1. For the understanding of method, it will be necessary for me to repeat the definition of philosophy, delivered above (Chap. I, art. 2.) in this manner, Philosophy is the knowledge we acquire, by true ratiocination, of appearances, or apparent effects, from the knowledge we have of some possible production or generation of the same; and of such production, as has been or may be, from the knowledge we have of the effects. Method, therefore, in the study of philosophy, is the shortest way of finding out effects by their known causes, or of causes by their known effects. But we are then said to know any effect, when we know that there be causes of the same, and in what subject those causes are, and in what subject they produce that effect, and in what manner they work the same. And this is the science of causes, or, as they call it, of the διότι. All other science, which is called the ὄτι, is either perception by sense, or the imagination, or memory remaining after such perception.
The first beginnings, therefore, of knowledge, are the phantasms of sense and imagination; and that there be such phantasms we know well enough by nature; but to know why they be, or from what causes they proceed, is the work of ratiocination; which consists (as is said above, in the 1st Chapter, Art. 2) in composition, and division or resolution. There is therefore no method, by which we find out the causes of things, but is either compositive or resolutive, or partly compositive, and partly resolutive. And the resolutive is commonly called analytical method, as the compositive is called synthetical.
2. It is common to all sorts of method, to proceed from known things to unknown; and this is manifest from the cited definition of philosophy. But in knowledge by sense, the whole object is more known, than any part thereof; as when we see a man, the conception or whole idea of that man is first or more known, than the particular ideas of his being figurate, animate, and rational; that is, we first see the whole man, and take notice of his being, before we observe in him those other particulars. And therefore in any knowledge of the ὅτι, or that any thing is, the beginning of our search is from the whole idea; and contrarily, in our knowledge of the διότι, or of the causes of any thing, that is, in the sciences, we have more knowledge of the causes of the parts than of the whole. For the cause of the whole is compounded of the causes of the parts; but it is necessary that we know the things that are to be compounded, before we can know the whole compound. Now, by parts, I do not here mean parts of the thing itself, but parts of its nature; as, by the parts of man, I do not understand his head, his shoulders, his arms, &c. but his figure, quantity, motion, sense, reason, and the like; which accidents being compounded or put together, constitute the whole nature of man, but not the man himself. And this is the meaning of that common saying, namely, that some things are more known to us, others more known to nature; for I do not think that they, which so distinguish, mean that something is known to nature, which is known to no man; and therefore, by those things, that are more known to us, we are to understand things we take notice of by our senses, and, by more known to nature, those we acquire the knowledge of by reason; for in this sense it is, that the whole, that is, those things that have universal names, (which, for brevity's sake, I call universal) are more known to us than the parts, that is, such things as have names less universal, (which I therefore call singular); and the causes of the parts are more known to nature than the cause of the whole; that is, universals than singulars.
3. In the study of philosophy, men search after science either simply or indefinitely; that is, to know as much as they can, without propounding to themselves any limited question; or they enquire into the cause of some determined appearance, or endeavour to find out the certainty of something in question, as what is the cause of light, of heat, of gravity, of a figure propounded, and the like; or in what subject any propounded accident is inherent; or what may conduce most to the generation of some propounded effect from many accidents; or in what manner particular causes ought to be compounded for the production of some certain effect. Now, according to this variety of things in question, sometimes the analytical method is to be used, and sometimes the synthetical.
4. But to those that search after science indefinitely, which consists in the knowledge of the causes of all things, as far forth as it may be attained, (and the causes of singular things are compounded of the causes of universal or simple things) it is necessary that they know the causes of universal things, or of such accidents as are common to all bodies, that is, to all matter, before they can know the causes of singular things, that is, of those accidents by which one thing is distinguished from another. And, again, they must know what those universal things are, before they can know their causes. Moreover, seeing universal things are contained in the nature of singular things, the knowledge of them is to be acquired by reason, that is, by resolution. For example, if there be propounded a conception or idea of some singular thing, as of a square, this square is to be resolved into a plain, terminated with a certain number of equal and straight lines and right angles. For by this resolution we have these things universal or agreeable to all matter, namely, line, plain, (which contains superficies) terminated, angle, straightness, rectitude, and equality; and if we can find out the causes of these, we may compound them altogether into the cause of a square. Again, if any man propound to himself the conception of gold, he may, by resolving, come to the ideas of solid, visible, heavy, (that is, tending to the centre of the earth, or downwards) and many other more universal than gold itself; and these he may resolve again, till he come to such things as are most universal. And in this manner, by resolving continually, we may come to know what those things are, whose causes being first known severally, and afterwards compounded, bring us to the knowledge of singular things. I conclude, therefore, that the method of attaining to the universal knowledge of things, is purely analytical.
5. But the causes of universal things (of those, at least, that have any cause) are manifest of themselves, or (as they say commonly) known to nature; so that they need no method at all; for they have all but one universal cause, which is motion. For the variety of all figures arises out of the variety of those motions by which they are made; and motion cannot be understood to have any other cause besides motion; nor has the variety of those things we perceive by sense, as of colours, sounds, savours, &c. any other cause than motion, residing partly in the objects that work upon our senses, and partly in ourselves, in such manner, as that it is manifestly some kind of motion, though we cannot, without ratiocination, come to know what kind. For though many cannot understand till it be in some sort demonstrated to them, that all mutation consists in motion; yet this happens not from any obscurity in the thing itself, (for it is not intelligible that anything can depart either from rest, or from the motion it has, except by motion), but either by having their natural discourse corrupted with former opinions received from their masters, or else for this, that they do not at all bend their mind to the enquiring out of truth.
6. By the knowledge therefore of universals, and of their causes (which are the first principles by which we know the διότι of things) we have in the first place their definitions, (which are nothing but the explication of our simple conceptions.) For example, he that has a true conception of place, cannot be ignorant of this definition, place is that space which is possessed or filled adequately by some body; and so, he that conceives motion aright, cannot but know that motion is the privation of one place, and the acquisition of another. In the next place, we have their generations or descriptions; as (for example) that a line is made by the motion of a point, superficies by the motion of a line, and one motion by another motion, &c. It remains, that we enquire what motion begets such and such effects; as, what motion makes a straight line, and what a circular; what motion thrusts, what draws, and by what way; what makes a thing which is seen or heard, to be seen or heard sometimes in one manner, sometimes in another. Now the method of this kind of enquiry, is compositive. For first we are to observe what effect a body moved produceth, when we consider nothing in it besides its motion; and we see presently that this makes a line, or length; next, what the motion of a long body produces, which we find to be superficies; and so forwards, till we see what the effects of simple motion are; and then, in like manner, we are to observe what proceeds from the addition, multiplication, subtraction, and division, of these motions, and what effects, what figures, and what properties, they produce; from which kind of contemplation sprung that part of philosophy which is called geometry.
From this consideration of what is produced by simple motion, we are to pass to the consideration of what effects one body moved worketh upon another; and because there may be motion in all the several parts of a body, yet so as that the whole body remain still in the same place, we must enquire first, what motion causeth such and such motion in the whole, that is, when one body invades another body which is either at rest or in motion, what way, and with what swiftness, the invaded body shall move; and, again, what motion this second body will generate in a third, and so forwards. From which contemplation shall be drawn that part of philosophy which treats of motion.
In the third place we must proceed to the enquiry of such effects as are made by the motion of the parts of any body, as, how it comes to pass, that things when they are the same, yet seem not to be the same, but changed. And here the things we search after are sensible qualities, such as light, colour, transparency, opacity, sound, odour, savour, heat, cold, and the like; which because they cannot be known till we know the causes of sense itself, therefore the consideration of the causes of seeing, hearing, smelling, tasting, and touching, belongs to this third place; and all those qualities and changes, above mentioned, are to be referred to the fourth place; which two considerations comprehend that part of philosophy which is called physics. And in these four parts is contained whatsoever in natural philosophy may be explicated by demonstration, properly so called. For if a cause were to be rendered of natural appearances in special, as, what are the motions and influences of the heavenly bodies, and of their parts, the reason hereof must either be drawn from the parts of the sciences above mentioned, or no reason at all will be given, but all left to uncertain conjecture.
After physics we must come to moral philosophy; in which we are to consider the motions of the mind, namely, appetite, aversion, love, benevolence, hope, fear, anger, emulation, envy, &c.; what causes they have, and of what they be causes. And the reason why these are to be considered after physics is, that they have their causes in sense and imagination, which are the subject of physical contemplation. Also the reason, why all these things are to be searched after in the order above-said, is, that physics cannot be understood, except we know first what motions are in the smallest parts of bodies; nor such motion of parts, till we know what it is that makes another body move; nor this, till we know what simple motion will effect. And because all appearance of things to sense is determined, and made to be of such and such quality and quantity by compounded motions, every one of which has a certain degree of velocity, and a certain and determined way; therefore, in the first place, wewe are to search out the ways of motion simply (in which geometry consists); next the ways of such generated motions as are manifest; and, lastly, the ways of internal and invisible motions (which is the enquiry of natural philosophers). And, therefore, they that study natural philosophy, study in vain, except they begin at geometry; and such writers or disputers thereof, as are ignorant of geometry, do but make their readers and hearers lose their time.
7. Civil and moral philosophy do not so adhere to one another, but that they may be severed. For the causes of the motions of the mind are known, not only by ratiocination, but also by the experience of every man that takes the pains to observe those motions within himself. And, therefore, not only they that have attained the knowledge of the passions and perturbations of the mind, by the synthetical method, and from the very first principles of philosophy, may by proceeding in the same way, come to the causes and necessity of constituting commonwealths, and to get the knowledge of what is natural right, and what are civil duties; and, in every kind of government, what are the rights of the commonwealth, and all other knowledge appertaining to civil philosophy; for this reason, that the principles of the politics consist in the knowledge of the motions of the mind, and the knowledge of these motions from the knowledge of sense and imagination; but even they also that have not learned the first part of philosophy, namely, geometry and physics, may, notwithstanding, attain the principles of civil philosophy, by the analytical method. For if a question be propounded, as, whether such an action be just or unjust; if that unjust be resolved into fact against law, and that notion law into the command of him or them that have coercive power; and that power be derived from the wills of men that constitute such power, to the end they may live in peace, they may at last come to this, that the appetites of men and the passions of their minds are such, that, unless they be restrained by some power, they will always be making war upon one another; which may be known to be so by any man's experience, that will but examine his own mind. And, therefore, from hence he may proceed, by compounding, to the determination of the justice or injustice of any propounded action. So that it is manifest, by what has been said, that the method of philosophy, to such as seek science simply, without propounding to themselves the solution of any particular question, is partly analytical, and partly synthetical; namely, that which proceeds from sense to the invention of principles, analytical; and the rest synthetical.
8. To those that seek the cause of some certain and propounded appearance or effect, it happens, sometimes, that they know not whether the thing, whose cause is sought after, be matter or body, or some accident of a body. For though in geometry, when the cause is sought of magnitude, or proportion, or figure, it be certainly known that these things, namely magnitude, proportion, and figure, are accidents; yet in natural philosophy, where all questions are concerning the causes of the phantasms of sensible things, it is not so easy to discern between the things themselves, from which those phantasms proceed, and the appearances of those things to the sense; which have deceived many, especially when the phantasms have been made by light. For example, a man that looks upon the sun, has a certain shining idea of the magnitude of about a foot over, and this he calls the sun, though he know the sun to be truly a great deal bigger; and, in like manner, the phantasm of the same thing appears sometimes round, by being seen afar off, and sometimes square, by being nearer. Whereupon it may well be doubted, whether that phantasm be matter, or some body natural, or only some accident of a body; in the examination of which doubt we may use this method. The properties of matter and accidents already found out by us, by the synthetical method, from their definitions, are to be compared with the idea we have before us; and if it agree with the properties of matter or body, then it is a body; otherwise it is an accident. Seeing, therefore, matter cannot by any endeavour of ours be either made or destroyed, or increased, or diminished, or moved out of its place, whereas that idea appears, vanishes, is increased and diminished, and moved hither and thither at pleasure; we may certainly conclude that it is not a body, but an accident only. And this method is synthetical.
9. But if there be a doubt made concerning the subject of any known accident (for this may be doubted sometimes, as in the precedent example, doubt may be made in what subject that splendour and apparent magnitude of the sun is), then our enquiry must proceed in this manner. First, matter in general must be divided into parts, as, into object, medium, and the sentient itself, or such other parts as seem most conformable to the thing propounded. Next, these parts are severally to be examined how they agree with the definition of the subject; and such of them as are not capable of that accident are to be rejected. For example, if by any true ratiocination the sun be found to be greater than its apparent magnitude, then that magnitude is not in the sun; if the sun be in one determined straight line, and one determined distance, and the magnitude and splendour be seen in more lines and distances than one, as it is in reflection or refraction, then neither that splendour nor apparent magnitude are in the sun itself, and, therefore, the body of the sun cannot be the subject of that splendour and magnitude. And for the same reasons the air and other parts will be rejected, till at last nothing remain which can be the subject of that splendour and magnitude but the sentient itself. And this method, in regard the subject is divided into parts, is analytical; and in regard the properties, both of the subject and accident, are compared with the accident concerning whose subject the enquiry is made, it is synthetical.
10. But when we seek after the cause of any propounded effect, we must in the first place get into our mind an exact notion or idea of that which we call cause, namely, that a cause is the sum or aggregate of all such accidents, both in the agents and the patient, as concur to the producing of the effect propounded; all which existing together, it cannot be understood but that the effect existeth with them; or that it can possibly exist if any one of them be absent. This being known, in the next place we must examine singly every accident that accompanies or precedes the effect, as far forth as it seems to conduce in any manner to the production of the same, and see whether the propounded effect may be conceived to exist, without the existence of any of those accidents; and by this means separate such accidents, as do not concur, from such as concur to produce the said effect; which being done, we are to put together the concurring accidents, and consider whether we can possibly conceive, that when these are all present, the effect propounded will not follow; and if it be evident that the effect will follow, then that aggregate of accidents is the entire cause, otherwise not; but we must still search out and put together other accidents. For example, if the cause of light be propounded to be sought out; first, we examine things without us, and find that whensoever light appears, there is some principal object, as it were the fountain of light, without which we cannot have any perception of light; and, therefore, the concurrence of that object is necessary to the generation of light. Next we consider the medium, and find, that unless it be disposed in a certain manner, namely, that it be transparent, though the object remain the same, yet the effect will not follow; and, therefore, the concurrence of transparency is also necessary to the generation of light. Thirdly, we observe our own body, and find that by the indisposition of the eyes, the brain, the nerves, and the heart, that is, by obstructions, stupidity, and debility, we are deprived of light, so that a fitting disposition of the organs to receive impressions from without is likewise a necessary part of the cause of light. Again, of all the accidents inherent in the object, there is none that can conduce to the effecting of light, but only action (or a certain motion), which cannot be conceived to be wanting, whensoever the effect is present; for, that anything may shine, it is not requisite that it be of such or such magnitude or figure, or that the whole body of it be moved out of the place it is in (unless it may perhaps be said, that in the sun, or other body, that which causes light is the light it hath in itself; which yet is but a trifling exception, seeing nothing is meant thereby but the cause of light; as if any man should say that the cause of light is that in the sun which produceth it); it remains, therefore, that the action, by which light is generated, is motion only in the parts of the object. Which being understood, we may easily conceive what it is the medium contributes, namely, the continuation of that motion to the eye; and, lastly, what the eye and the rest of the organs of the sentient contribute, namely, the continuation of the same motion to the last organ of sense, the heart. And in this manner the cause of light may be made up of motion continued from the original of the same motion, to the original of vital motion, light being nothing but the alteration of vital motion, made by the impression upon it of motion continued from the object. But I give this only for an example, for I shall speak more at large of light, and the generation of it, in its proper place. In the mean time it is manifest, that in the searching out of causes, there is need partly of the analytical, and partly of the synthetical method; of the analytical, to conceive how circumstances conduce severally to the production of effects; and of the synthetical, for the adding together and compounding of what they can effect singly by themselves. And thus much may serve for the method of invention. It remains that I speak of the method of teaching, that is, of demonstration, and of the means by which we demonstrate.
11. In the method of invention, the use of words consists in this, that they may serve for marks, by which, whatsoever we have found out may be recalled to memory; for without this all our inventions perish, nor will it be possible for us to go on from principles beyond a syllogism or two, by reason of the weakness of memory. For example, if any man, by considering a triangle set before him, should find that all its angles together taken are equal to two right angles, and that by thinking of the same tacitly, without any use of words either understood or expressed; and it should happen afterwards that another triangle, unlike the former, or the same in different situation, should be offered to his consideration, he would not know readily whether the same property were in this last or no, but would be forced, as often as a different triangle were brought before him (and the difference of triangles is infinite) to begin his contemplation anew; which he would have no need to do if he had the use of names, for every universal name denotes the conceptions we have of infinite singular things. Nevertheless, as I said above, they serve as marks for the help of our memory, whereby we register to ourselves our own inventions; but not as signs by which we declare the same to others; so that a man may be a philosopher alone by himself, without any master; Adam had this capacity. But to teach, that is, to demonstrate, supposes two at the least, and syllogistical speech.
12. And seeing teaching is nothing but leading the mind of him we teach, to the knowledge of our inventions, in that track by which we attained the same with our own mind; therefore, the same method that served for our invention, will serve also for demonstration to others, saving that we omit the first part of method which proceeded from the sense of things to universal principles, which, because they are principles, cannot be demonstrated; and seeing they are known by nature, (as was said above in the 5th article) they need no demonstration, though they need explication. The whole method, therefore, of demonstration, is synthetical, consisting of that order of speech which begins from primary or most universal propositions, which are manifest of themselves, and proceeds by a perpetual composition of propositions into syllogisms, till at last the learner understand the truth of the conclusion sought after.
13. Now, such principles are nothing but definitions, whereof there are two sorts; one of names, that signify such things as have some conceivable cause, and another of such names as signify things of which we can conceive no cause at all. Names of the former kind are, body, or matter, quantity, or extension, motion, and whatsoever is common to all matter. Of the second kind, are such a body, such and so great motion, so great magnitude, such figure, and whatsoever we can distinguish one body from another by. And names of the former kind are well enough defined, when, by speech as short as may be, we raise in the mind of the hearer perfect and clear ideas or conceptions of the things named, as when we define motion to be the leaving of one place, and the acquiring of another continually; for though no thing moved, nor any cause of motion be in that definition, yet, at the hearing of that speech, there will come into the mind of the hearer an idea of motion clear enough. But definitions of things, which may be understood to have some cause, must consist of such names as express the cause or manner of their generation, as when we define a circle to be a figure made by the circumduction of a straight line in a plane, &c. Besides definitions, there is no other proposition that ought to be called primary, or (according to severe truth) be received into the number of principles. For those axioms of Euclid, seeing they may be demonstrated, are no principles of demonstration, though they have by the consent of all men gotten the authority of principles, because they need not be demonstrated. Also, those petitions, or postulata, (as they call them) though they be principles, yet they are not principles of demonstration, but of construction only; that is, not of science, but of power; or (which is all one) not of theorems, which are speculations, but of problems, which belong to practice, or the doing of something. But as for those common received opinions, Nature abhors vacuity, Nature doth nothing in vain, and the like, which are neither evident in themselves, nor at all to be demonstrated, and which are oftener false than true, they are much less to be acknowledged for principles.
To return, therefore, to definitions; the reason why I say that the cause and generation of such things, as have any cause or generation, ought to enter into their definitions, is this. The end of science is the demonstration of the causes and generations of things; which if they be not in the definitions, they cannot be found in the conclusion of the first syllogism, that is made from those definitions; and if they be not in the first conclusion, they will not be found in any further conclusion deduced from that; and, therefore, by proceeding in this manner, we shall never come to science; which is against the scope and intention of demonstration.
14. Now, seeing definitions (as I have said) are principles, or primary propositions, they are therefore speeches; and seeing they are used for the raising of an idea of some thing in the mind of the learner, whensoever that thing has a name, the definition of it can be nothing but the explication of that name by speech; and if that name be given it for some compounded conception, the definition is nothing but a resolution of that name into its most universal parts. As when we define man, saying man is a body animated, sentient, rational, those names, body animated, &c. are parts of that whole name man; so that definitions of this kind always consist of genus and difference; the former names being all, till the last, general; and the last of all, difference. But if any name be the most universal in its kind, then the definition of it cannot consist of genus and difference, but is to be made by such circumlocution, as best explicateth the force of that name. Again, it is possible, and happens often, that the genus and difference are put together, and yet make no definition; as these words, a straight line, contain both the genus and difference; but are not a definition, unless we should think a straight line may be thus defined, a straight line is a straight line: and yet if there were added another name, consisting of different words, but signifying the same thing which these signify, then these might be the definition of that name. From what has been said, it may be understood how a definition ought to be defined, namely, that it is a proposition, whose predicate resolves the subject, when it may; and when it may not, it exemplifies the same.
15. The properties of a definition are:
First, that it takes away equivocation, as also all that multitude of distinctions, which are used by such as think they may learn philosophy by disputation. For the nature of a definition is to define, that is, to determine the signification of the defined name, and to pare from it all other signification besides what is contained in the definition itself; and therefore one definition does as much, as all the distinctions (how many soever) that can be used about the name defined.
Secondly, that it gives an universal notion of the thing defined, representing a certain universal picture thereof, not to the eye, but to the mind. For as when one paints a man, he paints the image of some man; so he, that defines the name man, makes a representation of some man to the mind.
Thirdly, that it is not necessary to dispute whether definitions are to be admitted or no. For when a master is instructing his scholar, if the scholar understand all the parts of the thing defined, which are resolved in the definition, and yet will not admit of the definition, there needs no further controversy betwixt them, it being all one as if he refused to be taught. But if he understand nothing, then certainly the definition is faulty; for the nature of a definition consists in this, that it exhibit a clear idea of the thing defined; and principles are either known by themselves, or else they are not principles.
Fourthly, that, in philosophy, definitions are before defined names. For in teaching philosophy, the first beginning is from definitions; and all progression in the same, till we come to the knowledge of the thing compounded, is compositive. Seeing, therefore, definition is the explication of a compounded name by resolution, and the progression is from the parts to the compound, definitions must be understood before compounded names; nay, when the names of the parts of any speech be explicated, it is not necessary that the definition should be a name compounded of them. For example, when these names, equilateral, quadrilateral, right-angled, are sufficiently understood, it is not necessary in geometry that there should be at all such a name as square; for defined names are received in philosophy for brevity's sake only.
Fifthly, that compounded names, which are defined one way in some one part of philosophy, may in another part of the same be otherwise defined; as a parabola and an hyperbole have one definition in geometry, and another in rhetoric; for definitions are instituted and serve for the understanding of the doctrine which is treated of. And, therefore, as in one part of philosophy, a definition may have in it some one fit name for the more brief explanation of some proposition in geometry; so it may have the same liberty in other parts of philosophy; for the use of names is particular (even where many agree to the settling of them) and arbitrary.
Sixthly, that no name can be defined by any one word; because no one word is sufficient for the resolving of one or more words.
Seventhly, that a defined name ought not to be repeated in the definition. For a defined name is the whole compound, and a definition is the resolution of that compound into parts; but no total can be part of itself.
16. Any two definitions, that may be compounded into a syllogism, produce a conclusion; which, because it is derived from principles, that is, from definitions, is said to be demonstrated; and the derivation or composition itself is called a demonstration. In like manner, if a syllogism be made of two propositions, whereof one is a definition, the other a demonstrated conclusion, or neither of them is a definition, but both formerly demonstrated, that syllogism is also called a demonstration, and so successively. The definition therefore of a demonstration is this, a demonstration is a syllogism, or series of syllogisms, derived and continued, from the definitions of names, to the last conclusion. And from hence it may be understood, that all true ratiocination, which taketh its beginning from true principles, produceth science, and is true demonstration. For as for the original of the name, although that, which the Greeks called ἀποδέιξις, and the Latins demonstratio, was understood by them for that sort only of ratiocination, in which, by the describing of certain lines and figures, they placed the thing they were to prove, as it were before men's eyes, which is properly ἀποδεικνύειν, or to shew by the figure; yet they seem to have done it for this reason, that unless it were in geometry, (in which only there is place for such figures) there was no ratiocination certain, and ending in science, their doctrines concerning all other things being nothing but controversy and clamour; which, nevertheless, happened, not because the truth to which they pretended could not be made evident without figures, but because they wanted true principles, from which they might derive their ratiocination; and, therefore, there is no reason but that if true definitions were premised in all sorts of doctrines, the demonstrations also would be true.
17. It. is proper to methodical demonstration,
First, that there be a true succession of one reason to another, according to the rules of syllogizing delivered above.
Secondly, that the premises of all syllogisms be demonstrated from the first definitions.
Thirdly, that after definitions, he that teaches or demonstrates any thing, proceed in the same method by which he found it out; namely, that in the first place those things be demonstrated, which immediately succeed to universal definitions (in which is contained that part of philosophy which is called philosophia prima). Next, those things which may be demonstrated by simple motion (in which geometry consists). After geometry, such things as may be taught or shewed by manifest action, that is, by thrusting from, or pulling towards. And after these, the motion or mutation of the invisible parts of things, and the doctrine of sense and imaginations, and of the internal passions, especially those of men, in which are comprehended the grounds of civil duties, or civil philosophy; which takes up the last place. And that this method ought to be kept in all sorts of philosophy, is evident from hence, that such things as I have said are to be taught last, cannot be demonstrated, till such as are propounded to be first treated of, be fully understood. Of which method no other example can be given, but that treatise of the elements of philosophy, which I shall begin in the next chapter, and continue to the end of the work.
18. Besides those paralogisms, whose fault lies either in the falsity of the premises, or the want of true composition, of which I have spoken in the precedent chapter, there are two more, which are frequent in demonstration; one whereof is commonly called petitio principii; the other is the supposing of a false cause; and these do not only deceive unskilful learners, but sometimes masters themselves, by making them take that for well demonstrated, which is not demonstrated at all. Petitio principii is, when the conclusion to be proved is disguised in other words, and put for the definition or principle from whence it is to be demonstrated; and thus, by putting for the cause of the thing sought, either the thing itself or some effect of it, they make a circle in their demonstration. As for example, he that would demonstrate that the earth stands still in the centre of the world, and should suppose the earth's gravity to be the cause thereof, and define gravity to be a quality by which every heavy body tends towards the centre of the world, would lose his labour; for the question is, what is the cause of that quality in the earth? and, therefore, he that supposes gravity to be the cause, puts the thing itself for its own cause.
Of a false cause I find this example in a certain treatise where the thing to be demonstrated is the motion of the earth. He begins, therefore, with this, that seeing the earth and the sun are not always in the same situation, it must needs be that one of them be locally moved, which is true; next, he affirms that the vapours, which the sun raises from the earth and sea, are, by reason of this motion, necessarily moved, which also is true; from whence he infers the winds are made, and this may pass for granted; and by these winds he says, the waters of the sea are moved, and by their motion the bottom of the sea, as if it were beaten forwards, moves round; and let this also be granted; wherefore, he concludes, the earth is moved; which is, nevertheless, a paralogism. For, if that wind were the cause why the earth was, from the beginning, moved round, and the motion either of the sun or the earth were the cause of that wind, then the motion of the sun or the earth was before the wind itself; and if the earth were moved, before the wind was made, then the wind could not be the cause of the earth's revolution; but, if the sun were moved, and the earth stand still, then it is manifest the earth might remain unmoved, notwithstanding that wind; and therefore that motion was not made by the cause which he allegeth. But paralogisms of this kind are very frequent among the writers of physics, though none can be more elaborate than this in the example given.
19. It may to some men seem pertinent to treat in this place of that art of the geometricians, which they call logistica, that is, the art, by which, from supposing the thing in question to be true, they proceed by ratiocination, till either they come to something known, by which they may demonstrate the truth of the thing sought for; or to something which is impossible, from whence they collect that to be false, which they supposed true. But this art cannot be explicated here, for this reason, that the method of it can neither be practised, nor understood, unless by such as are well versed in geometry; and among geometricians themselves, they, that have most theorems in readiness, are the most ready in the use of this logistica; so that, indeed, it is not a distinct thing from geometry itself; for there are, in the method of it, three parts; the first whereof consists in the finding out of equality betwixt known and unknown things, which they call equation; and this equation cannot be found out, but by such as know perfectly the nature, properties, and transpositions of proportion, as also the addition, subtraction, multiplication, and division of lines and superficies, and the extraction of roots; which are the parts of no mean geometrician. The second is, when an equation is found, to be able to judge whether the truth or falsity of the question may be deduced from it, or no; which yet requires greater knowledge. And the third is, when such an equation is found, as is fit for the solution of the question, to know how to resolve the same in such manner, that the truth or falsity may thereby manifestly appear; which, in hard questions, cannot be done without the knowledge of the nature of crooked-lined figures; but he that understands readily the nature and properties of these, is a complete geometrician. It happens besides, that for the finding out of equations, there is no certain method, but he is best able to do it, that has the best natural wit.