I have one thing more to add, and that is the disaffection I am charged

withal to the universities. Concerning the Universities of Oxford and

Cambridge, I ever held them for the greatest and noblest means of

advancing learning of all kinds, where they should be therein employed,

as being furnished with large endowments and other helps of study, and

frequented with abundance of young gentlemen of good families and good

breeding from their childhood. On the other side, in case the same means

and the same wits should be employed in the advancing of the doctrines

that tend to the weakening of the public, and strengthening of the power

of any private ambitious party, they would also be very effectual for

that; and consequently that if any doctrine tending to the diminishing

of the civil power were taught there, not that the Universities were to

blame, but only those men that in the universities, either in lectures,

sermons, printed books, or theses, did teach such doctrine to their

hearers or readers. Now you know very well that in the time of the Roman

religion, the power of the Pope in England was upheld principally by

such teachers in the universities. You know also how much the divines

that held the same principles in Church government with you, have

contributed to our late troubles. Can I therefore be justly taxed with

disaffection to the universities for wishing this to be reformed? And it

hath pleased God of late to reform it in a great measure, and indeed as

I thought totally, when out comes this your _Thesis_ boldly maintained

to show the contrary. Nor can I yet call this your doctrine the doctrine

of the university; but surely it will not be unreasonable to think so,

if by public act of the university it be not disavowed, which done, and

that as often as there shall be need, there can be no longer doubt but

that the universities of England are not only the noblest of all

Christian universities, but also absolutely, and of the greatest benefit

to this commonwealth that can be imagined, except that benefit of the

head itself that uniteth and ruleth all. I have not here particularized

at length all the ill consequences that may be deduced from this

_Thesis_ of yours, because I may, when further provoked, have somewhat

to say that is new. So much for the third ϛιγμὴ.

AN EXTRACT OF A LETTER CONCERNING THE

GRAMMATICAL PART OF THE CONTROVERSY

BETWEEN MR. HOBBES AND DR. WALLIS.

Mr. Hobbes hath these words: “_Longitudinem percursam motu uniformi, cum

impetu ubique ipsi B D æquali_.” Dr. Wallis saith _cum_ were better out,

unless you would have _impetus_ to be only a companion, not a _cause_.

Mr. Hobbes answered it was the _ablative case of the manner_. The truth

is the ablative case of the _manner_ and _cause_ both, may be used with

the conjunction _cum_, as may be justified. Cicero in Lib. II. _De Nat.

Deorum_: “_Moliri aliquid cum labore operoso ac molesto_;” and in his

oration for Cæcina: “_De se autem hoc prædicat, Antiocho Ebulii servo

imperasse ut in Cæcinam advenientem cum ferro invaderet_.” Let us see

then what Dr. Wallis objects against Tully, where a casualty is

imported, though we may use _with_ in English, yet not _cum_ in Latin;

to kill with a sword, importing this to have an instrumental or causal

influence, and not only that it hangs by the man’s side whilst some

other weapon is made use of, is not in Latin _occidere cum gladio_, but

_gladio occidere_. This shows that the Doctor hath not forgot his

grammar, for the subsequent examples as well as this rule are borrowed

thence. But yet he might have known that great personages have never

confined themselves to this pedantry, but have chosen to walk in a

greater latitude. Most of the elegancies and idioms of every language

are exceptions to his grammar. But since Mr. Hobbes saith it is the

ablative case of the manner, there is no doubt it may be expressed with

_cum_. The Doctor in the meantime knew no more than what Lilly had

taught him; Alvarez would have taught him more; and Vossius in his book,

_De Constructione_, _cap._ XLVII. expressly teacheth, “_Ablativos causæ,

instrumenti, vel modi, non a verbo regi sed a præpositione omissa, a vel

ab, de, e vel ex, præ, aut cum, ac præpositiones eas quandoque exprimi

nisi quod cum ablativis instrumenti haud temere invenias_;” and

afterwards he saith, “_non timere imitandum_.” If this be so, then did

Mr. Hobbes speak grammatically, and with Tully, but not _usually_. And

might not one retort upon the Doctor, that Vossius is as great a critic

as he?

His next reflection is upon _prætendit scire_, this he saith is an

Anglicism. If this be all his accusation, upon this score we shall lose

many expressions that are used by the best authors, which I take to be

good Latinisms, though they be also Anglicisms, the latter being but an

imitation of the former. The Doctor therefore was too fierce to condemn

upon so general an account, that which was not to have been censured for

being an Anglicism, unless also it had been no Latinism. Mr. Hobbes

replies, that the printer had omitted _se_. He saith, this mends the

matter a little. It is very likely, for then it is just such another

Anglicism as that of Quintilian: “_Cum loricatus in foro ambularet,

prætendebat se id metu facere_.” The Doctor certainly was very

negligent, or else he could not have missed this in Robert Stephen. Or

haply he was resolved to condemn Quintilian for this and that other

Anglicism, “_Ignorantia prætendi non potest_,” as all those that have

used _prætendo_, which are many and as good authors as Dr. Wallis, that

makes his own encomiasts (not an Englishman amongst them) to write

Anglicisms.

Then he blames “_Tractatus hujus partis tertiæ, in qua motus et

magnitudo per se et abstracte consideravimus, terminum hic statuo_.”

Here I must confess the exception is colourable, yet I can parallel it

with the like objection made by Erasmus against Tully, out of whom

Erasmus quotes this passage: “_Diutius commorans Athenis, quoniam venti

negabant solvendi facultatem, erat animus ad te scribere_;” and excuses

it thus, that Tully might have had at first in his thoughts _volebam_ or

_statuebam_, which he afterwards relinquished for _erat animus_, and did

not remember what he had antecedently written, which did not vary from

his succeeding thoughts, but words. And this excuse may pass with any

who know that Mr. Hobbes values not the study of words, but as it serves

to express his thoughts, which were the same whether he wrote _in qua

motus et magnitudo per se at abstracte considerati sunt_ or

_consideravimus_. And if the Doctor will make this so capital, he must

prove it _voluntary_, and show that it is greater than what is legible

in the puny letter of his encomiast, whom he would have to be beyond

exception.

Now follows his ridiculous apology for _adducis malleum, ut occidas

muscam_. The cause why he did use that proverb, of his own phrasing, was

this. Mr. Hobbes had taken a great deal of pains to demonstrate what Dr.

Wallis thought he could have proved in short; upon this occasion he

objects, _adducis malleum ut occidas muscam_, which I shall suppose he

intended to English thus, _you bring a beetle to kill a fly_. Mr. Hobbes

retorted, that _adduco_ was not used in that sense. The Doctor

vindicates himself thus: _duco_, _deduco_, _reduco_, _perduco_,

_produco_, &c. signify the same thing, ergo, _adduco_ may be used in

that sense; which is a most ridiculous kind of arguing, where we are but

to take up our language from others, and not to coin new phrases. It is

not the grammar that shall secure the Doctor, nor weak analogies, where

elegance comes in contest. To justify his expression he must have showed

it _usu tritum_, or alleged the authority of some author of great note

for it. I have not the leisure to examine his impertinent citations

about those other compounds, nor yet of that simple verb _duco_; nay, to

justify his saying he hath not brought one parallel example. He talks

indeed very high, that _duco_, with its compounds, is a word of a large

signification, and amongst the rest _to bring_, _fetch_, _carry_, &c. is

so exceeding frequent in all authors, Plautus, Terence, Tully, Cæsar,

Tacitus, Pliny, Seneca, Virgil, Horace, Ovid, Claudian, &c. that he must

needs be either maliciously blind, or a very stranger to the Latin

tongue, that doth not know it, or can have the face to deny it. I read,

what will be my doom for not allowing his Latin; yet I must profess I

dare secure the Doctor for having read all authors, notwithstanding his

assertion, and I hope he will do the like for me. And for those which he

hath read, had he brought no better proofs than these, he had, I am

sure, been whipped soundly in Westminster School, for his impudence as

well as ignorance, by the learned master thereof at present. But I dare

further affirm, the Doctor hath not read in this point any, but only

consulted with Robert Stephen’s _Thesaurus Linguæ Latinæ_, whence he

hath borrowed his allegations in _adduco_; and for the other, I had not

so much idle time as to compare them. And, lest the fact might be

discovered, he hath sophisticated those authors whence Stephen cites the

expressions, and imposed upon them others. If it be not so, or that the

Doctor could not write it right when the copy was right before him, let

him tell me where he did ever read in Plautus, _adducta res in

fastidium_. I find the whole sentence in Pliny’s preface to Vespasian

(out of whom in the precedent paragraph he cites it) about the middle:

_alia vero ita multis prodita, ut in factidium sint adducta_, which is

the very example Stephanus useth, although he doth premise his _adducta

res in fastidium_. Let the Doctor tell where he ever did read in Horace,

_Ova noctuæ_, &c. _tædium vini adducunt_. Did he, or any else, with the

interposition of an &c. make Trochaics? I say, and Stephanus says so,

too, that it is in Pliny, lib. xiii. cap. 15, near the end; the whole

sentence runs thus: _Ebriosis Ova noctuæ per triduum data in vino,

tædium ejus adducunt_. I doubt not but these are the places he aimed at,

although he disguised and minced the quotations; if they be not, I

should be glad to augment my Stephanus with his additions.

These things premised, I come to consider the Doctor’s proofs: _Res eo

adducta est_: _adducta vita in extremum_: _adducta res in fastidium_:

_rem ad mucrones et manus adducere_: _contractares et adducta in

augustum_: _res ad concordiam adduci potest_: _in ordinem adducerem_:

_adducere febres, sitim, tedium vini_ (all in Robert Stephen) betwixt

which and _adducere malleum_, what a vast difference there is, I leave

them to umpire _qui terretes et religiosas nacti sunt aures_, who are

the competent judges of elegancy, and only cast in the verdict of one or

two, who are in any place (where the purity of the Latin tongue

flourisheth) of great esteem. Losæus, in his _Scopæ Linguæ Latinæ, ad

purgandam Linguam a barbarie_, &c. (would any think that the Doctor’s

elegant expression, frequent in all authors, which none but the

malicious or ignorant can deny, should suffer so contumelious an

expurgation?) Losæus, I say, hath these words: _Adferre plerique minus

attenti utuntur pro adducere. Quod Plautus, in Pseudolo, insigni exemplo

notat_.

_CA._--Attuli hunc.

_PS._--Quid attulisti?

_CA._--Adduxi volui dicere.

_PS._--Quis istic est?

_CA._--Charinus.

_Satis igitur admonet discriminis inter ducere, reducere, adducere, et

abducere, quæ de persona; et ferre, adferre_, &c. _quæ de re dicuntur_.

Idem, _Demetrium, quem ego novi, adduce: argentum non moror quin feras_.

_Cavendum igitur est ne vulgi more_, (let the Doctor mark this, and know

that _this author is authentic amongst the Ciceronians_), _adferre de

persona, dicamus, sed adducere; licet et hoc de certis quibusdam rebus

non inepte dicatur_. In this last clause he saith as much as Mr. Hobbes

saith, and what the Doctor proves; but, that ever the Doctor brought an

example which might resemble _adducis malleum_, is denied; for I have

mentioned already his allegations, every one, of _adduco_. Another

author, (a fit antagonist for the elegant Doctor), is the _Farrago

sordidorum Verborum_, joined with the Epitome of L. Valla’s

_Elegancies_. He saith: _Accerse, adhuc Petrum, Latine dicitur, pro eo

quod pueri dicunt, adfer Petrum_. And this may suffice to justify Mr.

Hobbes’s exception who proceeded no further than this author to tell the

Doctor that _adduco_ was used of animals. But the Doctor replies, _this

signification is true, but so may the other be also_. I say if it never

have been used so, it cannot be so, for we cannot coin new Latin words,

no more than French or Spanish who are foreigners. Mr. Hobbes was upon

the negative, and not to disprove the contrary opinion. If the Doctor

would be believed, he must prove it by some example, (which is all the

proof of elegancy), and till he do so, not to believe him, it is

sufficient not to have cause. But, Doctor Wallis, _why not adduco for a

hammer as well as a tree?_ I answer yes, equally for either, and yet for

neither. Did ever anybody go about to mock his readers thus solemnly? I

do not find, to my best remembrance, any example of it in Stephen, and

the Doctor is not wiser than his book; if there be, it is strange the

Doctor should omit the only pertinent example, and trouble us with such

impertinences for three or four pages. In Stephen there are _adducere

habenas_ and _adducere lorum_, but in a different sense. It is not

impossible I may guess at the Doctor’s aim. In Tully _de Nat. Deor._ as

I remember, there is this passage: _Quum autem ille respondisset, in

agro ambulanti ramulum adductum ut remissus esset, in oculum suum

recidisse_, where it signifies nothing else but to be _bent_, _bowed_,

_pulled back_, and in that sense, _the hammer of a clock_, or that of a

_smith, when he fetcheth his stroke_, may be said _adduci_. And this, I

conceive, the Doctor would have us in the close think to have been his

meaning; else, what doth he drive at in these words? “When you have done

the best you can, you will not be able to find better words than

_adducere malleum_ and _reducere_, to signify the two contrary motions

of the _hammer_, the one when you strike with it (_excellently

trivial!_) the other when you take it back (_better and better_), _What

to do?_ to fetch another stroke. If any can believe that this was his

meaning, I shall justify his Latin, but must leave it to him to prove

its sense. If he intended no more, why did he go about to defend the

other meaning, and never meddle with this? Which yet might have been

proved by this one example of mine? May not, therefore, his own saying

be justly retorted upon him in this case, _Adducis malleum, ut occidas

muscam_?

Another exception is, _Falsæ sunt, et multa istiusmodi_

(_propositiones_). I wish the Doctor could bring so good parallels, and

so many, out of any author, for his _Adducis malleum_, as Tully affords

in this case. Take one for all, out of the beginning of his _Paradoxes_:

_Animadverti sæpe Catonem, cum in senatu sententiam diceret, Locos

graves ex Philosophia tractare, abhorrentes ab hoc usu forensi, et

publico, sed dicendo consequi tamen, ut illa etiam populo probabilia

viderentur_. This is but a _Solæcophanes_, and hath many precedents

more, as in the second book of his _Academical Questions_, &c.

I cannot now stay upon each particular passage; I do not see any

necessity of tracing the Doctor in all his vagaries. Now, he disallows

_tanquam diceremus_, _as if we should say_. But why is that less

tolerable than _tanquam feceris_, _as if you had done_? “It should be

_quasi_, (forsooth!) or _ac si_, or _tanquam si_, which is Tully’s own

word.” What is _tanquam si_ become but one word? _Tanquam si tua res

agatur_, &c. Good Doctor, leave out Tully and all _Ciceronians_, or you

will for ever suffer for this, and your _Adducis malleum_. Is not this

to put yourself on their verdict when you oppose Mr. Hobbes with Tully?

But the Doctor gives his reason. And though he hath had the luck in his

_Adducis malleum_, to follow the first part of that saying, _Loquendum

cum vulgo_, yet now it is, _sentiendum cum sapientibus_. For _tanquam_

without _si_ signifies but _as_, not _as if_. It is pity the Doctor

could not argue in symbols too, that so we might not understand him; but

suppose all his papers to carry evidence with them, because they are

_mathematically_ scratched. How does he construe this:--

“Plance tumes alto Drusorum sanguine, tanquam

Feceris ipse aliquid, propter quod nobilis esses.”

So Cœlius, one much esteemed by Cicero, who hath inserted his Epistles

into his works, saith, in his fifth Epistle (Tul. Epist. Fam. lib. viii.

ep. 5), _Omnia desiderantur ab eo tanquam nihil denegatum sit ei quo

minus paratissimus esset qui publico negotio præpositus est_. But it was

not possible the Doctor should know this, it not being in Stephen, where

his examples for _tanquam si_ are.

But, the Doctor having pitched upon this criticism, and penned it,

somebody, I believe, put him in mind of the absurdity thereof; and yet

the generous _Professor_, (who writes running hand and never transcribed

his papers, if I am not misinformed), presumed nobody else could be more

intelligent than he, who had perused Stephen. He would not retract

anything, but subjoins, “That he will allow it as passable, because

other modern writers, and some of the ancients, have so used it, as Mr.

Hobbes hath done.” I know not what authors the Doctor meant, for, if I

am not much mistaken, I do not find any in Stephen. His citation of

Columella is not right, (lib. v. cap. 5), nor can I deduce anything

thence till I have read the passage, but, if he take Juvenal and Cœlius

for modern authors, I hope he will admit of Accius, Nævius, and

Carmenta, for the only ancients. Let him think upon this criticism, and

never hope pardon for his _Adducis malleum_, which is not half so well

justified, and yet none but _madmen_ or _fools_ reject it.

But certainly the Doctor should not have made it his business to object

_Anglicisms_, in whose Elenchus I doubt not but there may be found such

phrases as may serve to convince him that he is an Englishman, however

Scottified in his principles. If the Doctor doubt of it, or but desire a

catalogue, let him but signify his mind, and he shall be furnished with

a _Florilegium_. But I am now come to the main controversy about Empusa.

The Doctor saith nothing in defence of his _quibble_, nor gives any

reason why he jumbled languages to make a silly clinch, which will not

pass for wit either at Oxford or at Cambridge; no, nor at Westminster.

It seems he had derived _Empusa_ from ἓν and ποῦς, and said it was a

kind of _Hobgoblin_ that hopped upon one leg: and hence it was that the

boys’ play (_Fox come out of thy hole_) came to be called _Empusa_. I

suppose he means _Ludus Empusæ_. This derivation he would have to be

good, and that we may know his reading, (though he hath scarce consulted

any of the authors), he saith Mr. Hobbes did laugh at it, until somebody

told him that it was in the Scholiast of Aristophanes (as good a critic

as Mr. Hobbes), Eustathius, Erasmus, Cœlius Rhodiginus, Stephanus,

Scapula, and Calepine. But sure he doth not think to scape so. To begin

with the last; Calepine doth indeed say, _uno incedit pede, unde et

nomen_. But he is a _Modern_, and I do not see why his authority should

outweigh mine if his author’s reasons do not. He refers to Erasmus and

Rhodiginus. Erasmus in the adage, _Proteo mutabilior_ hath these words

of Empusa: _Narrant autem uno videri pedi_--this is not to hop--_unde et

nomen inditum putant_, Ἔμπουσαν ὁιονεὶ ἑνίποδα. He doth not testify his

approbation of the derivation at all, only lets you know what

etymologies some have given before him. And doth anybody think that Dr.

Harmar was the first which began to show his wit, (or folly), in

etymologizing words? Cœlius Rhodiginus doth not own the derivation, only

saith, _Nominis ratio est, ut placet Eustathio, quia uno incedit

pede_;--is this to hop?--_sed nec desunt qui alterum interpretentur

habere æneum pedem, et inde appellatam Empusam; quod in Batrachis

Aristophanes expressit_. And then he recites the interpretation that

Aristophanes’s Scholiast doth give upon the text, of which by and by. If

any credit be to be attributed to this allegation, his last thoughts are

opposite to Dr. Wallis; and _Empusa_ must be so called, not because she

hopped upon one leg, but because she had but one, the other being brass.

But for the former derivation he refers to Eustathius.

As to Eustathius, I do easily conjecture that the reader doth believe

that Rhodiginus doth mean Eustathius upon Homer, for that is the book of

most repute and fame, his other piece being no way considerable for bulk

or repute. But it is not that book, nor yet his History of Ismenias, but

his notes upon the 725th verse of Dionysius Περῖηγητής. The poet had

said of the stone _Jaspis_, that it was

Ἐχθρηὶν Ἐμπούσησι καὶ ἄλλοις ἔιδώλοισιν,

Upon which Eustathius thus remarks: Δοκεῖ γαρ ἀλεξίκακος εἶναι ἡ λίθος

ἅυτη, καὶ ἀποτροπιαςτικὴ φασμἀτων, ὧν ἕν ἐςτι καὶ ἡ Ἔμπουσα, δαιμονιόν

τι τερί τἰὼ Ἑκάτην, ἑνὶ ποδὶ δοκοῦν δἰήκεσθαι· (_fortè_ διερείδεσθαι

_Steph._) ὄθεν καὶ παρονομάζεται, ὡς ἔι τις ἔιπη μονόπους ποδι ζωοῦ· ὡς

τοῦ ἑτέρου ποδος χαλκοῦ ὄντος, κατὰ τὸν μῦθον. This testimony doth not

prove anything of _hopping_, and, as to the derivation, I cannot but say

that Eustathius had too much of the grammarian in him, and this is not

the first time, neither in this book, nor elsewhere, wherein he hath

trifled. It is observable out of the place, that there were more

_Empusas_ than one, as, indeed, the name is applied by several men to

any kind of frightful phantasm. And so it is used by several authors,

and for as much as phantasms are various, according as the persons

affrighted have been severally educated, &c. every man did impose this

name upon his own apprehensions. This gave men occasion to fain _Empusa_

as such--for who will believe that she was not apprehended as having

four legs, when she appeared in the form of a cow, dog, &c.--but, as

apprehended by _Bacchus_ and his man at that time. I do not find that

she appeared in any shape but such as made use of legs in going, whence

I imagine that _Empusæ_ might be opposite to the θεοὶ νεποδες, which

appellation was anciently fixed upon the gods, (_propitious_) upon a

two-fold account; first, for that they were usually effigiated as having

no feet, which is evident from ancient sculpture, and secondly, for that

they are all said not to walk, but rather swim, if I may so express that

_non gradiuntur, sed fluunt_, which is the assertion of all the

commentators I have ever seen upon that verse of Virgil:--

“Et vera incessu patuit dea”----

This whole discourse may be much illustrated from a passage in

Heliodorus, Æthiop. lib. iii. sec. 12, 13. Calasiris told Cnemon that

the Gods Apollo and Diana did appear unto him; Cnemon replied, Ἀλλὰ τίνα

δὴ τρόπον ἒφασκες ἐνδεδεῖχθαἱ σοι τοῦς θεοῦς ὅτι μὴ ἐνύπνιον ἦλθον, ἀλλ’

ἐναργῶς ἐφᾶνησαν; upon this the old priest answered, that both gods and

demons, when they appear to men, may be discovered by the curious

observer, both in that they never shut their eyes, καὶ τῳ βαδίσματι

πλέον, οὐ κατὰ διάστησιν τῶν ποδῶν οὐδέ μετάθεσιν ἀνυομένω, ἀλλὰ κατὰ

τινα ρὕμην ἀέριον, καὶ ὁρμὴν ἀπαραπόδιστον, τεμνόντων μᾶλλον τὸ περιεχον

ἢ διαπορευομένων. Δὶο δὴ καὶ τὰ ἀγάλματα τῶν θεῶν Ἀιγύπτιοι τὼ πὸδέ

ζευγνύντες καὶ ὥσπερ ἑνοῦντες ἵστᾶσιν. ἅ δὴ καὶ Ὅμηρος ἐιδῶς, ἅτε

Ἀιγύπτιος, καὶ τὴν ἱερὰν πάιδευσιν ἐκδιδαχθείς, συμβολικῶς τοῖς ἔπεσιν

ἐναπεθετο, τοῖς δυναμένοις συνιέναι γνωριζειν καταλιπών, ἐπι τοῦ

ποσειδῶνος, το

Ἴχνια γὰρ μετόπισθε, ποδῶν ἠδέ κνημάων

Ῥεῖ ἔγνων ἀπιὸντος.

οἴον ῥέοντος ἐν τῆ πορεία, τοῦτο γάρ εστι τό ῥεῖ ἀπιόντος, καὶ οῦχ ὥς

τινες ἠπάτηνται, ῥᾳδίως ἔγνων ὑπολαμβάνοντες. Farnaby, upon the place in

Virgil, observes, that _Deorum incessus est continuus et æqualis, non

dimotis pedibus, neque transpositis_, ἀλλὰ κατὰ ῥύμην ἀέριον. Cornelius

Schrevelius in the new Leyden notes saith, _Antiquissima quæque Deorum

simulachra, quod observarunt viri magni, erant_ τοῦς πόδας συμβεβηκότα,

_diique ipsi non gradiuntur sed fluunt_. Their statues were said to

stand rather upon columns than upon legs, for they seem to have been

nothing but columns shaped out into this or that figure, the base

whereof carrying little of the representation of a foot. These things

being premised, I suppose it easy for the intelligent reader to find out

the true etymology of _Empusa, quasi_ ἐν ποσιν οῦσα, or βάινουσα, from

going on her feet, whereas the other _gods_ and _demons_ had a different

gait. If any can dislike this deduction, and think her so named from

ἑνιπους, whereas she always went upon two legs, (if her shape permitted

it) though she might draw the one after her, as a man doth a wooden leg:

I say, if any, notwithstanding what hath been said, can join issue with

the Doctor, my reply shall be Σοὶ μὲν ταῦτα δοκοῦντ’ ἐστὶν, ἐμὸι δὲ

τάδε.

Now, as to the words of Aristophanes upon which the Scholiast descants,

they are these:--speaking of an apparition strangely shaped, sometimes

like a camel, sometimes like an ox, a beautiful woman, a dog, &c.

Bacchus replies:

Ἔμπουσα τοινὺν γ’ἐστι.

ΞΑ. πυρὶ γοῦν λάμπεται

ἅπαν το προσωπον, καὶ σκελος χαλκοῦν ἔχει.

ΔΙ. Νὴ τὸν Ποσειδῶ, καὶ βολιτινον θάτερον.

ΞΑ. Σἁφ’ ἵσθι.

The Scholiast hereupon tells us that _Empusa_, was Φαντασμα δαιμονιῶδες

ὑπὸ Ἑκάτης ἐπιπεμπόμενον καὶ φαινόμενον τοἴς δυστυχοῦσιν, ὅ δοκεῖ πολλὰς

μορφας αλλασσεω καὶ ὁι μεν φασιν ἀυτην μονοποδα εῖναι, καὶ

ἐτυμολογοῦσιν’ ὁιονεὶ ἑνιποδα, διὰ το ἑνὶ ποδι κεχρῆσθαι. And this is

all that is material in the Scholiast, except that he adds by and by,

that βολιτινον σκελος is all one with the leg of an ass. And this very

text and Scholiast is that to which all the authors he names, and more,

do refer.

I come now to Stephen, who, in his index, and in the word ποδίζω, gives

the derivation of _Empusa_. Ποδιζω, _gradior, incedo_, (not to hop) _sic

Suidas_ Ἔμπουσαν _dictam ait_ παρὰ το ἑνὶ ποδιζειν. In the index thus:

_sunt qui dictam putent_ παρὰ τὸ ἑνὶ ποδὶζειν, _quod uno incedat pedi,

quasi_ Ἔμπουσαν, _alterum enim pedem æneum habet_. But neither Stephen,

nor any else, except _Suidas_, whom the hypercritical Doctor had not

seen, no, not the Scholiast of Aristophanes (a better critic than Mr.

Hobbes) doth relate the etymology as their own. Nay, there is not one

that saith _Empusa_ hopped on one leg, which is to be proved out of

them. The great Etymological Dictionary deriveth it παρὰ τὸ ἐμποδιζειν,

to _hinder_, _let_, &c. its apparition being a token of ill luck. But,

as to the Doctor’s deduction, it saith, Ἔμπουσα Ψιλοῦπαι, εἰ καὶ δοκεῖ

παρὰ τὸ ἕνα συγκεῖσθαι. It doth only _seem_ so. And it is strange that

ἑν should not alter only its _aspiration_, but change its ν into μ,

which I can hardly believe admittable in Greek, least there should be no

difference betwixt its derivatives and those of ἐν. When I consider the

several μορμόνες which the Grecians had, some whereof did fly, some had

no legs, &c., I can think that the origin of this name may have been

thus: some amazed person saw a _spectrum_, and, giving another notice of

it, his companion might answer, it is Βριμὼ, Μορμὼ Ἡκὰτη, but he,

meeting with a new phantasm, cries, ἐν ποσὶ βαίνει or βαδίζει, for which

apprehension of his, somebody coined this expression of Ἔμποῦσα. It may

also be possibly deduced from Ἐμποδὶζω, so that τύχη ἐμποδιζουσα might

afterwards be reduced to the single term of _Empusa_. Nor do I much

doubt but that those who are conversant in languages, and know how that

several expressions are often jumbled together to make up one word upon

such like cases, will think this a probable origination. I believe,

then, that Mr. Hobbes’s friend did never tell him it was in Eustathius,

or that _Empusa_ was an _hopping phantasm_. It had two legs and went

upon both, as a man may upon a wooden leg. Ἔμποῦσα is also a name for

Lamia, and such was that which Menippus might have married, which, I

suppose, did neither hop nor go upon one leg, for he might have

discovered it. But Mr. Hobbes did not except against the derivation,

(although he might justly, derivations made afterwards carrying more of

fancy than of truth, and the Doctor is not excused for asserting what

others barely relate, none approve), but asked him where that is, in

what authors _he read that boys’ play to be so called_. To which

question, the Doctor, to show his reading and the good authors he is

conversant in, replies, _in Junius’s Nomenclator, Rider and Thomas’s

Dictionary, sufficient authors in such a business_, which, methinks, no

man should say that were near to so copious a library. It is to be

remembered that the trial now is in Westminster School, and amongst

Ciceronians, neither whereof will allow those to be sufficient authors

of any Latin word. Alas, they are but _Vocabularies_; and, if they bring

no author for their allegation, all that may be allowed them is, that,

by way of allusion, our modern play may be called _Ludus Empusæ_. But

that it is so called we must expect, till some author do give it the

name. These are so good authors, that I have not either of them in my

library. But I have taken the pains to consult, first, Rider; I looked

in him, (who was only author of the English Dictionary) and I could not

find any such thing. It is true, in the Latin Dictionary, which is

joined with Rider, but made by Holyoke; (O that the Doctor would but

mark!) in the index of obsolete words, there is _Ascoliasmus, Ludus

Empusæ_, _Fox to thy hole_, for which word, not signification, he

quoteth Junius. The same is in Thomasius, who refers to Junius in like

manner. But could the Doctor think the word obsolete, when the play is

still in fashion? Or, doth he think that this play is so ancient as to

have had a name so long ago, that it should now be grown obsolete? As

for Junius’s interpretation of _Empusa_, it is this: _Empusa, spectrum,

quod se infelicibus ingerit, uno pede ingrediens_. Had the Doctor ever

read him, he would have quoted him for his derivation of _Empusa_, I

suppose. In Ascoliasmus, he saith, _Ascoliasmus, Empusæ Ludus, fit ubi,

altero pede in aere librato, unico subsiliunt pede:_ ἀσκολιασμὸς

_Pollux; Almanicè, Hinckelen; Belgicè,_ _Op een been springhen;

Hinckepincken, Flandris_. But what is it in English he doth not tell,

although he doth so in other places often. What the Doctor can pick out

of the Dutch I know not; but, if that do not justify him, as I think it

doth not, he hath wronged Junius, and greatly imposed upon his readers.

But, to illustrate this controversy further, I cannot be persuaded the

Doctor ever looked into Junius, for, if he had, I am confident,

according to his wonted accurateness, he would have cited Pollux’s

_Onomasticon_ into the bargain, for Junius refers to him, and I shall

set down his words, that so the reader may see what _Ascoliasmus_ was,

and all the Doctor’s authors say _Ludus Empusæ_ and _Ascoliasmus_ were

one and the same thing. Julius Pollux (lib. ix. cap. 7): Ὁ δε

Ἀσκολὶασμὸς, (old editions read it, Ἀ’σκολιασμὸς et ασκολιάζω) τοῦ

ἑτέρου ποδὸς αἰωρουμένου, κατὰ μόνου τοῦ ἑτέρου πηδᾶν ἔπόιει; ὅπερ

Ἀσκωλιάζὲιν ὠνόμαζον· ἤτοι εἰς μἢκος ἐνήλλαντο, ἢ ὁ μὲν ἐδίωκεν οὕτως,

οἱ δὲ ὑπέφευγον ἐπ’ ἀμφοῖν θὲοντες, ἕως τινὸς τῳ φερομένῳ ποδὶ ὁ διὼκων

δυνηθῇ τυχεῖν· ἤ καὶ στάντες ἐπήδων, ἀριθμοῦντες τὰ πηδήματα· προσέκειτο

γὰρ τῷ πλήθει τὸ νικᾶν. Ἀσκωλιάζειν δὲ ἐκαλεῖτο καὶ τὸ ἐπιπηδᾶν ἀσκῷ

κενῷ καὶ ὑποπλέω πνευματος, ἠλείμμένω, ἵναπερ ὀλισθάνοιεν περὶ τὴν

ἀλοιφὴν. “So that _Ascoliasmus_, and consequently, _Ludus Empusæ_, was a

certain sport which consisted in hopping, whether it were by striving

who could hop furthest, or whether only one did pursue the rest hopping,

and they fled before him on both legs, which game he was to continue

till he had caught one of his fellows, or whether it did consist in the

boys’ striving who could hop longest. Or, lastly, whether it did consist

in hopping upon a certain bladder, which, being blown up and well oiled

over, was placed upon the ground for them to hop upon, that so the

unctuous bladder might slip from under them and give them a fall.” And

this is all that Pollux holds forth. Now, of all these ways, there is

none that hath any resemblance with our _Fox to thy hole_; but the

second: and yet, in its description, there is no mention of beating him

with gloves, as they do now-a-days, and wherein the play consists as

well as in hopping. It might, notwithstanding, be called _Ludus Empusæ_,

but not in any sort our _Fox to thy hole_; so that the Doctor and his

authors are out, imposing that upon Junius and Pollux which they never

said. And thus much may suffice as to this point. I shall only add out

of Meursius’s _Ludi Græci_, that _Ascolia_ were not _Ludus Empusæ_ but

_Bacchisacra_, and he quotes Aristophanes’s Scholiast in Plutus, Ἀσκώλια

ἑορτὴ Διονύσου ἀσκὸν γαρ οἵνου πληροῦντες, ἑνὶ ποδὶ τοῦτον ἐπεπήδον, καὶ

ὁ πηδήσας ἆθλον εἶχε τὸν οἵνου. As also Hesychius, Ἀσκωλιάζειν, κυρίως

τὸ ἐπὶ τοῦς ἀσκοὺς ἅλλεσθαι.

But I could have told the Doctor where he might have read of _Empusa_ as

being the name of a certain sport or game, and that is, _in Turnebus

Adversaria_, lib. xxvii. cap. 33. There he speaks of several games

mentioned by Justinian in his _Code_, at the latter end of the third

book, one of which he takes to be named _Empusa_; adding withal, _that

the other are games, it is indisputable_, only _Empusa in lite et causa

erit, quod nemo nobis facile assensurus sit Ludum esse, cum constet

spectrum quoddam fuisse formas, varie mutans. Sed quid vetat eo nomine

Ludum fuisse? Certe ad vestigia vitiatæ Scripturæ quam proximo accedit._

Yet he only is satisfied in this conjecture, till somebody else shall

produce a better. And now what shall I say? Was not Turnebus as good a

critic, and of as great reading as Dr. Wallis, who had read over Pollux,

and yet is afraid that nobody will believe _Empusa_ to have been a game,

and all he allegeth for it is, _quid vetat_? Truly, all I shall say, and

so conclude this business, is, that he had read over an infinity of

books, yet, had not had the happiness, which the Doctor had, to consult

with _Junius’s Nomenclator, Thomasius and Rider’s Dictionary, authors

sufficient in such a case_.

I now come to the Doctor’s last and greatest triumph, at which I cannot

but stand in admiration, when I consider he hath not got the victory.

Had the Doctor been pleased to have conversed with some of the fifth

form in Westminster School, (for he needed not to have troubled the

learned master), he might have been better informed than to have exposed

himself thus.

Mr. Hobbes had said that στιγμὴ signified _a mark with a hot iron_; upon

which saying the Doctor is pleased to play the droll thus: “Prithee tell

me, good Thomas, before we leave this point, (O the wit of a divinity

doctor!) who it was told thee that στιγμὴ was a mark with an hot iron,

for it is a notion I never heard till now, and do not believe it yet.

Never believe him again that told thee that lie, for as sure as can be,

he did it to abuse thee; ϛιγμὴ signifies a distinctive point in writing,

made with a pen or quill, not a mark made with a _hot iron_, such as

they brand rogues withal; and, accordingly, ϛιζω δῖαϛιζω, _distinguo_,

_interstinguo_, are often so used. It is also used of a _mathematical_

point, or somewhat else that is very small, στιγμὴ χρὸνου, a moment, or

the like. What should come in your cap, to make you think that ϛῖγμὴ

signifies a mark or brand with a _hot iron_? I perceive where the

business lies; it was ϛίγμα ran in your mind when you talked of ϛιγμὴ,

and, because the words are somewhat alike, you jumbled them both

together, according to your usual care and accurateness, as if they had

been the same.”

When I read this I cannot but be astonished at the Doctor’s confidence,

and applaud him who said, ἀμάθεια θάρσὸς φέρει. That the Doctor should

never hear that ϛιγμὴ signifies _a mark with a hot iron_, is a manifest

argument of his ignorance. But, that he should advise Mr. Hobbes not to

believe his own readings, or any man’s else that should tell him it did

signify any such thing, is a piece of notorious impudence. That ϛιγμὴ

_signifies a distinctive point in writing made with a pen or quill_, (is

a pen one thing and a quill another to write with?) nobody denies. But,

it must be withal acknowledged it signifies many things else. I know the

Doctor is a _good historian_, else he should not presume to object the

want of history to another; let him tell us how long ago it is since men

have made use of pens or quills in writing; for, if that invention be of

no long standing, this signification must also be such, and so it could

not be that from any allusion thereunto the mathematicians used it for a

point. Another thing I would fain know of this great historian, how long

ago ϛίζω and διαϛίζω began to signify _interpungo_? For, if the

mathematics were studied before the mystery of printing was found out,

(as shall be proved whenever it shall please the Doctor, out of his no

reading, to maintain the contrary), then the _mathematical_ use thereof

should have been named before the _grammatical_. And, if this word be

translatitious, and that sciences were the effect of long contemplation,

the names used wherein are borrowed from talk, Mr. Hobbes did well to

say, that στιγμὴ precedaneously to that _indivisible_ signification

which it afterwards had, did signify a _visible mark_ made by a hot

iron, or the like. And, in this procedure, he did no more than any man

would have done, who considers that all our knowledge proceeds from our

senses; as also that words do, _primarily_, signify things obvious to

_sense_, and only _secondarily_, such as men call _incorporeal_. This

leads me to a further consideration of this word. Hesychius, (of whom it

is said that he is _Legendus non tanquam Lexicographus, sed tanquam

justus author_), interprets στιγμὴ, νυγμή, which is a point of a greater

or lesser size, made with any thing. So ϛίζω signifies to prick or mark

with anything in any manner, and hath no impropriated signification in

itself, but according to the writer that useth it. Thus, in a

_grammarian_ ϛίζω signifies to _distinguish_, by _pointing_ often;

sometimes, even in them, it is the same with ὀβελίζω; sometimes it

signifies to set a mark that something is wanting in that place, which

marks were called ϛιγμαί. In matters of policy, ϛίζω signifies to

_disallow_, because they used to put a ϛιγμὴ (not ϛίγμα) before his name

who was either disapproved or to be mulcted. In punishment it signifies

to _mark_ or _brand_, whereof I cannot at present remember any other

ways than that of an _hot iron_, which is most usual in authors, because

most practised by the ancients. But, that the mark which the _Turks_ and

others do imprint without burning may be said ϛίζεσθαι, I do not doubt,

no more than that Herodian did to give that term to the ancient Britons,

of whom he says, τὰ σώματα ἐϛίζοντο γραφαῖς ποικίλαις, καὶ ζώων

παντοδαπῶν εἰκόσι. Thus, horses that were branded with κάππα and σαν

(κοππἀτιαι and σαμφοραι) were said ϛίζεσθαι. Thus, in its origin, ϛιγμὴ

doth signify a _brand or mark with an hot iron_, or the like; and that

must be the proper signification of στιγμὴ, which is proper to ϛίζω,

none but such as Dr. Wallis can doubt. In its _descendants_ it is no

less evident, for, from στιγμὴ comes _stigmosus_, which signifies to be

branded; _Vitelliana cicatrice stigmosus_, not _stigmatosus_. So Pliny

in his Epistles, as Robert Stephen cites it. And στιγματιας (the

derivative of στιγμὴ, which signifies any mark, as well as a brand, even

such as remain after stripes, being black and blue), was a nickname

imposed upon the grammarian Nicanor, ὅτι περὶ στιγμῶν ἐπολυλόγησε. And,

though we had not any examples of στῖγμὴ being used in this sense, yet,

from thence, for any man to argue against it, (but he who knows no more

than Stephen tells him) is madness, unless he will deny that any word

hath lost its right signification, and is used only, by the authors we

have, although neither the Doctor nor I have read all them, in its

analogical signification. I have always been of opinion, that στιγμὴ

signified a _single point_, big or little, it matters not; and στίγμα, a

_composure of many_; as γραμμὴ signifies a _line_, and γράμμα a

_letter_, made of several lines. For στίγμα signified the _owl_, the

_sæmæna_, the letter K, yea, _whole words, lines, epigrams_ engraven in

men’s faces; and στιγμὴ, I doubt not, had signified _a single point_,

had such been used, and so it became translatitiously used by

grammarians and mathematicians. I could give grounds for this

conjecture, and not be so impertinent as the Doctor in his sermon, where

he told men that σοφός was not in Homer; that from ἄφρων came _ebrius_;

that _sobrietas_ was not bad Latin, and that _sobrius_ was once, as I

remember, in Tully. Is this to speak suitably to the oracles of God, or

rather to lash out into idle words? Hath the Doctor any ground to think

these are not impertinences? Or, are we, poor mortals, accountable for

such _idle_ words as fall from us in private discourses, whilst these

ambassadors from heaven _droll_ in the pulpit without any danger of an

after-reckoning?

But I proceed to a further survey of the Doctor’s intolerable ignorance.

His charge in the end of the _school-master’s_ rant is, that he should

_remember_ στίγμα and στιγμὴ _are not all one_. I complained before that

he hath not cited Robert Stephen aright; now I must tell him he hath

been negligent in the reading of Henry Stephen: for in him he might have

found that στίγμα was sometimes all one with στιγμὴ, though there be no

example in him wherein στιγμὴ is used for στίγμα. Hath not Hesiod, (as

Stephen rightly citeth it), in his _Scutum_, 166-67.

Στἴγματα δ’ ὥς ἐπέφαντο ἴδεῖν δεινοῖσι δράκουσι

Κυανέα κατὰ νῶτα

_ubi scholiastes_ ὥσπερ δὲ στιγμαὶ ἦσαν ἐπάνω, τῶν ῥάχεων τῶν δρακόντων,

κατάστίκτοι γὰρ καὶ ποικίλοι ὁι ὄφεις. So Johannes Diaconus upon the

place, a man who (if I may use the Doctor’s phrase) was _as good a

critic as_ the Geometry Professor.

Thus much for the _Doctor_. To the understanding _reader_, I say that

στιγμὴ is used for burning with a hot iron: _2 Macchab._ ix. 11, where

speaking of Antiochus’s lamentable death, his body putrefying and

breeding worms, he is said, ἐις ετίγνωσιν τοῦ θεοῦ ἔρχεθαι θείᾳ μάστιγι,

κατα στιγμὴν ἐπιτεινόμενος ταῖς ἀλγηδόσι; _being pained as if he had

been pricked or burned with hot irons_. And that this is the meaning of

that elegant writer, shall be made good against the Doctor, when he

shall please to defend the vulgar interpretation. Pausanias, in

_Bœoticis_, speaking of Epaminondas, who had taken a town belonging to

the Sicyonians, called Phœbia (Φουβία) wherein were many Bœotian

fugitives, who ought, by law, to have been put to death, saith he

dismissed them under other names, giving them only a _brand_ or _mark_.

Πόλισμα ἑλὼν Σικυωνἰων Φουβίαν, ἔνθὰ ἦσαν το πολὺ οἱ Βοιώτιοι φυγάδες,

στιγμήν ἀφίησι τοῦς ἐγκαταληφθέντας ἄλλην σφίσιν ἣν ετυχε πατρίδα

ἐπονομάζων ἐκάστω. It is true στιγμὴν is here put _adverbially_, but

that doth not alter the case. Again, Zonaras, in the third tome of his

History, in the life of the Emperor Theophilus, saith, that when

Theophanes and another monk had reproved the said emperor for

demolishing images, he took and _stigmatized_ each of them with twelve

_iambics_ in their faces: εἶτα καὶ τὰς ὄψεις ἀυτῶν κάτεστιξε καὶ ταῖς

στιγμαῖς μέλαν ἐπέχεε γράμματα δὲ ἐτύπουν τὰ στιγματα, τὰ δὲ ἦσαν ἴαμβοι

οὗτοι. A place so evident, that I know not what the Doctor can reply.

This place is just parallel to what the same author saith in the life of

Irene, τἀς ὄψέις σφών καταστιξας ἐν γράμμασι, μέλανος εγχεομένου τοῖς

στίγμασι. If the Doctor object that he is a modern author, he will never

be able to render him as inconsiderable as Adrianus Junius’s

_Nomenclator_, Thomasius and Rider. If any will deny that he writes good

Greek, Hieronymus Wolfius will tell them, his only fault is

περισσολογια, _redundancy_ in words, and not the use of _bad_ ones.

Another example of στιγμὴ used in this sense, is in the collections out

of Diodorus Siculus, lib. xxxiv. as they are to be found at the end of

his works, and as Photius hath transcribed them into his _Bibliotheca_.

He saith that the Romans did buy multitudes of servants and employ them

in Sicily: Οἷς, ἐκ τῶν σωματοτροφείων ἀγεληδὸν απαχθεῖσιν, ἐυθύς

χαρακτῆρα ἐπέβαλλον, καὶ στιγμὰς τοἴς σώμασιν. These are the words but

of one author, but ought to pass for the judgment of two, seeing

Photius, by inserting them, hath made them his own.

Besides, it is the judgment of a great _master_ of the Greek tongue,

that _stigmata non tam puncta ipsa quam punctis variatam superficiem

Græci vocaverunt_. I need not, I suppose, name him, so great a critic as

the Doctor cannot be ignorant of him.

Nor, were στίγματα commonly, but upon extraordinary occasions, imprinted

with an hot iron. The letters were first made by incision, then the

blood _pressed_, and the place filled up with ink, the composition

whereof is to be seen in Aetius. And thus they did use to _matriculate_

soldiers also in the hand. Thus, did the Grecian emperor, in the

precedent example of Zonaras. And if the Doctor would more, let him

repair to Vinetus’s comment upon the fifteenth Epigram of Ausonius.

And now I conceive enough hath been said to vindicate Mr. Hobbes, and to

show the insufferable ignorance of the puny professor, and unlearned

critic. If any more shall be thought necessary, I shall take the pains

to collect more examples and authorities, though I confess I had rather

spend time otherwise, than in matter of so little moment. As for some

other passages in his book, I am no competent judge of _symbolic

stenography_. The Doctor (Sir Reverence) might have used a cleanlier

expression than that of a _shitten piece_, when he censures Mr. Hobbes’s

book.

Hitherto the letter.[1] By which you may see _what came into my (not

square) cap to call_ στιγμὴ _a mark with a hot iron, and that they who

told me_ that, did no more tell me a lie than they told you a lie that

said the same of στίγμα; and, if στιγμὴ be not right as I use it now,

then call these notes not στιγρας, but στίγματα. I will not contend with

you for a trifle. For, howsoever you call them, you are like to be known

by them. Sir, the calling of a divine hath justly taken from you some

time that might have been employed in geometry. The study of algebra

hath taken from you another part, for algebra and geometry are not all

one; and you have cast away much time in practising and trusting to

symbolical writings; and for the authors of geometry you have read, you

have not examined their demonstrations to the bottom. Therefore, you

perhaps may be, but are not yet, a geometrician, much less a good

divine. I would you had but so much ethics as to be civil. But you are a

notable critic; so fare you well, and consider what honour you do,

either to the University where you are received for professor, or to the

University from whence you came thither, by your geometry; and what

honour you do to Emanuel College by your divinity; and what honour you

do to the degree of Doctor, with the manner of your language. And take

the counsel which you publish out of your encomiast his letter; think me

no more worthy of your pains, you see how I have fouled your fingers.

-----

Footnote 1:

Written by Henry Stubbe, M.A. of Christ Church, Oxford, who was,

according to Anthony a Wood, “the most noted personage of his age that

these late times have produced.”

-----

THREE PAPERS

PRESENTED TO THE ROYAL SOCIETY

AGAINST DR. WALLIS.

TOGETHER WITH

CONSIDERATIONS

ON DR. WALLIS’S ANSWER TO THEM,

BY

THOMAS HOBBES,

OF MALMESBURY.

THREE PAPERS

PRESENTED TO THE ROYAL SOCIETY.

==========

TO THE RIGHT HONOURABLE AND OTHERS, THE LEARNED MEMBERS OF THE ROYAL

SOCIETY, FOR THE ADVANCEMENT OF SCIENCES.

PRESENTETH _to your consideration, your most humble servant, Thomas

Hobbes, (who hath spent much time upon the same subject), two

propositions, whereof the one is lately published by Dr. Wallis, a

member of your Society, and Professor of Geometry; which if it should be

false, and pass for truth, would be a great obstruction in the way to

the design you have undertaken. The other is a problem, which, if well

demonstrated, will be a considerable advancement of geometry; and though

it should prove false, will in no wise be an impediment to the growth of

any other part of philosophy._

DR. WALLIS,

DE MOTU, _Cap._ v. _Prop._ 1.

If there be understood an infinite row of quantities beginning with 0 or

(1)/(0), and increasing continually according to the natural order of

numbers, 0, 1, 2, 3, &c. or according to the order of their squares, as,

0, 1, 4, 9, &c. or according to the order of their cubes, as, 0, 1, 8,

27, &c. whereof the last is given; the proportion of the whole, shall be

to a row of as many, that are equal to the last, in the first case, as 1

to 2; in the second case, as 1 to 3; in the third case, as 1 to 4, &c.

This proposition is the ground of all his doctrine concerning the

centres of gravity of all figures. Wherein may it please you to

consider:

First, whether there can be understood an infinite row of quantities,

whereof the last can be given. Secondly, whether a finite quantity can

be divided into an infinite number of lesser quantities, or a finite

quantity can consist of an infinite number of parts, which he buildeth

on as received from Cavallieri. Thirdly, whether (which in consequence

he maintaineth) there be any quantity greater than infinite. Fourthly,

whether there be, as he saith, any finite magnitude of which there is no

centre of gravity. Fifthly, whether there be any number infinite. For it

is one thing to say, that a quantity may be divided perpetually without

end, and another thing to say, that a quantity may be divided into an

infinite number of parts. Sixthly, if all this be false, whether that

whole book of _Arithmetica Infinitorum_, and that definition which he

buildeth on, and supposeth to be the doctrine of Cavallieri, be of any

use for the confirming or confuting of any propounded doctrine.

Humbly praying you would be pleased to declare herein your judgment, the

examination thereof being so easy, that there needs no skill either in

geometry, or in the Latin tongue, or in the art of logic, but only of

the common understanding of mankind to guide your judgment by.

THOMAS HOBBES,

ROSET. _Prop._ v.

_To find a straight line equal to two-fifths of the arc of a

quadrant._

I describe a square A B C D, and in it a quadrant D A C. Suppose D T be

two-fifths of D C, then will the quadrantal arc T V be two-fifths of the

arc C A. Again let D R be a mean proportional between D C and D T; then

will the quadrantal arc R S be a mean proportional between the arc C A

and the arc T V.

Suppose further a right line were given equal to the arc C A, and a

quadrantal arc therewith described; then will D C, C A, the arc on C A

be continually proportional. Set these proportionals in order by

themselves.

D C, C A, arc on C A∺

D R, R S, arc on R S∺

D T, T V, arc on T V∺

which are in continual proportion of the semi-diameter of the arc. And D

C, D R, D T are in a continual proportion by construction, and therefore

also C A, R S, T V, and arc on C A, arc on R S, arc on T V, in continual

proportion.

Therefore as D C to R S, so is R S to the arc on T V. And D C, R S, the

arc on T V will be continually proportional. And because D C, C A, the

arc on C A are also continually proportional, and have the first

antecedent D C common; the proportion of the arc on C A to the arc on T

V is (by Eucl. xiv. 28) duplicate of the proportion of C A to R S, and

the arc on R S a mean proportional between the arc on C A and the arc on

T V.

Now if D C be greater than R S, also R S must be greater than the arc on

T V; and the arc C A greater than the arc on R S. Therefore seeing D C,

C A, arc on C A, are continually proportional; the arc on T V, the arc

on R S, the arc on C A cannot be continually proportional, which is

contrary to what has been demonstrated. Therefore D C is not greater

than R S. Suppose, then, R S to be greater than D C, then will the arc

on R S be a mean proportional between the arc on T V, and a greater arc

than that on C A; and so the inconvenience returneth. Therefore the

semidiameter D C is equal to the arc R S, and D R equal to T V, that is

to say to two-fifths of the arc C A, which was to be demonstrated. Nor

needeth there much geometry for examining of this demonstration.

Therefore I submit them both to your censure, as also the whole

_Rosetum_, a copy whereof I have caused to be delivered to the secretary

of your society.

[Illustration]

TO THE

RIGHT HONOURABLE AND OTHERS,

THE LEARNED MEMBERS

OF

THE ROYAL SOCIETY,

FOR THE ADVANCEMENT OF THE SCIENCES.

-------

Presenteth to your consideration, your most humble servant Thomas

Hobbes, a confutation of a theorem which hath a long time passed for

truth; to the great hinderance of Geometry, and also of Natural

Philosophy, which thereon dependeth.

THE THEOREM.

_The four sides of a square being divided into any number of equal

parts, for example into 10; and straight lines drawn through the

opposite points, which will divide the square into 100 lesser squares;

the received opinion, and which Dr. Wallis commonly useth, is, that the

root of those 100, namely 10, is the side of the whole square._

THE CONFUTATION.

_The root 10 is a number of those squares, whereof the whole containeth

100, whereof one square is an unity; therefore the root 10, is 10

squares: Therefore the root of 100 squares is 10 squares, and not the

side of any square; because the side of a square is not a superficies,

but a line. For as the root of 100 unities is 10 unities, or of 100

soldiers 10 soldiers: so the root of 100 squares is 10 of those squares.

Therefore the theorem is false; and more false, when the root is

augmented by multiplying it by other greater numbers._

Hence it followeth, that no proposition can either be demonstrated or

confuted from this false theorem. Upon which, and upon the numeration of

infinites, is grounded all the geometry which Dr. Wallis hath hitherto

published.

And your said servant humbly prayeth to have your judgment hereupon: and

that if you find it to be false, you will be pleased to correct the

same: and not to suffer so necessary a science as geometry to be

stifled, to save the credit of a professor.

TO THE

RIGHT HONOURABLE AND OTHERS,

THE LEARNED MEMBERS

OF

THE ROYAL SOCIETY,

FOR THE ADVANCEMENT OF THE SCIENCES.

---

Your most humble servant Thomas Hobbes presenteth, that the quantity of

a line calculated by extraction of roots is not to be truly found. And

further presenteth to you the invention of a straight line equal to the

arc of a circle.

A square root is a number which multiplied into itself produced a

number.

DEFINITION.

And the number so produced is called a square number. For example:

Because 10 multiplied by 10 makes 100; the root is 10, and the square

number 100.

CONSEQUENT.

In the natural row of numbers, as 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12,

13, 14, 15, 16, &c. every one is the square of some number in the same

row. But square numbers (beginning at 1) intermit first two numbers,

then four, then six, &c. So that none of the intermitted numbers is a

square number, nor has any square root.

PROP. I.

A square root (speaking of quantity) is not a line, such as Euclid

defines, without latitude, but a rectangle.

[Illustration]

Suppose A B C D be the square, and A B, B C, C D, D A, be the sides, and

every side divided into 10 equal parts, and lines drawn through the

opposite points of division; there will then be made 100 lesser squares,

which taken altogether are equal to the square A B C D. Therefore the

whole square is 100, whereof one square is an unit; therefore 10 units,

which is the root, is ten of the lesser squares, and consequently has

latitude; and therefore it cannot be the side of a square, which,

according to Euclid, is a line without latitude.

CONSEQUENT.

It follows hence, that whosoever taketh for a principle, that a side of

a square is a mere line without latitude, and that the root of a square

is such a line (as Dr. Wallis continually does) demonstrates nothing.

But if a line be divided into what number of equal parts soever, so the

line have breadth allowed it (as all lines must, if they be drawn), and

the length be to the breadth as number to an unit; the side and the roof

will be all of one length.

PROP. II.

[Illustration]

Any number given is produced by the greatest root multiplied into

itself, and into the remaining fraction. Let the number given be two

hundred squares, the greatest root is 14(4)/(14) squares. I say that 200

is equal to the product of 14 into itself, together with 14 multiplied

into (4)/(14). For 14 multiplied into itself makes 196. And 14 into

(4)/(14) makes (56)/(14) which is equal to 4. And 4 added to 196 maketh

200; as was to be proved. Or take any other number 8, the greatest root

is 2; which multiplied into itself is 4, and the remainder (2)/(4)

multiplied into 2, is 4, and both together 8.

PROP. III.

But the same square calculated geometrically by the like parts,

consisteth (by Euclid II. 4) of the same numeral great square 196, and

of the two rectangles under the greatest side 14, and the remainder of

the side, or (which is all one) of one rectangle under the greatest

side, and double the remainder of the side; and further of the square of

the less segment; which altogether make 200, and moreover (1)/(49) of

those 200 squares, as by the operation itself appeareth thus:

The side of the greater segment is 14(4)/(14)

14(4)/(14)

Which multiplied into itself makes 200.

The product of 14, the greatest segment, into the two fractions

(4)/(14), that is, into (4)/(14) (or into twice (2)/(14)) is (56)/(14)

(that is 4); and that 4 added to 196 makes 200.

Lastly, the product of (2)/(14) into (2)/(14) or (1)/(7) into (1)/(7) is

(1)/(49). And so the same square calculated by roots is less by (1)/(49)

of one of those two hundred squares, than by the true and geometrical

calculation; as was to be demonstrated.

CONSEQUENT.

It is hence manifest, that whosoever calculates the length of an arc or

other line by the extraction of roots, must necessarily make it shorter

than the truth, unless the square have a true root.

-------

_The Radius of a Circle is a Mean Proportion between the Arc of a

Quadrant and two-fifths of the same._

Describe a square A B C D, and in it a quadrant D C A. In the side D C

take D T two-fifths of D C, and between D C and D T a mean proportional

D R, and describe the quadrantal arcs R S, T V. I say the arc R S is

equal to the straight line D C. For seeing the proportion of D C to D T

is duplicate of the proportion of D C to D R, it will be also duplicate

of the proportion of the arc C A to the arc R S, and likewise duplicate

of the proportion of the arc R S to the arc T V.

Suppose some other arc, less or greater than the arc R S, to be equal to

D C, as for example _r s_: then the proportion of the arc _r s_ to the

straight line D T will be duplicate of the proportion of R S to T V, or

D R to D T. Which is absurd; because D _r_ is by construction greater or

less than D R. Therefore the arc R S is equal to the side D C, which was

to be demonstrated.

COROL.

[Illustration]

Hence it follows that D R is equal to two-fifths of the arc C A. For R

S, T V, D T, being continually proportional, and the arc T V being

described by D T, the arc R S will be described by a straight line equal

to T V. But R S is described by the straight line D R. Therefore D R is

equal to T V, that is to two-fifths of C A.

And your said servant most humbly prayeth you to consider, if the

demonstration be true and evident, whether the way of objecting against

it by square root, used by Dr. Wallis; and whether all his geometry, as

being built upon it, and upon his supposition of an infinite number, be

not false.

CONSIDERATIONS

UPON THE ANSWER OF DOCTOR WALLIS

TO THE

THREE PAPERS OF MR. HOBBES.

Dr. Wallis says, all that is affirmed, is but _if we_ SUPPOSE _that,

this will follow_.

But it seemeth to me, that if the supposition be impossible, then that

which follows will either be false, or at least undemonstrated.

First, this proposition being founded upon his _Arithmetica

Infinitorum_, if there he affirm an absolute infiniteness, he must here

also be understood to affirm the same. But in his thirty-ninth

proposition he saith thus: “_Seeing that the number of terms increasing,

the excess above sub-quadruple is perpetually diminished, so at last it

becomes less than any proportion that can be assigned; if it proceed in

infinitum it must utterly vanish. And therefore if there be propounded

an infinite row of quantities in triplicate proportion of quantities

arithmetically proportioned (that is, according to the row of cubical

numbers) beginning from a point or 0; that row shall be to a row of as

many, equal to the greater, as 1 to 4._” It is therefore manifest that

he affirms, that in an infinite row of quantities the last is given; and

he knows well enough that this is but a shift.

Secondly, he says, that usually in Euclid, and all after him, by

_infinite_ is meant but, more than any assignable _finite_, or the

greatest possible. I am content it be so interpreted. But then from

thence he must demonstrate those his conclusions, which he hath not yet

done. And when he shall have done it, not only the conclusions, but also

the demonstration, will be the same with mine in Cap. XIV. Art. 2, 3,

&c. of my book _De Corpore_. And so he steals what he once condemned. A

fine quality.

Thirdly, he says, (by Euclid’s tenth proposition, but he tells not of

what book), that a line may be bisected, and the halves of it may again

be bisected, and so onwards infinitely; and that upon such supposed

section infinitely continued, the parts must be supposed infinitely

many.

I deny that; for Euclid, if he says a line may be divisible into parts

perpetually divisible, he means that all the divisions, and all the

parts arising from those divisions, are perpetually finite in number.

Fourthly, he says, that there may be supposed a row of quantities

infinitely many, and continually increasing, whereof the last is given.

It is true, a man may say, (if that be supposing) that white is black:

but, if _supposing_ be _thinking_, he cannot suppose an infinite row of

quantities whereof the last is given. And if he say it, he can

demonstrate nothing from it.

Fifthly, he says (for one absurdity begets another) _that a superficies

or solid may be supposed so constituted as to be_ infinitely long, _but_

finitely great, _(the breadth continually decreasing in greater

proportion than the length increaseth), and so as to have no centre of

gravity. Such is Toricellio’s Solidum Hyperbolicum acutum, and others

innumerable, discovered by Dr. Wallis, Monsieur Fermat, and others. But,

to determine this, requires more of geometry and logic, (whatsoever it

do of the Latin tongue), than Mr. Hobbes is master of._

I do not remember this of Toricellio, and I doubt Dr. Wallis does him

wrong and Monsieur Fermat too. For, to understand this for sense, it is

not required that a man should be a geometrician or a logician, but that

he should be mad.

In the next place, he puts to me a question as absurd as his answers are

to mine. Let him ask himself, saith he, if he be still of opinion, _that

there is no argument in natural philosophy to prove that the world had a

beginning_. First, whether, in case it had no beginning, there must not

have passed an infinite number of years before Mr. Hobbes was born.

Secondly, whether, at this time, there have not passed more, that is,

more than that infinite number. Thirdly, whether, in that infinite (or

more than infinite) number of years, there have not been a greater

number of days and hours, and of which, hitherto, the last is given.

Fourthly, whether, if this be an absurdity, we have not then, (contrary

to what Mr. Hobbes would persuade us), an argument in nature to prove

the world had a beginning.

To this I answer, not willingly, but in service to the truth, that, by

the same argument, he might as well prove that God had a beginning.

Thus, in case he had not, there must have passed an infinite length of

time before Mr. Hobbes was born; but there hath passed at this day more

than that infinite length, by eighty-four years. And this day, which is

the last, is given. If this be an absurdity, have we not then an

argument in nature to prove that God had a beginning? Thus it is when

men entangle themselves in a dispute of that which they cannot

comprehend. But, perhaps, he looks for a solution of his argument to

prove that there is somewhat greater than infinite; which I shall do so

far as to show it is not concluding. If from this day backwards to

eternity be more than infinite, and from Mr. Hobbes his birth backwards

to the same eternity be infinite, then take away from this day backwards

to the time of Adam, which is more than from this day to Mr. Hobbes his

birth, then that which remains backwards must be less than infinite. All

this arguing of infinites is but the ambition of school-boys.

TO THE LATTER PART OF THE FIRST PAPER.

There is no doubt if we give what proportion we will of the radius to

the arc, but that the arc upon that arc will have the same proportion.

But that is nothing to my demonstration. He knows it, and wrongs the

Royal Society in presuming they cannot find the impertinence of it.

My proof is this: that if the arc on T V, and the arc R S, and the

straight line C D, be not equal, then the arc on T V, the arc on R S,

and the arc on C A, cannot be proportional; which is manifest by

supposing in D C a less than the said D C, but equal to R S, and another

straight line, less than R S, equal to the arc on T V; and anybody may

examine it by himself.

I have been asked by some that think themselves logicians, why I

proceeded upon ⅖ rather than any other part of the radius. The reason I

had for it was, that, long ago, some Arabians had determined, that a

straight line, whose square is equal to 10 squares of half the radius,

is equal to a quarter of the perimeter; but their demonstrations are

lost. From that equality it follows, that the third proportional to the

quadrant and radius, must be a mean proportional between the radius and

⅖ of the same. But, my answer to the logicians was, that, though I took

any part of the radius to proceed on, and lighted on the truth by

chance, the truth itself would appear by the absurdity arising from the

denial of it. And this is it that Aristotle means, where he

distinguishes between a direct demonstration and a demonstration leading

to an absurdity. Hence it appears that Dr. Wallis’s objections to my

_Rosetum_ are invalid as built upon roots.

TO THE SECOND PAPER.

First, he says that it concerns him no more than other men, which is

true. I meant it against the whole herd of them who apply their algebra

to geometry. Secondly, he says that a bare number cannot be the side of

a square figure. I would know what he means by a bare number. Ten lines

may be the side of a square figure. Is there any number so bare, as by

it we are not to conceive or consider anything numbered? Or, by 10

nothings understands he bare 10? He struggles in vain, his conscience

puzzles him. Thirdly, he says 10 squares is the root of 100 square

squares. To which I answer, first, that there is no such figure as a

square square. Secondly, that it follows hence, that a root is a

superficies, for such is 10 squares. Lastly, he says that, neither the

number 10, nor 10 soldiers, is the root of 100 soldiers; because 100

soldiers is not the product of 10 soldiers into 10 soldiers. This last I

grant, because nothing but numbers can be multiplied into one another. A

soldier cannot be multiplied by a soldier. But no more can a square

figure by a square figure, though a square number may. Again, if a

captain will place his 100 men in a square form, must he not take the

root of 100 to make a rank or file? And are not those 10 men?

TO THE THIRD PAPER.

He objects nothing here, but that _the side of a square is not a

superficies, but a line_, and that a _square root (speaking of quantity)

is not a line, but a rectangle_, is a contradiction. The reader is to

judge of that.

To his scoffings I say no more, but that they may be retorted in the

same words, and are therefore childish.

And now I submit the whole to the Royal Society, with confidence that

they will never engage themselves in the maintenance of these

unintelligible doctrines of Dr. Wallis, that tend to the suppression of

the sciences which they endeavour to advance.

LETTERS

AND OTHER PIECES.

LETTERS AND OTHER PIECES.

==========

I.

A LETTER FROM MR. HOBBS TO MY MR.[2]

HONORABLE SIR,

Though I may goe whither and when I will for anie necessity you have of

my service, yet there is a necessity of good manners that obliges me as

yo^r servant to lett you knowe att all times where to find me. Wee goe

out of Paris 3 weekes hence, or sooner, towards Venice, but by what way

I knowe not, because the ordinary high way through the territory of

Milan is encumbered with the warre betweene the French and the

Spaniards. Howsoever, wee have to be there in October next. If you

require anie service that I can doe there, it may please you to convey

your command by Devonshire house. But if you command me nothing, I have

forbidden my letters to look for answer: their busines being only to

informe and to lett you knowe that the image of your noblenes decayes

not in my memory, but abides fresh to keepe me eternally

Your

THO. HOBBS.

-----

Footnote 2:

This letter is to be found in the British Museum, amongst the

Lansdowne MSS. 238, entitled “a collection of letters to and from

persons of eminence in the reigns of Elizabeth, James I, and Charles

I, made by some person in the service of Sir Gervas Clifton”. It is

without date: but the allusion to the war between France and Spain,

and the passage in the VITA THO. HOBBES, “Anno sequente qui erat

Christi 1629, rogatus a nobilissimo viro domino Gervasio Clifton”, &c.

(p. xiv), show that it must have been written in either 1629 or 1630.

-----

II.

TO A FRIEND IN ENGLAND.

WORTHY SIR,

I have been behind hand with you a long time for a letter I received of

yours at Angers, that place affording nothing wherewith to pay a debt of

that kind, all matter of news being sooner known in England than here:

and the news you writ me was of that kind, that none from England could

be more welcome, because it concerned the honour of Welbeck and Clifton,

two houses in which I am very much obliged.

Monsieur having given the slip to the Spaniards at Bruxelles, came to

the King about ten days ago at St. Germains, where he was received with

great joy. The next day the Cardinal entertained him at Ruelle: and the

day after that he went to Limours, where he is now, and from thence he

goes away shortly to Bloys, to stay there this winter. The Cardinal of

Lyons is going to Rome to treat about the annulling of Monsieur’s

marriage, which is here by Parliament declared void, but yet they

require the sentence of the Pope. There goes somebody thither on the

part of his wife, to get the marriage approved: but who that is, I ’know

not. The Swedish party in Germany is in low estate, but the French

prepare a great army for those parts, pretending to defend the places

which the Swedes have put into the King of France his protection,

whereof Philipsbourgh is one; a place of importance for the Lower

Palatinate. This is all the French news.

For your question, _why a man remembers less his own face, which he sees

often in a glass, than the face of a friend that he has not seen of a

great time_, my opinion in general is, that a man remembers best those

faces whereof he has had the greatest impressions, and that the

impressions are the greater for the oftener seeing them, and the longer

staying upon the sight of them. Now you know men look upon their own

faces but for short fits, but upon their friends’ faces long time

together, whilst they discourse or converse together; so that a man may

receive a greater impression from his friend’s face in a day, than from

his own in a year; and according to this impression, the image will be

fresher in his mind. Besides, the sight of one’s friend’s face two hours

together, is of greater force to imprint the image of it, than the same

quantity of time by intermissions. For the intermissions do easily

deface that which is but lightly imprinted. In general, I think that

lasteth longer in the memory which hath been stronglier received by the

sense.

This is my opinion of the question you propounded in your letter. Other

new truths I have none, at least they appear not new to me. Therefore if

this resolution of your first question seems probable, you may propound

another, wherein I will endeavour to satisfy you, as also in any thing

of any other nature you shall command me, to my utmost power; taking it

for an honour to be esteemed by you, as I am in effect,

Your humble and faithful servant

THO. HOBBES.

_Paris, Oct. 21/31, 1634._

My Lord Fielding and his Lady came to Paris on Saturday night last.

III.

TO MY WORTHY FRIEND MR. GLEN.[3]

WORTHY SIR,

I received here in Florence, two days since, a letter from you of the

19th of January. It was long by the way; but when it came it did

thoroughly recompence that delay. For it was worth all the pacquets I

had received a great while together. All that passeth in these parts is

equally news, and therefore no news; else I would labour to requite your

letter in that point, though in the handsome setting down of it, I

should still be your inferior.

I long infinitely to see those books of the Sabbaoth[4], and am of your

mind they will put such thoughts into the heads of vulgar people, as

will confer little to their good life. For when they see one of the ten

commandments to be _jus humanum_ merely, (as it must be if the Church

can alter it), they will hope also that the other nine may be so too.

For every man hitherto did believe that the ten commandments were the

moral, that is, the eternal law.

I desire also to see Selden’s _Mare Clausum_, having already a great

opinion of it.

You may perhaps, by some that go to Paris, send me those of the

Sabbaoth, for the other being in Latin, I doubt not to find it in the

Rue St. Jaques.

We are now come hither from Rome, and hope to be in Paris by the end of

June. I thank you for your letter, and desire you to believe that I can

never grow strange to one, the goodness of whose acquaintance I have

found by so much experience. But I have to write to so many, that I

write to you seldomer than I desire; which I pray pardon, and esteem me

Your most affectionate friend

and humble servant

THO. HOBBES.

_Florence, Apr. (6)/(16) 1636._

My Lord and Mr. Nicholls, and all our company commend them to you.

-----

Footnote 3:

Probably George Glen, who was installed Prebend of Worcester in 1660,

and died in 1669.

Footnote 4:

The History of the Sabbath. In two books. By Peter Heylyn. 4to. 1636.

-----

IV.

LETTER TO SIR CHARLES CAVENDISH.[5]

HONORABLE SIR,

[Illustration]

The last weeke I had the honor to receave two letters from you at once,

one of the 30 of Dec., the other of the 7^{th} of Jan., w^{ch} I

acknowledged, but could not answer in my last. In the first you begin

with a difficulty on the principle of Mons^r de Cartes, _that it is all

one to move a weight two spaces, or the double of that waight one

space_, and so on in other proportions: to w^{ch} you object the

difference of swiftnesse, w^{ch} is greater when a waight is moved two

spaces than when double waight is moved one space. Certenly de Cartes

his meaning was by force the same that mine, namely, a multiplication of

the weight of a body in to the swiftnesse wherew^{th} it is moved. So

that when I move a pound two foote at the rate of a mile an howre, I do

the same as if of 2 poundes I moved one pound a foote at y^e rate of a

mile an howre, the other pound another foote at the same rate, not in

directū, but parallell to the first pound. As if the wayt A B were moved

to C D at the rate of a mile an howre, ’tis all one as if the waight A E

were moved to F H at the same rate. Here is all the difference: this

swiftnesse or rate of a mile an howre is, in the first case, layd out in

the 2 spaces A G, G C, the latter, in the 2 spaces A G, E G. The first

case, as like as if a footman should run w^{th} double swiftnesse

endwayes, w^{ch} is y^e doubling of swiftnesse in one man: in the other,

it is as if you doubled the swiftnesse by doubling the man: for every

man has his owne swiftnesse. And so A H is the swiftnesse A G doubled,

as well as A D. For that, that Mons^r de Cartes will not have just twice

the force requisite to move the same weight twice as fast, I can say

nothing. The papers I have of his touching that are in my trunk, w^{ch}

hath bene taken by Dunkerkers, and taken againe from them by French, and

at length recovered by frends I made: but I shall not have it yet this

fortnight. In the meane time I am not in that opinion, but do assure

myself, the patient being the same, double force in the agent shall

worke upon it double effect.

In the same letter you require a better explication of y^e proportion I

gather betweene wayght and swiftnesse: wherein, because you have not my

figure, I imagine you have mistaken me very much. And first, you thinke,

I suppose, D E equall to A B: w^{ch} I am sure is a mistake. For I put A

B for any line you will to expresse a _minutū secundum_. I will,

therefore, go over againe the demonstration I sent you before, and see

if I can do it cleerer.

[Illustration]

Let A B stand for the time knowne wherein the waight D descendeth to E.

And let there bee a cylinder of the same matter the waight D consisteth

of, and let the altitude of that cylinder be D C: w^{ch} I shew before

was the swiftnesse wherew^{th} that cylinder _presseth_, not wherew^{th}

it _falleth_. And wee are now to enquire how farre such matter as the

cylinder is made of must descend from D, before it attayne a swiftnesse

equall to this pressing swiftnesse D C. And I say it must fall to L. For

in the time A B it is knowne that the waight in D will fall to E: and it

is demonstrated by Gallileo, that when such waight comes to E, it shall

be able to go twice the space it hath fallen in the same time. Therefore

the waight D being in E, hath velocity to carry him the space D K

(w^{ch} I put double to D E) in the same time A B. But I put B F equall

to D K. Therefore, in the time A B, the waight’s velocity acquired in E

shall be such as to go from B to F without decrease of velocity by the

way. Hence I go on to finde in what point the waight in D comes to where

it getteth a velocity equall to C D. Therefore, I apply D C to G H,

parallel to B F: and then it is, as the time A B to the time A G, so the

velocity acquired at the end of the time A B to the velocity acquired at

the end of the time A G. For the swiftnesse acquired from time to time

(I say, not from place to place, but from time to time) are

proportionable to the times wherein they are acquired: w^{ch} is the

postulate on w^{ch} Galileo builds all his doctrine. And as A B to A G,

so the line B F to the line G H. But, at the end of the time A B, the

waight D is by supposition in E, in that degree of velocity as to go B F

or D K in the same time A B. The question therefore is, where the waight

D shall be at the end of the time A G. For there it hath the velocity of

going G H or D C in the same time, because the velocity G H is to the

velocity B F as the line G H to the line B F, or as the time of descent

A G to the time A B. But, because the spaces of the descent are in

double the proportion of the times of descent, make it as B F to G H,

that is, D K to D C, so D C to another, D L. The velocity, therefore,

acquired in the point of descent E, namely the velocity D K or B F, is

to the velocity acquired in the point L, namely, the velocity G H or D

C, (w^{ch} is the velocity of the cylinder’s waight), as D K to D L. And

therefore in L the waight D has acquired a velocity equal to the

velocity of the waight of the cylinder.

In the same letter you desire to knowe, how any mediū, as water,

retardeth the motion of a stone that falls into it. To w^{ch} I answer

out of that you say afterwards, that nothing can hinder motion but

contrary motion: that the motion of the water, when a stone falls into

it, is point blanke contrary to the motion of the stone. For the stone

by descent causeth so much water to ascend as the bignesse of the stone

comes to. For imagine so much water taken out of the place w^{ch} the

stone occupies, and layd upon the superficies of the water: it presseth

downeward as the stone does, and maketh the water that is below to rise

upwards, and this rising upwards is contrary to the descent, and is no

other operation than we see in scales, when of two equal bullets in

magnitude that w^{ch} is of heavier metal maketh the other to rise. And

thus farre goes your letter of Dec. 30.

For the first quære in your second letter, concerning how we see in the

time the lucide body contracts itselfe, I have no other solution but

that w^{ch} your selfe hath given: w^{ch} is, that the reciprocation is

so quicke, that the effect of the first motion lasteth till the next

comes, and longer. For by experience we observe that the end of a

firebrand swiftely moved about in circle, maketh a circle of fire:

w^{ch} could not be, if the impression made at the beginning of the

circulation did not last till the end of it. For if the same firebrand

be moved slower, there will appear but a peece of a circle, bigger or

lesser according to the swiftnesse or slownesse of y^e motion. For the

cause of such reciprocation, it is hard to guess what it is. It may well

be the reaction of the medium. For though the mediū yeld, yet it

resisteth to: for there can be no passion w^{th}out reaction. And if a

man could make an hypothesis to salve that contraction of y^e sun, yet

such is the nature of naturall thinges, as a cause may be againe

demanded of such hypothesis: and never should one come to an end

w^{th}out assigning the immediate hand of God. Whereas in mathematicall

sciences wee come at last to a definition, w^{ch} is a beginning or

principle, made true by pact and consent amongst ourselves. Further, you

conceave a difficulty how the medium can be continually driven on, if

there be such an alternate contraction. To w^{ch}, first I answer, that

the motion forward is propagated to the utmost distance in an instant,

and the first push is therefore enough, and in another instant is made

the returne back in y^e like manner. And though it were not done in an

instant, yet we see by experience in rivers, as in y^e Thames, that the

tide goes upward towards London pushed by the water below, and yet at

the same instant the water below is going backe to the sea. For seeing

it is high-water at Blackwall before ’tis so at Greenwich, the water

goes backe from Blackwall when it goes on at Greenwich. And so it would

happen, though Blackwall and Greenwich were nerer together then that any

quantity given could come betweene.

[Illustration]

In my letter from London, speaking of the refraction of a bullet, I

thinke I delivered my opinion to be, that a bullet falling out of a

thinner medium into a thicker, looseth in the entring nothing but motion

perpendicular: but being entred, he looseth proportionably both of one

and the other. For suppose a bullet, whose diameter is A B, be in the

thiner mediū, and enter at C into the thicker medium. The thicker

medium, at the first touch of B in the point C, worketh nothing upon the

line A B. And when the diameter A B is entred, suppose halfe way, yet

the thicker medium operates laterally but on one halfe of it. So that in

the somme there is a losse of velocity perpendicular (to the quantity

that the diameter A B requires) without any offence to the motion

laterall, but so much of the diameter as is within the thicker mediū is

retarded both wayes, and looses of his absolute motion, w^{ch} is

compounded of perpendicular and laterall, and that proportionally.

Suppose now that a bullet passe from A to D, and receave a peculiar

losse of his perpendicular motion by entring at D, so great that he

proceed in the perpendicular but halfe so farre, as for example from D

to I: and then being in, the thicknesse of the medium take away more of

his velocity both perpendicular and laterall, suppose halfe that w^{ch}

was left of the perpendicular motion and halfe of his first laterall

motion, so that the perpendicular motion is but D K, and the laterall

motion D E. Then will the line of refraction be D G. As for that

argumentation of Des Cartes, it is, in my opinion, as I have heretofore

endeavored to shew you, a mere paralogism.

Lastly, you make this quære, why light hath not at severall inclinations

severall swiftnesses as well as a bullet. The bullet itself passeth

through the severall media: whereas in the motion of light, the body

moved, w^{ch} is the mediū, entreth not into the other medium, but

thrusteth it on: and so the parts of that medium thrust on one another,

whereby the laterall motion of the thicker medium hath nothing to worke

upon, because nothing enters, but stoppes onely and retardes, in oblique

_incidence_, that end w^{ch} comes first to it, and thereby causes a

refraction the contrary way to that of a bullet, in such manner as I set

forth to you in one of my letters from hence concerning the cause of

refraction. And this is all I can say for the present to the quæres of

y^r two last letters.

I have enquired concerning perspectives after the manner of De Cartes.

Mydorgius tells me there is none that goes about them, as a thing too

hard to do. And I believe it. For here is one Mons^r de Bosne in towne,

that dwells at Bloys, an excellent workman, but by profession a lawier,

and is counsellor of Bloys, and a better philosopher in my opinion then

De Cartes, and not inferior to him in the analytiques. I have his

acquaintance by Pere Mersenne. He tells me he hath tryed De Cartes his

way, but cannot do it: and now he workes upon a crooked line of his owne

invention. He sayes he shall have made one w^{th}in a moneth after he

shall returne to Bloys: after that he will see what he can discover in

the heavens himselfe, and then if he discover any new thing he will let

his way be publique together w^{th} the effects. This is all the hope I

can give you yet. So w^{th} my prayers to God to keepe you in prosperity

this troublesome time, I rest

Your most humble and obedient servant

TH. HOBBES.

_Paris, Feb. 8, stile no. 1641._

To the Right Honorable

Sr CHARLES CAVENDYSSHE

present these

/

/

/

/

at Wellinger.

-----

Footnote 5:

Harleian MS. 6796.

-----

V.

LETTER TO MR. BEALE.[6]

SIR,

The young woman at Over-Haddon hath been visited by divers persons of

this house. My Lord himself hunting the hare one day at the Town’s end,

with other gentlemen and some of his servants, went to see her on

purpose: and they all agree with the relation you say was made to

yourself. They further say on their own knowledge, that part of her

Belly touches her Back-bone. She began (as her Mother says) to loose her

appetite in December last, and had lost it quite in March following:

insomuch as that since that time she has not eaten nor drunk any thing

at all, but only wetts her lips with a feather dipt in water. They were

told also that her gutts (she alwayes keeps her bed) lye out by her at

her fundament shrunken. Some of the neighbouring ministers visit her

often: others that see her for curiosity give her mony, sixpence or a

shilling, which she refuseth, and her mother taketh. But it does not

appear they gain by it so much as to breed a suspition of a cheat. The

woman is manifestly sick, and ’tis thought she cannot last much longer.

Her talk (as the gentlewoman that went from this house told me) is most

heavenly. To know the certainty, there bee many things necessary which

cannot honestly be pryed into by a man. First, whether her gutts (as

’tis said) lye out. Secondly, whether any excrement pass that way, or

none at all. For if it pass, though in small quantity, yet it argues

food proportionable, which may, being little, bee given her secretly and

pass through the shrunken intestine, which may easily be kept clean.

Thirdly, whether no urine at all pass: for liquors also nourish as they

go. I think it were somewhat inhumane to examin these things too nearly,

when it so little concerneth the commonwealth: nor do I know of any law

that authoriseth a Justice of peace, or other subject, to restrain the

liberty of a sick person so farr as were needful for a discovery of this

nature. I cannot therefore deliver any judgment in the case. The

examining whether such a thing as this bee a miracle, belongs I think to

the Church. Besides, I myself in a sickness have been without all manner

of sustenance for more than six weeks together: which is enough to make

mee think that six months would not have made it a miracle. Nor do I

much wonder that a young woman of clear memory, hourely expecting death,

should bee more devout then at other times. ’Twas my own case. That

which I wonder at most, is how her piety without instruction should bee

so eloquent as ’tis reported.

THO. HOBBES.

_Chatsworth, Oct. 20. 68._

-----

Footnote 6:

Amongst the MSS. of the Royal Society.

-----

VI.

LETTER TO MR. OLDENBURG.[7]

WORTHY S^R

In the last Transactions for September and October I find a letter

addressed to you from D^r Wallis, in answer to my LUX MATHEMATICA. I

pray you tell me that are my old acquaintance, whether it be (his words

and characters supposed to be interpreted) intelligible. I know very

well you understand sense both in Latine, Greeke, and many other

languages. He shows you no ill consequence in any of my arguments.

Whereas I say there is no proportion of _infinite_ to _finite_. He

answers, he meant _indefinite_; but derives not his conclusion from any

other notion than simply _infinite_. I said the root of a square number

cannot be the length of the side of a square figure, because a root is

part of a square number, but length is no part of a square figure. To

which he answers nothing. In like manner, he shuffles off all my other

objections, though he know well enough that whatsoever he has written in

Geometry (except what he has taken from me and others) dependeth on the

truth of my objections. I perceive by many of his former writings that I

have reformed him somewhat as to the Principles of Geometry, though he

thanke me not. He shuffles and struggles in vaine, he has the hooke in

his guills, I will give him line enough: for (which I pray you tell him)

I will no more teach him by replying to any thing he shall hereafter

write, whatsoever they shall say that are confident of his Geometry.

_Qui volunt decipi, decipiuntur._ He tells you that I bring but _crambe

sæpe cocta_. For which I have a just excuse, and all men do the same;

they repeat the same words often when they talk with them that cannot

heare.

I desire also this reasonable favour from you: that, if hereafter I

shall send you any paper tending to the advancement of physiques or

mathematiques, and not too long, you will cause it to be printed by him

that is printer to the Society, as you have done often for D^r Wallis:

it will save me some charges.

I am, S^r,

Your affectionate frend and humble seruant

THOMAS HOBBES.

_November the 26th, 1672._

ffor my worthy and much honoured

frend M^r HENRY OLDENBURGH,

Secretary to the Royal Society.

-----

Footnote 7:

Amongst the MSS. of the Royal Society.

-----

VII.

TO THE RIGHT HONOURABLE

THE MARQUIS OF NEWCASTLE.[8]

The passions of man’s mind, except onely one, may bee observed all in

other living creatures. They have desires of all sorts, love, hatred,

feare, hope, anger, pitie, æmulation, and y^e like: onely of curiositie,

which is y^e desire to know y^e causes of thinges, I never saw signe in

any other living creature but in man. And where it is in man, I find

alwaies a defalcation or abatement for it of another passion, which in

beastes is commonly predominant, namely, a ravenous qualitie, which in

man is called _avarice_. The desire of knowledge and desire of needlesse

riches are incompatible, and destructive one of another. And therefore

as in the cognitive faculties reason, so in the motive curiositie, are

the markes that part y^e bounds of man’s nature from that of beastes.

Which makes mee, when I heare a man, upon the discovery of any new and

ingenious knowledge or invention, aske gravely, that is to say,

scornefully, _what ’tis good for_, meaning what monie it will bring in,

(when he knows as little, to one that hath sufficient what that overplus

of monie is good for), to esteeme that man not sufficiently removed bn

484.png from brutalitie. Which I thought fit to say by way of

anticipation to y^e grave scorners of philosophie, and that your

lordship, after having performed so noble and honourable acts for

defence of your countrie, may thinke it no dishonour in this unfortunate

leasure to have employed some thoughts in the speculation of the noblest

of the senses, _vision_.

That which I have written of it is grounded especially upon that w^{ch}

about 16 yeares since I affirmed to your Lo^{PP} at Welbeck, that light

is a fancy in the minde, caused by motion in the braine, which motion

againe is caused by the motion of y^e parts of such bodies as we call

_lucid_: such as are the sunne and y^e fixed stars, and such as here on

earth is fire. By putting you in mind hereof, I doe indeed call you to

witnesse of it: because, the same doctrine having since been published

by another, I might bee challenged for building on another man’s ground.

Yett philosophical ground I take to be of such a nature, that any man

may build upon it that will, especially if the owner himselfe will nott.

But upon this ground, with the helpe of some other speculations drawne

from the nature of motion and action, I have, I thinke, derived y^e

reason of all the phænomena I have mett with concerning light and

vision, both solidly enough nott to be confuted, and withall easilie

enough to be understood by such as can give that attention thereto which

the figures, whereby such motion as causeth vision is described, do

require. All that I shall bee ever able to adde to it, is polishing:

for, being the first draught, it could nott bee so perfect as I hope

hereafter to make it in Latin. Butt as it is, it will sufficiently give

your Lo^{PP} satisfaction in those _quæres_ you were pleased to make

concerning this subject. I am content that it passe, in respect of some

drosse that yett cleaves to it, for ore: w^{ch} is much better than old

ends raked out of the kennell of sophisters’ bookes. And for such I

commend it to your Lo^p, and myselfe to your accustomed good opinion:

which hath beene hitherto so greate honour to mee, as I am nott known to

the world by any thing so much as by being,

My most noble lord,

Your Lo^{p’s} most humble

and most obliged servant

THO. HOBBES.

The treatise ends with the following passage:--

To conclude, I shall doe like those that build a new house where an

old one stood before, that is to say, carry away the rubbish.

And first, away goes the old opinion that the _shewes_ (which they

call visible species) of all objects, are in all places, and all the

babble _de extramittendo et intromittendo_. For their species are

nothing else but fancie, made by the light proceeding directly or by

repurcussion or refraction made from the object to y^e eye, and so

moving the braine and other parts within.

Secondly, the opinion which Vitellio takes for an axiome and

foundation of his _Catoptricques_, that y^e place of y^e image by

reflexion is in the perpendicular drawn from the object to the glasse.

For it is false both in plaine glasses and in sphæricall, whether

convexe or concave.

Thirdly, the opinion that light is engendred faster in hard bodies, as

glasse, than in thin and fluid, as aire.

Fourthly, that objects are seen by _penicilli_ that have their common

base in the pupills: for y^e center of y^e eye is in their common

base.

Fifthly, the opinion that there bee other visuali lines by which wee

see distinctly besides y^e optique axis.

Sixthly, the opinion that perspective glasses and amplifying glasses

are best made of hyperbolicall figures.

Seventhly, the opinion that light is a bodie, or any other such thing

than such light as wee have in dreames.

Eighthly, that y^e object appeares greater and lesse in ye same

proportion that y^e angles have under which they are seene.

Lastly, is to be cast away the conceipt of millions of strings in ye

optique nerve, by which the object playes upon the braine, and makes

y^e soule listen unto it, and other innumerable such trash.

How doe I feare that y^e attentive reader will find that which I have

delivered concerning y^e _Optiques_ fitt to bee cast outt as rubbish

among the rest. If hee doe, hee will recede from y^e authoritie of

experience, which confirmeth all I have said. Butt if it bee found

true doctrine, (though yett it wanteth polishing), I shall deserve the

reputation of having beene y^e first to lay the grounds of two

sciences; this of _Optiques_, y^e most curious, and y^t other of

_Natural Justice_, which I have done in my booke DE CIVE, y^e most

profitable of all other.

-----

Footnote 8:

Harleian MS. 3360: a treatise on Optics, entitled “A minute or first

draught of the Optiques. In two parts. By Thomas Hobbes. At Paris,

1646.” The second part, _On Vision_, we have in Latin, in the DE

HOMINE: the first, _On Illumination_, was never published. The

dedication to the Marquis of Newcastle, and the concluding paragraph,

is all that is here given of the treatise.

-----

VIII.

TO THE KING’S MOST EXCELLENT MAJESTY

THE HUMBLE PETITION OF THOMAS HOBBES[9]

Sheweth, that though your Majesty hath been pleased to take off the

restraint of late years laid upon the pensions payable out of your privy

purse, yet your Majesty’s Officers refuse to pay the pension of your

petitioner without your Majesty’s express command.

And humbly beseaceth your Majesty, (considering his extreme age,

perpetual infirmity, frequent and long sickness, and the aptness of his

enemies to take any occasion to report that your petitioner by some ill

behaviour hath forfeited your wonted favour), that you would be pleased

to renew your order for the payment of it in such manner as to his great

comfort he hath for many years enjoyed it.[10]

And daily prayeth to God Almighty to bless your Majesty with long life,

constant health, and happinesse.

-----

Footnote 9:

Additional MSS. 4292. Brit. Mus.

Footnote 10:

Deinde redux mihi Rex concessit habere quotannis

Centum alias libras ipsius ex loculis:

Dulce mihi donum.

VITA _Carm. expres._ p. xcviii.

-----

END OF VOL. VII.

RICHARDS, PRINTER, 100, ST. MARTIN’S LANE.

------------------------------------------------------------------------

Transcriber’s Note

Some Greek passages employ the stigma ligature (‘st’). The available

Unicode character (ϛ) is nearly indistinguishable from the final form of

sigma (ς). Occasionally, the ‘ου’ ligature is employed. The only

available character (ᴕ) is a Latin, not a Greek character. It is

rendered here as ‘ου’. There were also a number of instances of improper

placement of diacritical marks, particularly in cases where the

breathing mark and accents appear on the first rather than the second of

two leading vowels, e.g. ‘ὅυτως’ rather than ‘οὕτως’.

At 93.4, the response ‘No sure’ is obviously incorrect. It is most

likely that it should have read ‘Not sure.’, but it may also have been

an unfinished line.

Other errors deemed most likely to be the printer’s have been corrected,

and are noted here. Given the age of the text, any corrections were made

sparingly. The references are to the page and line in the original.

8.35 with increasing [s]wiftness? Restored.

12.34 being so very heavy[?] Added.

54.8 too much or too[l i/ li]ttle Replaced.

62. was to be demonst[r]ated. Inserted.

65.33 which is 72[.] Added.

67.1 and multip[l]ying lines Inserted.

72.5 and subtil doc[t]rines. Inserted.

74.1 who begi[u/n]s his history Inverted.

91.16 the space be[t]ween. Inserted.

91.18 whose tap[-]hole is very little Inserted.

96.5 and th[a/e]n H will be east Replaced.

114.27 a spring[ ]upon the top Inserted.

158.19 the air which[ which] was Redundant.

163.11 8 degrees 30 minutes[.]? Removed.

192.19 (called by him [ε/ἐ]φαρμόζοντα) Replaced.

200.5 may so precisely deter[ter]mine Removed.

206.1 lines whi[e/c]h shall never meet Replaced.

208.10 [ὅυ/οὕ]τως ἔχει Replaced.

208.13 [ὅυ/οὕ]τως ἔχει Replaced.

225.8 as by raref[r]action and condensation. Removed.

263.17 [“]_The magnitude of an angle_ Added.

277.33 th[e/a]n of one in nine? Replaced.

297.26 At the seventee[n]th chapter Inserted.

300.22 _that of G K to G [E,/E.]_” Replaced.

323.7 _tanquam dicta problematicè._[”] Added.

338.31 and so mis[s]pend it? Inserted.

351.16 by which you live[,/.] Replaced.

376.4 _propositione præcedente._[”] Added.

376.22 it shall quite vanish. [And so] Missing?

342.12 to the present purpose[)]. Added (likely).

382.12 whether διπλάσιος and διπλασ[ι]ίων be one Removed.

391.5 by the word Σημ[~ε/εῖ]ον in Euclid Replaced.

412.17 κα[ι/ὶ] ἡ Ἔμπουσα Replaced.

413.26 τῶν θεῶν [Α/Ἀ]ιγύπτιοι Replaced.

413.27 κα[ἱ/ὶ] ἅτε Ἀιγύπτιος, Replaced.

413.30 ποδῶν [ὴ/ἠ]δέ κνημάων Replaced.

414.1 ῥᾳδίως[ ]ἔγνων ὑπολαμβάνοντες. Inserted.

414.4 ἀλλὰ κατὰ ῥύμην [ὰ/ἀ]έριον Replaced.

415.23 deriveth it [τ/π]αρὰ τὸ ἐμποδιζειν Replaced.

415.25 it saith, [Ἕ/Ἔ]μπουσα Ψιλοῦπαι Replaced.

415.33 some had no legs, &c[.] Added.

416.7 τύχη [ὲ/ἐ]μποδιζουσα Replaced.

416.16 [Ἕ/Ἔ]μποῦσα is also a name for Lamia Replaced.

418.16 [ὁι/οἱ] δὲ ὑπέφευγον Transposed.

418.20 καὶ τὸ [ὲ/ἐ]πιπηδᾶν Replaced.

419.13 γαρ [ὅι/οἵ]νου πληροῦντες, Replaced.

419.14.1 εἶχε τὸν [ὅι/οἵ]νου. Replaced.

419.14.2 [Α/Ἀ]σκωλιάζειν Replaced.

423.1 καὶ ζώων παντοδαπῶν [ἐι/εἰ]κόσι Replaced.

455.27 two spaces th[e/a]n when double Replaced.

456.3 a pound two foote a[t] the rate of Added.

456.6 rate of a mile an how[er/re] Transposed.