Chapter X (6)

To the eighth, you object only the too great length and labour of it, because you can do it a shorter way. Perhaps so now, as being easy to shorten many of the demonstrations both of Euclid, and other the best geometricians that are or have been. And this is all you had to say to my nineteenth chapter. Before I proceed, I must put you in mind that these words of yours, “_adducis malleum, ut occidas muscam_,” are not good Latin, _malleum affers_, _malleum adhibes_, _malleo uteris_, are good. When you speak of bringing bodies animate, _ducere_ and _adducere_ are good, for there _to bring_, is _to guide or lead_. And of bodies inanimate, _adducere_ is good for _attrahere_, which is to draw to. But when you bring a hammer, will you say _adduco malleum_, _I lead a hammer_? A man may lead another man, and a ninny may be said to lead another ninny, but not a hammer. Nevertheless, I should not have thought fit to reprehend this fault upon this occasion in an Englishman, nor to take notice of it, but that I find you in some places nibbling, but causelessly, at my Latin.

Concerning the twentieth chapter, before I answer to the objections against the propositions themselves, I must answer to the exception you first take to these words of mine, “_Quæ de dimensione circuli et angulorum pronuntiata sunt tanquam exactè inventa, accipiat lector tanquam dicta_ _problematicè._” To which you say thus: “_We are wont in geometry to call some propositions theorems, others problems, &c. of which a theorem is that wherein some assertion is propounded to be proved; a problem that wherein something is commanded to be done_.” Do you mean _to be done_, and not proved? By your favour, a problem in all ancient writers signifies no more but a proposition uttered, to the end to have it, by them to whom it is uttered, examined whether it be true or not true, faisable or not faisable; and differs not amongst geometricians from a theorem but in the manner of propounding. For this proposition, _to make an equilateral triangle_, so propounded they call a problem. But if propounded thus: _If upon the ends of a straight line given be described two circles, whose radius is the same straight line, and there be drawn from the intersection of the circles to their two centres, two straight lines, there will be made an equilateral triangle_, then they call it a theorem; and yet the proposition is the same. Therefore these words, _accipiat lector tanquam dicta problematicè_ signify plainly this, that I would have the reader, take for propounded to him to examine, whether from my construction the quadrature of the circle can be truly inferred or not; and this is not to bid him, as you interpret it, to square the circle. And if you believe that _problematicè_ signifies probably, you have been very negligent in observing the sense of the ancient Greek philosophers in the word problem. Therefore your _solemus in geometria_, &c. is nothing to the purpose; nor had it been though you had spoken more properly, and said _solent_, leaving out yourselves.

_Six Lessons._
_Vol. VII. Eng. p.310_II. 325_
]

My first article hath this title, “_from a false supposition, a false quadrature of the circle_.” Seeing therefore you were resolved to show where I erred, you should have proved either that the supposition was true, and the conclusion falsely inferred, or contrarily, that though the supposition be false, yet the conclusion is true; for else you object nothing to my geometry, but only to my judgment, in thinking fit to publish it; which nevertheless you cannot justly do, seeing it was likely to give occasion to ingenious men (the practice of it being so accurate to sense) to inquire wherein the fallacy did consist. And for the problem as it was first printed, but never published, and consequently ought to have passed for a private paper stolen out of my study, your public objecting against it (in the opinion of all men that have conversed so much with honest company as to know what belongs to civil conversation), was sufficiently barbarous in divines. And seeing you knew I had rejected that proposition, it was but a poor ambition to take wing as you thought to do, like beetles from my egestions. But let that be as it will, you will think strange now I should resume, and make good, at least against your objection, that very same proposition. So much of the figure as is needful you will find noted with the same letters, and placed at the end of this fifth lesson. Wherein let B I, be an arch not greater than the radius of the circle, and divided into four equal parts, in L, N, O. Draw S N, the sine of the arch B N, and produce it to T, so as S T be double to S N, that is, equal to the chord B I. Draw likewise _a_ L, the sine of the arch B L, and produce it to _c_, so as _a c_ be quadruple to _a_ L, that is, equal to the two chords B N, N I. Upon the centre N with the radius N I, draw the arch I _d_, cutting B U the tangent in _d_. Then will B N produced cut the arch I _d_, in the midst at _o_. In the line B S produced take S _b_, equal to B S; then draw and produce _b_ N, and it will fall on the point _d_. And B _d_, S T, will be equal; and _d_ T joined and produced will fall upon _o_, the midst of the arch I _d_. Join I T, and produce it to the tangent B U in U. I say, that the straight line I T U shall pass through _c_. For seeing B S, S _b_, are equal, and the angle at S a right angle, the straight lines B N, and _b_ N, are also equal, and the triangles B N _b_, _d_ N _o_ like and equal; and the lines _d_ T, T _o_ equal. Draw _o i_ parallel to _d_ U, cutting I U in _i_; and the triangles _d_ T U, _o_ T _i_ will also be like and equal. Produce S T to the arch _d o_ I in _e_, and produce it further to _f_, so that the line _e f_ be equal to T _e_; and then S _f_ will be equal to _a c_. Therefore _f c_ joined will be parallel to B S. In _c f_ produced take _f g_ equal to _c f_; and draw _g m_ parallel to _d_ U, cutting I U in _m_, and _d o_ in _n_; and let the intersection of the two lines _a c_ and _d o_ be in _r_; which being done, the triangles _m n_ T, _r c_ T will be like and equal. Therefore _m n_ and _r c_ are equal; and consequently the straight line I _m_ T U shall pass through _c_. Dividing therefore _a c_ in the midst at _t_, and S N in the midst at _l_, and joining _t_ N, L _l_, the lines L _l_, _t_ N, and _c_ T produced, will all meet in one and the same point of B S produced; suppose at _q_. Therefore the point _q_ being given by the two known points T and I, the lines drawn from _q_ through equal parts of the sine of the arch B I, (for example through the points P, Q, R, of the sine M I), shall cut off equal arches, as B L, L N, N O, O I. And this is enough to make good that problem, as to your objection.

The straight line therefore B U, for any thing you have said, is proved equal to the arch B I, and the division of any angle given into any proportion given, the quadrature of any sector, and the construction of any equilateral polygon is also given. And though in this also I should have erred, yet it cannot be denied but that I have used a more natural, a more geometrical, and a more perspicuous method in the search of this so difficult a problem, than you have done in your _Arithmetica Infinitorum_. For though it be true that the aggregate of all the mean proportionals between the radius, together with an infinitely little part of the same, and the radius wanting an infinitely little part of the same; and again, between the radius, together with two infinitely little parts, and the radius wanting two infinitely little parts, and so on eternally, will be equal to the quadrant (a thing which every mean geometrician knew before); yet it was absurd to think those means could be calculated in numbers by interpoling of a symbol; especially when you make that symbol to stand for a number neither true nor surd; as if there were a number that could neither be uttered in words, nor not be uttered in words. For what else is surd, but that which cannot be spoken?

To the fifth article, though your discourse be long, you object but two things. One is, that “_Whereas the spiral of Archimedes is made of two motions, one straight, the other circular, both uniform, I taking the motion compounded of them both for one of those that are compounded, conclude falsely, that the generation of the spiral is like to the generation of the parabola_.” What heed you use to take in your reprehensions, appears most manifestly in this objection. For I say in that demonstration of mine, that _the velocity of the point A in describing the spiral increaseth continually in proportion to the times_. For seeing it goes on uniformly in the semidiameter, it is impossible it should not pass into greater and greater circles, proportionally to the times, and consequently it must have a swifter and swifter motion circular, to be compounded with the uniform motion in every point of the radius as it turneth about. This objection therefore is nothing but an effect of a will, without cause, to contradict.

The other objection is, that “_Granting all to be true hitherto, yet because it depends upon the finding of a straight line equal to a parabolical line in the eighteenth chapter, where I was deceived, I am also deceived here_.” True. But because in the eighteenth chapter of this English edition I have found a straight line equal to the spiral line of Archimedes. I must here put you in mind that by these words in your objections to the fifth article at your number two, _Quatenus verum est, etc._, _we have demonstrated prop. 10, 11, 13_, _Arithmetica Infinitorum_; you make it appear that you thought your spiral (made of arches or circles) was the true spiral of Archimedes; which is fully as absurd as the quadrature of Joseph Scaliger, whose geometry you so much despise.

To the sixth article, which is a digression concerning the analytics of geometricians, you deny _that the efficient cause of the construction ought to be contained in the demonstration_. As if any problem could be known to be truly done, otherwise than by knowing first how, that is to say, by what efficient cause, and in what manner, it is to be done. Whatsoever is done without that knowledge, cannot be demonstrated to be done; as you see in your computation of the parabola, and paraboloeides, in your _Arithmetica Infinitorum_.

And whereas I said that _the ends of all straight lines drawn from a straight line, and passing through one and the same point, if their parts be proportional, shall be in a straight line_; is true and accurate; as also, _if they begin in the circumference of a circle, they shall also be in the circumference of another circle_. And so is this: _if the proportion be duplicate, they shall be in a parabola_. All this I say is true and accurately spoken. But this was no place for the demonstration of it. Others have done it. And I perceive by that you put in by parenthesis (“_Intelligis credo inter duas peripherias concentricas_”) that you understand not what I mean.

Hitherto reach your objections to my geometry: for the rest of your book, it containeth nothing but a collection of lies, wherewith you do what you can, to extenuate as vulgar, and disgrace as false, that which followeth, and to which you have made no special objection.

I shall therefore only add in this place concerning your _Analytica per Potestates_, that it is no art. For the rule, both in Mr. Ougthred, and in Des Cartes, is this: “_When a problem or question is propounded, suppose the thing required done, and then using a fit ratiocination, put A or some other vowel for the magnitude sought_.” How is a man the better for this rule without another rule, how to know when the ratiocination is fit? There may therefore be in this kind of analysis more or less natural prudence, according as the analyst is more or less wise, or as one man in choosing of the unknown quantity with which he will begin, or in choosing the way of the consequences which he will draw from the hypothesis, may have better luck than another. But this is nothing to art. A man may sometimes spend a whole day in deriving of consequences in vain, and perhaps another time solve the same problem in a few minutes.

I shall also add, that symbols, though they shorten the writing, yet they do not make the reader understand it sooner than if it were written in words. For the conception of the lines and figures (without which a man learneth nothing) must proceed from words either spoken or thought upon. So that there is a double labour of the mind, one to reduce your symbols to words, which are also symbols, another to attend to the ideas which they signify. Besides, if you but consider how none of the ancients ever used any of them in their published demonstrations of geometry, nor in their books of arithmetic, more than for the roots and potestates themselves; and how bad success you have had yourself in the unskilful using of them, you will not, I think, for the future be so much in love with them as to demonstrate by them that first part you promise of your _Opera Mathematica_. In which, if you make not amends for that which you have already published, you will much disgrace those mathematicians you address your epistles to, or otherwise have commended; as also the Universities, as to this kind of learning, in the sight of learned men beyond sea. And thus having examined your pannier of Mathematics, and finding in it no knowledge, neither of quantity, nor of measure, nor of proportion, nor of time, nor of motion, nor of any thing, but only of certain characters, as if a hen had been scraping there; I take out my hand again, to put it into your other pannier of theology, and good manners. In the mean time I will trust the objections made by you the astronomer (wherein there is neither close reasoning, nor good style, nor sharpness of wit, to impose upon any man) to the discretion of all sorts of readers.

==========

OF MANNERS.

TO THE SAME EGREGIOUS PROFESSORS OF THE MATHEMATICS IN
THE UNIVERSITY OF OXFORD.

LESSON VI.

Having in the precedent lessons maintained the truth of my geometry, and sufficiently made appear that your objections against it are but so many errors of your own, proceeding from misunderstanding of the propositions you have read in Euclid, and other masters of geometry; I leave it to your consideration to whom belong, according to your own sentence, the unhandsome attributes you so often give me upon supposition, that you yourselves are in the right, and I mistaken; and come now to purge myself of those greater accusations which concern my manners. It cannot be expected that there should be much science of any kind in a man that wanteth judgment; nor judgment in a man that knoweth not the manners due to a public disputation in writing; wherein the scope of either party ought to be no other than the examination and manifestation of the truth. For whatsoever is added of contumely, either directly or _scommatically_, is want of charity and uncivil, unless it be done by way of reddition from him that is first provoked to it. I say unless it be by way of reddition; for so was the judgment given by the emperor Vespasian in a quarrel between a senator and a knight of Rome which had given him ill language. For when the knight had proved that the first ill language proceeded from the senator, the emperor acquitted him in these words: “_Maledici senatoribus non oportere; remaledicere, fas et civile esse_.” Nevertheless, now-a-days, uncivil words are commonly and bitterly used by all that write in matter of controversy, especially in divinity, excepting now and then such writers as have been more than ordinarily well bred, and have observed how heinous and hazardous a thing such contumely is amongst some sorts of men, whether that which is said in disgrace be true or false. For evil words by all men of understanding are taken for a defiance, and a challenge to open war. But that you should have observed so much, who are yet in your mother’s belly, was not a thing to be much expected.

The faults in manners you lay to my charge are these: 1. _Self-conceit._ 2. _That I will be very angry with all men that do not presently submit to my dictates._ 3. _That I had my doctrine concerning Vision, out of papers which I had in my hands of Mr. Warner’s._ 4. _That I have injured the universities._ 5. _That I am an enemy to religion._ These are great faults; but such as I cannot yet confess. And therefore I must, as well as I can, seek out the grounds upon which you build your accusation. Which grounds (seeing you are not acquainted with my conversation) must be either in my published writings, or reported to you by honest men, and without suspicion of interest in reporting it. As for my self-conceit and ostentation, you shall find no such matter in my writings. That which you allege from thence is first, that in the epistle dedicatory I say of my book _De Corpore_, “_though it be little, yet it is full; and if good may go for great, great enough._” When a man presenting a gift great or small to his betters, adorneth it the best he can to make it the more acceptable; he that thinks this to be ostentation and self-conceit, is little versed in the common actions of human life. And in the same epistle, where I say of civil philosophy: “_It is no ancienter than my book De Cive_;” these words are added: “_I say it provoked, and that my detractors may see they lose their labour_.” But that which is truly said, and upon provocation, is not boasting, but defence. A short sum of that book of mine, now publicly in French, done by a gentleman I never saw, carrieth the title of _Ethics Demonstrated_ . The book itself translated into French, hath not only a great testimony from the translator Sorberius, but also from Gassendus, and Mersennus, who being both of the Roman religion had no cause to praise it, or the divines of England have no cause to find fault with it. Besides, you know that the doctrine therein contained is generally received by all but those of the clergy, who think their interest concerned in being made subordinate to the civil power; whose testimonies therefore are invalid. Why therefore, if I commend it also against them that dispraise it publicly, do you call it boasting? “_You have heard_,” you say, “_that I had promised the quadrature of the circle, &c._” You heard then that which was not true. I have been asked sometimes, by such as saw the figure before me, what I was doing, and I was not afraid to say I was seeking for the solution of that problem; but not that I had done it. And afterwards being asked of the success, I have said, I thought it done. This is not boasting; and yet it was enough, when told again, to make a fool believe it was boasting. But you, the astronomer, in the epistle before your philosophical essay, say “_You had a great expectation of my philosophical and mathematical works, before they were published_.” It may be so. Is that my fault? Can a man raise a great expectation of himself by boasting? If he could, neither of you would be long before you raised it of yourselves; saving that what you have already published, has made it now too late. For I verily believe there was never seen worse reasoning than in that philosophical essay; which any judicious reader would believe proceeded from a prevaricator, rather than from a man that believed himself; nor worse principles, than those in your books of Geometry. The expectation of that which should be written by me, was raised partly by the _Cogitata Physica-Mathematica_ of Mersennus, wherein I am often named with honour; and partly by others with whom I then conversed in Paris, without any ostentation. That no man has a great expectation of any thing that shall proceed from either of you two, I am content to let it be your praise.

Another argument of my self-conceit, you take from my contempt of the writers of metaphysics and school-divinity. If that be a sign of self-conceit, I must confess I am guilty; and if your geometry had then been published, I had contemned that as much. But yet I cannot see the consequence (unless you lend me your better logic) from despising insignificant and absurd language, to self-conceit.

And again, in your _Vindiciæ Academiarum_, you put for boasting, that in my _Leviathan_ , page 331, I would have _that book by entire sovereignty imposed upon the Universities_; and in my _Review_ , p. 713, that I say of my _Leviathan_ , “_I think it may be profitably printed, and more profitably taught in the University_.” The cause of my writing that book, was the consideration of what the ministers before, and in the beginning of, the civil war, by their preaching and writing did contribute thereunto. Which I saw not only to tend to the abatement of the then civil power, but also to the gaining of as much thereof as they could (as did afterwards more plainly appear) unto themselves. I saw also that those ministers, and many other gentlemen who were of their opinion, brought their doctrines against the civil power from their studies in the Universities. Seeing therefore that so much as could be contributed to the peace of our country, and the settlement of sovereign power without any army, must proceed from teaching; I had reason to wish, that civil doctrine were truly taught in the Universities. And if I had not thought that mine was such, I had never written it. And having written it, if I had not recommended it to such as had the power to cause it to be taught, I had written it to no purpose. To me therefore that never did write anything in philosophy to show my wit, but, as I thought at least, to benefit some part or other of mankind, it was very necessary to commend my doctrine to such men as should have the power and right to regulate the Universities. I say my doctrine; I say not my _Leviathan_ . For wiser men may so digest the same doctrine as to fit it better for a public teaching. But as it is, I believe it hath framed the minds of a thousand gentlemen to a conscientious obedience to present government, which otherwise would have wavered in that point. This therefore was no vaunting, but a necessary part of the business I took in hand. You ought also to have considered, that this was said in the close of that part of my book which concerneth policy merely civil. Which part, if you, the astronomer, that now think the doctrine unworthy to be taught, were pleased once to honour with praises printed before it, you are not very constant nor ingenuous. But whether you did so or not, I am not certain, though it was told me for certain. If it were not you, it was somebody else whose judgment has as much weight at least as yours.

And for anything you have to say from your own knowledge, I remember not that I ever saw either of your faces. Yet you, the professor of geometry, go about obliquely to make me believe that Vindex hath discoursed with me, once at least, though I remember it not. I suppose it therefore true; but this I am sure is false, that either he or any man living did ever hear me brag of my science, or praise myself, but when my defence required it. Perhaps some of our philosophers that were at Paris at the same time, and acquainted with the same learned men that I was acquainted with, might take for bragging the maintaining of my opinions, and the not yielding to the reasons alledged against them. If that be ostentation, they tell you the truth. But you that are so wise should have considered, that even such men as profess philosophy are carried away with the passions of emulation and envy (the sole ground of this your accusation) as well as other men, and instanced in yourselves. And this is sufficient to shake off your aspersions of ostentation and self-conceit. For if I added, that my acquaintance know that I am naturally of modest rather than of boasting speech, you will not believe it; because you distinguish not between that which is said upon provocation, and that which is said without provocation, from vain glory.

The next accusation is: “_That I will be very angry with all men that do not presently submit to my dictates; and that for advancing the reputation of my own skill, I care not what unworthy reflections I cast on others_.” This is in the epistle placed before the _Vindiciæ Academiarum_, subscribed by N S, as the plain song for H D in the rest of the book to descant upon. I know well enough the authors’ names; and am sorry that N S has lent his name to be abused to so ill a purpose. But how does this appear? What argument, what witness is there of it? You offer none; nor am I conscious of any. I begin to suspect since you, the professor of geometry, have in your objections to the twentieth chapter these words concerning “_Vindex, ocularis ille testis de quo hic agitur, erat, ni fallor, ille ipse_,”--that Vindex himself, in other company, has bestowed a visit on me. Seeing you will have me believe it, let it be so; and, as it is likely, not long after my return into England. At which time (for the reputation, it seems, I had gotten by my boasting) divers persons that professed to love philosophy and mathematics, came to see me; and some of them to let me see them, and hear and applaud what they applauded in themselves. I see now it hath happened to me with Vindex, as it happened to Dr. Harvey with Moranus. Moranus, a jesuit, came out of Flanders hither, especially, as he says, to see what learned men in divinity, ethics, physics, and geometry, were here yet alive, to the end that by discoursing with them in these sciences, he might correct either his own, or their errors. Amongst others he was brought, he says, to that most civil and renowned old man Dr. Harvey. That is very well. And in good earnest if he had made good use of the time which was very patiently afforded him, he might have learned of him (or of no man living) very much knowledge concerning the circulation of the blood, the generation of living creatures, and many other difficult points of natural philosophy. And if he had had anything in him but common and childish learning, he could have showed it nowhere more to his advantage, than before him that was so great a judge of such matters. But what did he? That precious time (which was but little, because he was to depart again presently for Flanders) he bestowed wholly in venting his own childish opinions, not suffering the Doctor scarce to speak; losing thereby the benefit he came for, and discovering that he came not to hear what others could say, but to show to others how learned he was himself already. Why else did he take so little time, and so misspend it? Or why returned he not again? But when he had talked away his time, and found (though patiently and civilly heard) he was not much admired, he took occasion, writing against me, to be revenged of Dr. Harvey, by slighting his learning publicly; and tells me that his learning was only experiments; which he says I say have no more certainty than civil histories. Which is false. My words are: “_Ante hos nihil certi in physica erat præter experimenta cuique sua, et historias naturales, si tamen et hæ dicendæ certæ sint, quæ civilibus historiis certiores non sunt_.” Where I except expressly from uncertainty the experiments that every man maketh to himself. But you see the near cut, by which vain glory joined with ignorance passeth quickly over to envy and contumely.

Thus it seems by your own confession I was used by Vindex. He comes with some of my acquaintance in a visit. What he said I know not, but if he discoursed then, as in his philosophical essay he writeth, I will be bold to say of myself, I was so far from morosity, or, to use his phrase, from being tetrical, as I may very well have a good opinion of my own patience. And if there passed between us the discourse you mention in your _Elenchus_, page 116, it was an incivility in him so great, that without great civility I could not have abstained from bidding him be gone. That which passed between us you say was this: “_I complained that whereas I made sense, nothing but a perception of motion in the organ, nevertheless, the philosophy schools through all Europe, led by the text of Aristotle, teach another doctrine, namely, that sensation is performed by species_.” This is a little mistaken. For I do glory, not complain, that whereas all the Universities of Europe hold sensation to proceed from species, I hold it to be a perception of motion in the organ. The answer of Vindex, you say, was: “_That the other hypothesis, whereby sense was explicated by the principles of motion, was commonly admitted here before my book came out, as having been sufficiently delivered by Des Cartes, Gassendus, and Sir Kenelm Digby, before I had published anything in this kind_.” This then, it seems, was it that made me angry. Truly I remember not an angry word that ever I uttered in all my life to any man that came to see me, though some of them have troubled me with very impertinent discourse; and with those that argued with me, how impertinently soever, I always thought it more civility to be somewhat earnest in the defence of my opinion, than by obstinate and affected silence to let them see I contemned them, or hearkened not to what they said. If I were earnest in making good, that the manner of sensation by such motion as I had explicated in my _Leviathan_ , is in none of the authors by him named, it was not anger, but a care of not offending him, with any sign of the contempt which his discourse deserved. But it was incivility in him to make use of a visit, which all men take for a profession of friendship, to tell me that that which I had already published for my own, was found before by Des Cartes, Gassendus, and Sir Kenelm Digby. But let any man read Des Cartes; he shall find, that he attributeth no motion at all to the object of sense, but an inclination to action, which inclination no man can imagine what it meaneth. And for Gassendus, and Sir Kenelm Digby, it is manifest by their writings, that their opinions are not different from that of Epicurus, which is very different from mine. Or if these two, or any of those I conversed with at Paris, had prevented me in publishing my own doctrine, yet since it was there known and declared for mine by Mersennus in the preface to his _Ballistica_ (of which the three first leaves are employed wholly in the setting forth of my opinion concerning sense, and the rest of the faculties of the soul) they ought not therefore to be said to have found it out before me. And consequently this answer which you say was given me by Vindex was nothing else but untruth and envy; and, because it was done by way of visit, incivility. But you have not alleged, nor can allege, any words of mine, from which can be drawn that I am so angry as you say I am with those that submit not to my dictates. Though the discipline of the University be never so good; yet certainly this behaviour of yours and his are no good arguments to make it thought so. But you the professor of geometry, that out of my words spoken against Vindex in my twentieth chapter, argue my angry humour, do just as well, as when (in your _Arithmetica Infinitorum_) from the continual increase of the excess of the row of squares above the third part of the aggregate of the greatest, you conclude they shall at last be equal to it. For though you knew that Vindex had given me first the worst words that possibly can be given, yet you would have that return of mine to be a demonstration of an angry humour; not then knowing what I told you even now in the beginning of this lesson, of the sentence given by Vespasian. But to this point I shall speak again hereafter.

Your third accusation is: “_That I had my doctrine of vision, which I pretended to be my own, out of papers which I had a long time in my hands of Mr. Warner’s_.” I never had sight of Mr. Warner’s papers in all my life, but that of _Vision by Refraction_ (which by his approbation I carried with me to Park, and caused it to be printed under his own name, at the end of Mersennus his _Cogitata Physico-Mathematica_, which you may have there seen, and another treatise of the proportions of alloy in gold and silver coin; which is nothing to the present purpose). In all my conversation with him, I never heard him speak of anything he had written, or was writing, _De penicillo optico_. And it was from me that he first heard it mentioned that light and colour were but fancy. Which he embraced presently as a truth, and told me it would remove a rub he was then come to in the discovery of the place of the image. If after my going hence he made any use of it (though he had it from me, and not I from him), it was well done. But wheresoever you find my principles, make use of them, if you can, to demonstrate all the symptoms of vision; and I will do (or rather have done and mean to publish) the same; and let it be judged by that, whether those principles be of mine, or other men’s invention. I give you time enough, and this advantage besides, that much of my optics hath been privately read by others. For I never refused to lend my papers to my friends, as knowing it to be a thing of no prejudice to the advancement of philosophy, though it be, as I have found it since, some prejudice to the advancement of my own reputation in those sciences; which reputation I have always postposed to the common benefit of the studious.

You say further (you the geometrician) that I had the proposition of the spiral line equal to a parabolical line from Mr. Robervall: true. And if I had remembered it, I would have taken also his demonstration; though if I had published his, I would have suppressed mine. I was comparing in my thoughts those two lines, spiral and parabolical, by the motions wherewith they were described; and considering those motions as uniform, and the lines from the centre to the circumference, not to be little parallelograms, but little sectors, I saw that to compound the true motion of that point which described the spiral, I must have one line equal to half the perimeter, the other equal to half the diameter. But of all this I had not one word written. But being with Mersennus and Mr. Robervall in the cloister of the convent, I drew a figure on the wall, and Mr. Robervall perceiving the deduction I made, told me that since the motions which make the parabolical line, are one uniform, the other accelerated, the motions that make the spiral must be so also; which I presently acknowledged; and he the next day, from this very method, brought to Mersennus the demonstration of their equality. And this is the story mentioned by Mersennus, prop. 25, corol. 2, of his _Hydraulica_; which I know not who hath most magnanimously interpreted to you in my disgrace.

The fourth accusation is: “_That I have injured the Universities_.” Wherein? First, “_In that I would have the doctrine of my Leviathan by entire sovereignty be imposed on them_.” You often upbraid me with thinking well of my own doctrine; and grant by consequence, that I thought this doctrine good; I desired not therefore that anything should be imposed upon them, but what (at least in my opinion) was good both for the Commonwealth and them. Nay more, I would have the state make use of them to uphold the civil power, as the Pope did to uphold the ecclesiastical. Is it not absurdly done to call this an injury? But to question, you will say, whether the civil doctrine there taught be such as it ought to be, or not, is a disgrace to the Universities. If that be certain, it is certain also that those sermons and books, which have been preached and published, both against the former and the present government, directly or obliquely, were not made by such ministers and others as had their breeding in the Universities; though all men know the contrary. But the doctrine which I would have to be taught there, what is it? It is this: “_That all men that live in a Commonwealth, and receive protection of their lives and fortunes from the supreme governor thereof, are reciprocally bound, as far as they are able, and shall be required, to protect that governor_.” Is it, think you, an unreasonable thing to impose the teaching of such doctrine upon the Universities? Or will you say they taught it before, when you know that so many men which came from the Universities to preach to the people, and so many others that were not ministers, did stir the people up to resist the then supreme civil power? And was it not truly therefore said, that the Universities receiving their discipline from the authority of the pope, were the shops and operatories of the clergy? Though the competition of the papal and civil power be taken now away, yet the competition between the ecclesiastical and the civil power hath manifestly enough appeared very lately. But neither is this an upbraiding of an University (which is a corporation or body artificial), but of particular men, that desire to uphold the authority of a Church, as of a distinct thing from the Commonwealth. How would you have exclaimed, if, instead of recommending my _Leviathan_ to be taught in the Universities, I had recommended the erecting of a new and lay-university, wherein lay-men should have the reading of physics, mathematics, moral philosophy, and politics, as the clergy have now the sole teaching of divinity? Yet the thing would be profitable, and tend much to the polishing of man’s nature, without much public charge. There will need but one house, and the endowment of a few professions. And to make some learn the better, it would do very well that none should come thither sent by their parents, as to a trade to get their living by, but that it should be a place for such ingenuous men, as being free to dispose of their own time, love truth for itself. In the mean time divinity may go on in Oxford and Cambridge to furnish the pulpit with men to cry down the civil power, if they continue to do as they did. If I had, I say, made such a motion in my _Leviathan_ , though it would have offended the divines, yet it had been no injury. But it is an injury, you will say, to deny in general the utility of the ancient schools, and to deny that we have received from them our geometry. True, if I had not spoken distinctly of the schools of philosophy, and said expressly, that the geometricians passed not then under the name of philosophers; and that in the school of Plato (the best of the ancient philosophers) none were received that were not already in some measure geometricians. Euclid taught geometry; but I never heard of a sect of philosophers called Euclidians, or Alexandrians, or ranged with any of the other sects, as Peripatetics, Stoics, Academics, Epicureans, Pyrrhonians, &c. But what is this to the Universities of Christendom? Or why are we beholden for geometry to our universities, more than to Gresham College, or to private men in London, Paris, and other places, which never taught or learned it in a public school? For even those men that living in our Universities have most advanced the mathematics, attained their knowledge by other means than that of public lectures, where few auditors, and those of unequal proficiency, cannot make benefit by one and the same lesson. And the true use of public professors, especially in the mathematics, being to resolve the doubts, and problems, as far as they can, of such as come unto them with desire to be informed.

That the Universities now are not regulated by the Pope, but by the civil power, is true, and well. But where say I the contrary? And thus much for the first injury.

Another, you say, is this, that in my _Leviathan_ , p. 670, I say: “_The principal schools were ordained for the three professions of Roman religion, Roman law, and the art of medicine_.” Thirdly, that I say: “_Philosophy had no otherwise place there than as a hand-maid to Roman religion_.” Fourthly: “_Since the authority of Aristotle was received there, that study is not properly philosophy, but Aristotelity_.” Fifthly: “_That for geometry, till of late times it had no place there at all_.” As for the second, it is too evident to be denied; the fellowships having been all ordained for those professions; and (saving the change of religion) being so yet. Nor hath this any reflection upon the Universities, either as they now are, or as they then were, seeing it was not in their own power to endow themselves, or to receive other laws and discipline than their founder and the state was pleased to ordain. For the third, it is also evident. For all men know that none but the Roman religion had any stipend or preferment in any university, where that religion was established? No, nor for a great while, in their commonwealths; but were everywhere persecuted as heretics. But you will say, the words of my _Leviathan_ are not, philosophy “_had no place_,” but “_hath no place_.” Are you not ashamed to lay to my charge a mistake of the word _hath_ for _had_? which was either a mistake of the printer, or if it were so in the copy, it could be no other than the mistake of a letter in the writing, unless you think you can make men believe that after fifty years being acquainted with what was publicly professed and practised in Oxford and Cambridge, I knew not what religion they were of. This taking of advantage from the mistake of a word, or of a letter, I find also in the _Elenchus_, where for _prætendit se scire_, there is _prætendit scire_, which you the geometrician sufficiently mumble, mistaking it I think for an anglicism, not for a fault of the impression.

To the fourth, you pretend, that men are not now so tied to Aristotle as not to _enjoy a liberty of philosophising, though it were otherwise when I was conversant in Magdalen Hall_. Was it so then? Then am I absolved, unless you can show some public act of the university made since that time to alter it. For it is not enough to name some few particular ingenuous men that usurp that liberty in their private discourses, or, with connivance, in their public disputations. And your doctrine, that even here you avow, of _abstracted essences_, _immaterial substances_, and of _nunc-stans_; and your improper language in using the word (not as mine, for I have it nowhere) _successive eternity_; as also your doctrine of _condensation_, and your arguing from natural reason the incomprehensible mysteries of religion, and your malicious writing, are very shrewd signs that you yourselves are none of those which you say do _freely philosophise_; but that both your philosophy and your language are under the servitude, not of the Roman religion, but of the ambition of some other doctors, that seek, as the Roman clergy did, to draw all human learning to the upholding of their power ecclesiastical. Hitherto therefore there is no injury done to the universities. For the fifth, you grant it, namely, “_that till of late there was no allowance for the teaching of geometry_.” But lest you should be thought to grant me anything, you say, you the astronomer, “_geometry hath now so much place in the universities, that when Mr. Hobbes shall have published his philosophical and geometrical pieces, you assure yourself you shall be able to find a greater number in the university who will understand as much, or more, of them than he desired they should_,” &c. But though this be true of the _now_, yet it maketh nothing against my _then_. I know well enough that Sir Henry Savile’s lectures were founded and endowed since. Did I deny _then_ that there were in Oxford many good geometricians? But I deny _now_, that either of you is of the number. For my philosophical and geometrical pieces are published, and you have understood only so much in them, as all men will easily see by your objections to them, and by your own published geometry, that neither of you understand anything either in philosophy or in geometry. And yet you would have those books of yours to stand for an argument, and to be an index of the philosophy and geometry to be found in the universities. Which is a greater injury and disgrace to them, than any words of mine, though interpreted by yourselves.

Your last and greatest accusation, or rather railing (for an accusation should contain, whether true or false, some particular fact, or certain words, out of which it might seem at least to be inferred), is, that I am an enemy to religion. Your words are: “_It is said that Mr. Hobbes is no otherwise an enemy to the Roman religion, saving only as it hath the name of religion_.” This is said by Vindex. You, the geometrician, in your epistle dedicatory, say thus: “_With what pride and imperiousness he tramples on all things both human and divine, uttering fearful and horrible words of God_, (peace), _of sin, of the holy Scripture, of all incorporeal substances in general, of the immortal soul of man, and of the rest of the weighty points of religion_ (down), _it is not so much to be doubted as lamented_.” And at the end of your objections to the eighteenth chapter, “_Perhaps you take the whole history of the fall of Adam for a fable, which is no wonder, when you say the rules of honouring and worshipping of God are to be taken from the laws_.” Down, I say; you bark now at the supreme legislative power. Therefore it is not I, but the laws which must rate you off. But do not many other men, as well as you, read my _Leviathan_ , and my other books? And yet they all find not such enmity in them against religion. Take heed of calling them all atheists that have read and approved my _Leviathan_ . Do you think I can be an atheist and not know it? Or knowing it, durst have offered my atheism to the press? Or do you think him an atheist, or a contemner of the Holy Scripture, that sayeth nothing of the Deity but what he proveth by the Scripture? You that take so heinously that I would have the rules of God’s worship in a Christian commonwealth taken from the laws, tell me, from whom you would have them taken? From yourselves? Why so, more than from me? From the bishops? Right, if the supreme power of the commonwealth will have it so; if not, why from them rather than from me? From a consistory of presbyters by themselves, or joined with lay-elders, whom they may sway as they please? Good, if the supreme governor of the commonwealth will have it so; if not, why from them, rather than from me, or from any man else? They are wiser and learneder than I. It may be so; but it has not yet appeared. Howsoever, let that be granted. Is there any man so very a fool as to subject himself to the rules of other men in those things which so nearly concern himself, for the title they assume of being wise and learned, unless they also have the sword which must protect them. But it seems you understand the sword as comprehended. If so, do you not then receive the rules of God’s worship from the civil power? Yes, doubtless; and you would expect, if your consistory had that sword, that no man should dare to exercise or teach any rules concerning God’s worship which were not by you allowed. See therefore how much you have been transported by your malice towards me, to injure the civil power by which you live. If you were not despised, you would in some places and times, where and when the laws are more severely executed, be shipped away for this your madness to America, I would say, to Anticyra. What luck have I, when this, of the laws being the rules of God’s public worship, was by me said and applied to the vindication of the Church of England from the power of the Roman clergy, it should be followed with such a storm from the ministers, presbyterian and episcopal, of the Church of England? Again, for those other points, namely, that I approve not of incorporeal bodies, nor of other immortality of the soul, than that which the Scripture calleth eternal life, I do but as the Scripture leads me. To the texts whereof by me alleged, you should either have answered, or else forborne to revile me for the conclusions I derived from them. Lastly, what an absurd question is it to ask me whether it be in the power of the magistrate, whether the world be eternal or not? It were fit you knew it is in the power of the supreme magistrate to make a law for the punishment of them that shall pronounce publicly of that question anything contrary to that which the law hath once pronounced. The truth is, you are content that the papal power be cut off, and declaimed against as much as any man will; but the ecclesiastical power, which of late was aimed at by the clergy here, being a part thereof, every violence done to the papal power is sensible to them yet; like that which I have heard say of a man, whose leg being cut off for the prevention of a gangrene that began in his toe, would nevertheless complain of a pain in his toe, when his leg was cut off.

Thus much in my defence; which I believe if you had foreseen, this accusation of yours had been left out. I come now to examine (though it be done in part already) what manners those are which I find everywhere in your writings.