerning the Miseries of Man, and doctrine concerning his Prerogatives. Division of the doctrine concerning the League into doctrine concerning Indications and concerning Impressions. Assignation of Physiognomy and Interpretation of Natural Dreams to the doctrine concerning Indications.

IF any one should aim a blow at me (excellent King) for anything I have said or shall hereafter say in this matter, (besides that I am within the protection of your Majesty,) let me tell him that he is acting contrary to the rules and practice of warfare. For I am but a trumpeter, not a combatant; one perhaps of those of whom Homer speaks,

Χαίρετε κήρυκες, Διὸς ἄγγελοι, ἠδὲ καὶ ἀνδρῶν:1

and such men might go to and fro everywhere unhurt, between the fiercest and bitterest enemies. Nor is mine a trumpet which summons and excites men to cut each other to pieces with mutual contradictions, or to quarrel and fight with one another; but rather to make peace between themselves, and

1 Hom. Il. i. 334. :- Hail, heralds, messengers of Jove and men !

turning with united forces against the Nature of Things, to storm and occupy her castles and strongholds, and extend the bounds of human empire, as far as God Almighty in his goodness may permit.

Let us now come to that knowledge whereunto the ancient oracle directs us, which is the knowledge of ourselves; which deserves the more accurate handling in proportion as it touches us more nearly. This knowledge is for man the end and term of knowledges; but of nature herself it is but a portion. And generally let this be a rule; that all divisions of knowledges be accepted and used rather for lines to mark or distinguish, than sections to divide and separate them; in order that solution of continuity in sciences may always be avoided. For the contrary hereof has made particular sciences to become barren, shallow, and erroneous; not being nourished and maintained and kept right by the common fountain and aliment. So we see Cicero the orator complaining of Socrates and his school, that he was the first who separated philosophy and rhetoric; whereupon rhetoric became an empty and verbal art. So we may see that the opinion of Copernicus touching the rotation of the earth (which has now become prevalent) cannot be refuted by astronomical principles, because it is not repugnant to any of the phenomena; yet the principles of natural philosophy rightly laid down may correct it. Lastly we see that the science of medicine, if it be forsaken by natural philosophy, is not much better than an empirical practice. With this reservation therefore let us proceed to the doctrine concerning Man. It has two parts. For it considers man either segregate, or congregate and in society. The one I call the Philosophy of Humanity, the other Civil Philosophy. Philosophy of Humanity consists of parts similar to those of which man consists; that is, of knowledges which respect the body, and of knowledges which respect the mind. But before we pursue the particular distributions let us constitute one general science concerning the Nature and State of Man; a subject which certainly deserves to be emancipated and made a knowledge of itself. It is composed of those things which are common as well to the body as the soul; and may be divided into two parts; the one regarding the nature of man undivided, and the other regarding the bond and connexion between the mind and body; the first

1 Cicero De Orat. iii. c. 19.