Due correction for Mr Hobbes· Or Schoole discipline, for not saying his lessons right. In answer to his Six lessons, directed to the professors of mathematicks. / By the professor of geometry.

SECT. I. Concerning his Rhetorick and good Languge. (Book 1)

IT seems, M. Hobs, (by the fag end of your Book of Body in English) that you have a mind to say your lesson; and that the Mathematick Professors of Ox∣ford should heare you. Truth is, 'tis scarce worth the while ei∣ther for you or us. Yet we could be contented, for once, to hear you; (if we thought you would say any thing that were worth hearing) But to make a constant practice of it, or to entertain you as one of our Schollars, I have n•• mind at all. Because, I fear, you are to old to learne, (though you have as much need as those that be yonger;) and yet will think much to be whipt, when you doe not sa•• your Lesson right.

But, before we go further, I should ask you; what moved you to say your Lessons in English, when as the Books, a∣gainst which you doe chiefely intend them, were written in Latine? But I foresee a faire answer that you might possibly make; (and therefore doe nor much wonder at it.) There

be many grave and weighty reasons that might move you thereunto.

As first, because you doe presume, that there may be found divers persons, who may understand rayling in English, that yet doe not understand Mathematicks in Latin: and those being the persons on whom you have greatest hope of do∣ing good, you ought to have a speciall regard to them, and apply your selfe to their capacities.

Secondly, because in case you should have attempted an Answer in Latin; you had lost your labour as to the whole design: For then those who should read your answer, would be able also to read that against which you write: and, comparing both together, would presently see to how little purpose all is that you have said. Whereas now your English Readers must be faine to take upon trust what you please to tell them. (Whereby you gain clearly, as to them, the opportunity of misrepresenting at pleasure what you see good.) And for this Reason, if you shall think fit to make any reply to this; I would advise you to doe it in Latin; that so Forrainers, who understand not English, may take upon trust what you shall please to tell them.

But thirdly, and principally (which is the reason of greatest weight) because that when ever you have thought it convenient to repaire to Billingsgate, to leane the art of Well-speaking, for the perfecting of your naturall Rheto∣rick; you have not found that any of the Oister-women could teach you to raile in Latin, and therefore it was re∣quisite to apply your selfe to such lauguage as they could teach you.

But prithee tell me, in good earnest, (for I cannot think you so simple as you would seem to be,) Whether you doe indeed believe (though you thought good to set a good face upon it, and talk big,) that all that you have said is worth a straw, either as to the defending of your Repu∣tation, or the impairing of ours?

As to the Rhetorick and good language of it, (with which I shall first begin) that you can upon all occasions, or without occasion, give the titles of Foole, Beast, Asse, D••gge, &c. (which I take to be but barking,) with the rest of your course complements: You may take them, per∣haps, to be admirable in their kind; yet are they no better then a man might have at Billingsgate for a box o'th ear.

And of no better alloy are those other garnishes; That we un∣derstand not what is Quantity, Line, Superficies, Angle, and Pro∣portion: (and truly that's a sad case:) That neither of us un∣derstand any thing either in Philosophy or in Geometry; (A lack a day!) That you do verily believe (it's pitty you can't per∣swade some body else to be of your fai••h,) that since the be∣ginning of the World there hath not been (and who doubts but you are a good Historian,) nor ever shall be, (and you hope your Prognosticks may be believed, for you would have us think you have been taken for a Conjurer,) so much absurdi∣ty written in Geometry, as is to be found in these books of mine, (you should alwaies except your own Learned Works, which doubtlesse are, in this kind, incomparable pieces. But the truth is, you are not altogether out here; for in my Elenchus, which is one of the Books you mention, you may see that there hath been mach absurdity written in Geometry, and, they that read it, may know by whom.) But you have confuted them wholly and clearly (it seems you make cleare work where you come) in two or three leaves, (a quick rid∣dance!) That, the negligences of your own you need not be asha∣med of, (because you are ashamed of nothing;) That you ve∣rily believe there was never seen worse reasoning, then in that Philos••phicall Essay, (and that's all the confutation of it:) nor worse Principles then these in our Books of Geometry; (and that's another Article of your Faith) That, by the use of Symbols, and the way of Analysis by squares and cubes, &c. you never saw any thing added to the Science of Geometry; (by which a man may see what a good Geometer you are like to prove;) That the Scab of Symbols, or Gambols, (your tongue is your own, you may call them what you please,) or the Symbolick tongue is harder to understand then Welch or Irish, (no marvaile then, you never saw any thing there∣by added to Geometry.) That, to confute your Learned labours, is but to take wing like Beetles, from your egestions; (it seems it was but a shitten piece we had to deale with.) That, what you like not, is worthy to be gilded, but you doe not meane with gold; That Symbols are pior unhandsome scaf, folds of Demonstration; and ought no more to appeare in publike, then the most deformed necessary businesse which you doe in your Chamber; (one would think, by such stuffe as this, together with the ribauldry in your obscene Poem De Mirabilibus Pecci, that you had not learned all your Rhetorick at Bil∣lingsgate,

but had gone to Turn-ball-street for part of it.) That, your faults are not attended with shame, (It's no com∣mendations, to be past shame;) That, you shall without our leaves be bold to say, (who ever doubted but that you be bold enough?) that your selfe are the first that hath made the grounds of Geometry firm and coherent, (as if Geometry were no lesse beholden to you, then Civil Philosophy; which, you say, is not ancienter then your Book de Cive.) That you have rea∣son to blash (not for any of your own faults doubtlesse, but) considering the opinion men will have beyond Sea, of the Geo∣metry taugh' in Oxford, (no doubt but the University of Ox∣ford, if men knew all; are much beholden to you for your tender care of them;) yet withall, that the third definition of the fift of Euclide, is as bad as any thing was ever said in Geo∣metry by D. Wallis, (And, if so, then doubtlesse D. Wallis need not be much dismaid; for Euclide hath not been ac∣counted hitherto a despicable Author.) But such bumbast as this, and a great deale more of the same kind, I suppose, you doe not take to be Mathematicall demonstrations; nor to prove any thing, but the Forehead and Fury of him that speaks it.

But because the stresse of all this lies only upon what you verily believe, and what you never saw, and what you feare men will think of us beyond Sea: &c. To ease you of this fcar, I think it will not be amisse to let you heare the opinion of others both concerning your selfe and us, and the busi∣nesse of Symbols (with which I see no reason why you should be so angry, save that you do not understand them.) that you may see▪ whether others haze the same belief with you. I need not tell you what Morinus and Tacquet think of the businesse. For those you have heard already. I shall only give you an extract of two or three Letters, which I have received from Persons whose face•• I never saw; nor were they otherwise engaged to deliver an opinion in the case, then that they met with my books abroad: And yet no Clergy men, He assure you.

The first is from a Noble Gentleman of good worth, who hath deserved better of the Mathematicks then ever M. Hobs is like to doe; and whom, I heare, you use to commend. His words are these.

Eodem ibi tempore [Paristis] a Viro Nobili pagella vestra de Circuli Quadratura, Londino mittebatur; simul{que} Hobbii Philoso∣losophia

Nova. Quam ubi primum examinare concessum est, con∣tinuo Paralogismum eum animadverti, quo Parabolicae lineae re∣ctam aequare contendit, calculoque refutavi. Deinde alia quoque notavi, quae nihilo saniora erant, authoremque ingenio minime de∣faecato praeferebant. Miror te hunç dignum judicasse quem tam prolixe refelleres. Etsi non sine voluptate Elenchum tuum pervolvi, doctum equidem atque acutum.

You see he hath no great opinion of you: He finds you full of Paralogismes: He takes you to be a man of a muddy brain; and wonders only that I thought it worth while to foul my fingers abou•• ••uch a piece as yours.

The other is a publick Professor of Mathematicks, of known abilities, and beyond exception; and he speaks yet somewhat fuller to the whole businesse.

Cum aestate praeterita in manus inciderit Thomae Hobbes Ele∣mentorum Philosophiae Sectio prima; abs••inere non potui quin tra∣ctatum istum leviter evolverim. Instigabat me ad hoc, tum Au∣thoris hujus celebritas, tum etiam quod plura in eadem tractatu offen debam Geometrica, quae si Philosophiam non excelerent, sal∣tem ut quam maxime illustratura forent, opinabar. Sed me illum perlustrante, cum talia ibi invenerim ejus de Algebra sive Ana••ys•• judicia, equibus mihi facile fuit colligere, quod Author hic in ea∣dem Arte parum deberet esse versatus; (quandoquidem haec ill•• Ars existit, ut si liber suus in Geometria egregii ac ardui quid con∣tineret, qualia se passim invenisse praetendere mihi videhatur, id ipsum huic Arti, judicio meo, in totum deberet;) Cumque adhuc in perlustrando dum p••rgebam, non nulla de rectae ac curvae aequalitate, aliaque complura animadvertebam quorum cognitionem nunquam mihi pollicebar, ac inter seponenda not abam, vel certe si spos ali∣qua inveniendi illa mihi superesset, quin Algebram in partes vo∣carem non dubitabam: Aliam exinde de ipso ••pinionem concepi, credens quod illa quae illū ante e••proprio penu deprompsisse autuma∣bam, non nisi aliorum inventa esse, sed in alium sensum ab eo tra∣ducta aut correpta: Ideoque siquid boni in eo comprehenderetur, id quam maxime esse ventilandum ac excutiendum; ac proinde il∣lius examen, si vel utile aut necessum judicarem, in commodius tempus mihi esse differendum. Quemadmodum autem haec ita conceperam, ita quoque evenit ut amicus, cui me eo tempore invi∣senti dictum tractatum exhibueram, falsitatem plurium illius pro∣positionum haud longe post invenerit, illasque uno folio coram om∣nibus exponere decreverit. Qui edere ista utiliter rotus, ubi se ad hoc accinxerat, tuum interim, vir▪ Clarissime, Elenchum in lucent

proditum vidit, ac postquam te isto munere optime defunctum de∣prehendit, a proposito suo destitit. Egregie autem te eum, Vir Clarissime, sed pro merito tamen excepisse ibidem agnovi, ita ut credam eum in posterum a te prudentiorem doctioremque factum, licet ille tibi nullas gratias (judicio meo) pro beneficio isto sit ha∣biturus, Inter illa quae in Elencho tuo offendi, nihil expectatio∣nem majorem mihi excitavit, quam Arithmetica tua Infinitorum, de qua subinde mentionem facis: Quam novissime in lucem pro∣ditam, quamprimum cum caeteris tuis tractatibus vidi, mihi com∣paravi, ac multa praeclara & ingeniosa inventa, qualia mihi pro∣posueram, continere deprehendi. Perpl•••• et autem quod tum in Arithmetica tua Infinitorum, tum in Sectionibus tuis Conicis per∣tractandis, calculum Geometricum ubique adhibueris, tum propter brevitatem, tum quod is (ut ipse mones) demonstrationum om∣nium fons existat, atque demonstrationes omnes, solenni modo fa∣ctae, certa arte ex illo confi••i possint. Id quod prae aliis Clarissimus D. des Cartes in Demonstrationibus suis est molitus, qui neglecta Theorematum ac Lemmatum longa serie, quibus alias in demon∣strando difficulter carere liceret, calculo omnia constare voluit; atque in eum finem passim aequationes investigat, quibus rei veritas, ac quomodo illa cognosci possit, absque verborum involueris, brevi∣ter atque perspicue ob oculos ponatur. Quae autem de Circuli qua∣dratura tradis, utrum scilicet rem acu tetigeris necne nondum examinare mihi contigit: subtilissime autem cum illam prosecu∣tus mihi videaris, atque etiam calculo ipsam inquisiveris, non du∣bito quin omnium saltem proxime atque accuratissime ad scopum collimaveris.

You see what he thinks of you, and mee, and Symbols. He discerns presently by your judgement of Algebra, what a Geometer you are like to prove; that it must needs be one who understood it not, that rants at that rate; and will yet talke of squaring a Circle, and find a streight line equall to a crooked, and other fine things, without the help of Al∣gebra. He sees by a little what the rest is like to prove; ei∣ther little worth, or not your own. And therefore, though at first he made hast to get it, yet when he sees what is in it, he thinks your book may well be thrown aside, or at least be examined at leisure. He tells you of another, that, had not my Elenchus prevented him, meant to have been upon the bones of you. He tells you, that my Elen••hus, as sharp as it is, is no more then you had deserved. He supposed

withall (though therein it seems he was deceived) that you would have learned from thence, more Mathematicks, and more discretion for the future; and yet did believe (as well he might) 〈◊〉〈◊〉 you would scarce thank me for that favour. He is well enough satisfied also with my other Pieces, (what ever you think of them,) and likes them never the worse for that Scab of Symbols (as you call it) but much the better; (because, though you understand them not, he doth.) And much more to that purpose.

And by this time, I hope, you be pretty well eased of your feare, least the University of Oxford should suffer in the opinion of Learned men beyond Sea, by reason of the Ma∣thematicks that we have written. (Nor have you reason to think, that Malmesbury, will be much the more renowned for your skill in that kind.) And, that you may not despise their Testimonies, the persons are very well known to the World, by what Works they have extant in Print, to be no contemptible Mathematicians.

Beside these, I shall, for the satisfaction of your English Readers (who perhaps may not so well understand the words of the Authors above mentioned,) adde an extract of one Letter more; from a noble Gentleman, whom as yet (to my knowledge) I never saw, nor had formerly any the lest intercourse with him by letter or otherwise, though I had before heard of his worth and skill, both in Mathematicks and other learning: And which is more, he is neither of the Clergy; nor any great Admirer of them, beyond other persons of equall worth and Learning. He was pleased, though wholly a stranger to mee, upon view of my Elenchus, to intimate to me by a Letter directed to a third person, That D. Wallis had unhappily guessed, that those propositions which M. Hobs had concerning the measure of Para∣b••lasters, were not his own, but borrowed from some body else without acknowledging his Author: and signified withall, that they were to be found demonstrated in an exercitation of Caval∣lerius, De usu Indivisibilium in Potestatibus Cossicis; (a piece which I then had never read:) And that M. Hobs, endeavouring to demonstrate them anew, had missed in it. For which civility from a person of Quality, to mee a meer stranger, I could doe no lesse then returne him a civill answer of thanks for that favour. In reply to which (having in the mean time

seen and perused my Arithmetica Infinitorum) he was pleased to honour me farther with this.

I had not so long deferred &c. but that &c. And I beseech you receive it now from a Person, who much honours your emi∣nent Learning and Humanity, and would egerly imbrace an oc∣casiō to give you most ample testimony of the esteem he hath for you. I had not, (before &c.) seen your Arithmetica Infinitorum, which alone, although your other labours were not taken in to make up the value, may equall you with the best deservers in the Mathematicks. I was before acquainted with many excellent Propositions therein by you demonstrated (as you partly know,) but admired them, there, as wholly new, not because you had de∣monstrated them only another way, but by a generall method, so little touched at by others, so in effect wholly new, and of so rare consequence for entring into the secrets and Soul of Geometry (if my judgement may passe for any thing) as truly I believe the Art may reckon it among the most confiderable advances given it. Sir, I wish all prosperity to your deservings, and humbly thank you for the fair admittance you have given me to your acquaintance and friendship, which I shall preserve with a tendernesse due to a thing so estimable; and believe, Sir, you have Power at your own mea∣sure in Yours &c.

This is English, and therefore needs no exposition; your English Reader, whether Mathematician or not, may un∣derstand it without help. You see all are not of your opi∣nion concerning my scurvy book of Arithmetica Infinitorum.

I will not trouble your patience with reciting more te∣stimonies in this kind; (though, the truth is, very many persons of Honour and Worth, and eminent for their skill in these studies, have been forward of their own accord to put more honour upon me in this kind, then were fit in modesty for me to own.) These you have heard already, are more, I presume, then you take any great content in; and the lest of them, were abundantly sufficient to outway your verily believe; upon the strength of which, you have the confidence to utter all those reproaches which in your scur∣rilous piece you endeavour to cast upon us; but find them to fall back, and foul your self. And you see withall, both how little reason we have to fear the opinion that men will have beyond Sea, of the Geometry taught at Oxford; and with

how much vanity it is that you tel us according to your Rhe∣torick, that when you think, how dejected we will be for the fu∣ture; and how the grief of so much time irrecoverably lost, and the consideration of how much our friends will be ashamed of us, will accompany us for the rest of our life, you have more compassion for us then we have deserved. No doubt Sir, but you are a very pittifull man! (who have so much compassion for us:) And we are much bound to behold you. But since your cō∣passion of us, is not only more then you think we deserve, but, likewise, more then we think we stand in need of; we are loath your good nature should be injurious to your selfe. And therefore, knowing how much your selfe at present nay need compassion, we desire you to suffer that charity to begin at home, and not to be too lavish of that commodity upon us, of which at present we have so little need and you so much. But, that there may be no love lost between us; know, that we have the like compassion for you, upon the same account. You have but prevented us; and taught us, by your extreme civility, what might have better beseemed us to say. You tell us somewhere, the rea∣son, why the Ladies at Billingsgate, amongst all their com∣plements, have none readier then that of Whore, because, forsooth, when they remember themselves, they think that like∣liest to be true of others. And truly, we have reason to believe, that the anguish of such considerations as those you menti∣on, being so frequently present to your own thoughts, makes you so apt to think that others may be tormented in the like manner. (For who are more compassionate to those that feele the toothach, then those that are most tor∣mented with it themselves?) For, as your words are else∣where, A man of a tender forehead, after so much insolence, and so much contumelious language as yours, grounded upon arrogance and ignorance, would hardly endure to outlive it.

As for our selves; I do not find, that our friends do yet disowne us; or, that we need to feare, in this contest, the fury of our foes. And, whatever diseases you may believe my Conick, Sections, and Arithmetica Infinitorum, to be infe∣cted with: I do not see, that wiser Physitians can yet dis∣cerne, either the one to be troubled with the Scab, or the other with the Scurvy.

But you tell us, (and that may serve for answer to the Testimonies but now recited) Though the Beasts, that think

our railing to he roaring, have for a time admired us; yet, now that you have shewed them your eares, they will be lesse affrighted. Sir, those Persons (as they needed not the sight of your eares, but could tell by the voice what kind of creature brayed in your books: so they) doe not deserve such lan∣guage at your hands: And, you would not have said it to their faces. I know your Apology will be, that you say it provoked; and that by Vespasians law, when a man is provoked, it is not uncivill to give ill language. And that we may know you have been provoked, you tell us, how hainous and hazar∣dous a thing it is, to speake against some sorts of men, whether that which is said in disgrace be true or false; And by all men of understanding it is taken (not only for a provocation, but for a defiance, and a challenge to open Warre. And truly, so far as that may passe for Law, I cannot deny but that you have been provoked; for sure it is, that much hath been said a∣gainst you, and that, as is supposed, to your disgrace, and, I believe, the provocation hath been the greater, because that which hath been said, is true. But is this such a provocati∣on as may warrant you, by Vespasians Law, to rave at the next man you meet with? and to revenge your selfe upon him that comes next? Is it such a provocation of M. Hobs, for any man to admire us, that he may thenceforth, with∣out incivility, be called a Beast, or what you please? Is it not enough for you to involve the two Professors in the same crime, and consider us every where as one Author, and therefore both responsible, joyntly and severally, for what is said by either, because forsooth, we approve, you say, of one anothers doctrine: but must all that doe but admire us be un∣der the same condemnation? It's possible that some of them may admire our folly; (you see, one of them won∣ders at my discretion, that I would foule my fingers with you, or think you worth the Answering:) must they be called Beasts also? It seems 'tis a dangerous businesse for a man to admire any who do not admire you.

But I have done with the Rhetorick and good Lan∣guage. We have had a tast of it; and that's enough unlesse 'twere better. They that desire to have more of it, may ei∣ther read over your book, or goe to Billingsgate, whether they please.

But when men shall heare you rant it after this rate, and talk high; surely they must needs think, that you have very

good ground for it, must they not? A shallow foundation would never bear a confidence of such a towring hight. One would hardly believe mee, if I should say, That not∣withstanding these Braggadocian words, there is not any one assertion of mine, that you have either overthrown or shaken; nor any one of your own (which I charge to be false,) that you have defended; Yet that's the case. A great cry, and a little wooll! (as the man said when he shore his hoggs.)

Parturiunt Montes.— And that's it we have next to shew.