HOBBES'S QUARRELS

WITH

DR. WALLIS THE MATHEMATICIAN.

HOBBES's passion for the study of Mathematics began late in life-attempts to be an original discoverer-attacked by WALLIS-various replies and rejoinders nearly maddened by the opposition he encountered-after four years of truce, the war again renewed-character of HOBBES by Dr. WALLIS, a specimen of invective and irony; serving as a remarkable instance how the greatest genius may come down to us disguised by the arts of an adversary-HOBBES's noble defence of himself; of his own great reputation; of his politics; and of his religion—a literary stratagem of his-reluctantly gives up the contest, which lasted twenty years.

THE Mathematical War between HOBBES and the celebrated
Dr. WALLIS is now to be opened. A series of battles, the
renewed campaigns of more than twenty years,
can be
described by no term less eventful. Hobbes himself con-
sidered it as a war, and it was a war of idle ambition, in which
he took too much delight. His "Amata Mathemata "
became his pride, his pleasure, and at length his shame.
He attempted to maintain his irruption into a province
he ought never to have entered in defiance, by a new
method;" but having invaded the powerful natives, he seems
to have almost repented the folly, and retires, leaving "the
unmanageable brutes" to themselves:

Ergo meam statuo non ultra perdere opellam
Indocile expectans discere posse pecus.

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His language breathes war, while he sounds his retreat, and confesses his repulse. The Algebraists had all declared against the Invader.

And,

Wallisius contra pugnat; victusque videbar
Algebristarum Theiologumque scholis,

Et simul eductus Castris exercitus omnis
Pugnæ securus Wallisianus ovat.

Pugna placet vertor-
Bella mea audisti-&c.

So that we have sufficient authority to consider this Literary Quarrel as a war, and a "Bellum Peloponnesiacum" too, for it lasted as long. Political, literary, and even personal feelings were called in to heat the temperate blood of two Mathematicians.

What means this tumult in a Vestal's veins ?

Hobbes was one of the many victims who lost themselves in squaring the circle, and doubling the cube. He applied, late in life, to mathematical studies, not so much, he says, to learn the subtile demonstrations of its figures, as to acquire those habits of close reasoning, so useful in the discovery of new truths, to prove or to refute. So justly he reasoned on mathematics; but so ill he practised the science, that it made him the most unreasonable being imaginable, for he resisted mathematical demonstration itself!*

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His great and original character could not but prevail in everything he undertook; and his egotism tempted him to raise a name in the world of Science, as he had in that of Politics and Morals. With the ardour of a young mathematician, he exclaimed, "Eureka!" I have found it." The quadrature of the circle was indeed the common Dulcinea of the Quixotes of the time; but they had all been disenchanted. Hobbes alone clung to his ridiculous mistress. Repeatedly confuted, he was perpetually resisting old reasonings and producing new ones. Were only genius requisite for an able mathematician, Hobbes had been among the first; but patience and docility, not fire and fancy, are necessary. His reasonings were all paralogisms, and he had always much to say, from not understanding the subject of his inquiries.

When Hobbes published his "De Corpore Philosophico," 1655, he there exulted that he had solved the great mystery. Dr. Wallis, the Savilian professor of mathematics at Oxford,†

The origin of his taste for mathematics was purely accidental: begun in love, it continued to dotage. According to Aubrey, he was forty years old when, "being in a gentleman's library, Euclid's Elements lay open at the 47th Propos. lib. i., which, having read, he swore This is impossible! He read the demonstration, which referred him back to anotherat length he was convinced of that truth. This made him in love with geometry. I have heard Mr. Hobbes say that he was wont to draw lines on his thighs and on the sheets a-bed."

The author of the excellent Latin grammar of the English language, so useful to every student in Europe, of which work that singular patriot, Thomas Hollis, printed an edition, to present to all the learned Institutions of Europe. Henry Stubbe, the celebrated physician of Warwick, to

with a deep aversion to Hobbes's political and religious sentiments, as he understood them, rejoiced to see this famous combatant descending into his own arena. He certainly was eager to meet him single-handed; for he instantly confuted Hobbes, by his "Elenchus Geometria Hobbianæ." Hobbes, who saw the newly-acquired province of his mathematics in danger, and which, like every new possession, seemed to involve his honour more than was necessary, called on all the world to be witnesses of this mighty conflict. He now pubished his work in English, with a sarcastic addition, in a magisterial tone, of " Six Lessons to the Professors of Mathematics in Oxford." These were Seth Ward and Wallis, both no friends to Hobbes, and who hungered after him as a relishing morsel. Wallis now replied in English, by "Due Correction for Mr. Hobbes, or School-discipline for not saying his Lessons Right," 1656. That part of controversy which is usually the last had already taken place in their choice of phrases.t

whom the reader has been introduced, joined, for he loved a quarrel, in the present controversy, when it involved philosophical matters, siding with Hobbes, because he hated Wallis. In his "Oneirocritica, or an Exact Account of the Grammatical Parts of this Controversy," he draws a strong character of Wallis, who was indeed a great mathematician, and one of the most extraordinary decypherers of letters; for perhaps no new system of character could be invented for which he could not make a key; by which means he had rendered the most important services to the Parliament. Stubbe quaintly describes him as "the sub-scribe to the tribe of Adoniram" (i. e. Adoniram Byfield, who, with this cant name, was scribe to the fanatical Assembly of Divines), and "as the glory and pride of the Presbyterian faction."

* Dr. Seth Ward, after the Restoration made Bishop of Salisbury, said, some years before this event was expected, that "he had rather be the author of one of Hobbes's books than be king of England." But after

wards he seemed not a little inclined to cry out Crucifige! He who, to one of these books, the admirable treatise on "Human Nature," had prefixed one of the highest panegyrics Hobbes could receive!-Athen. Oxon. vol. ii. p. 647.

It is mortifying to read such language between two mathematicians, in the calm inquiries of square roots, and the finding of mean proportionals between two straight lines. I wish the example may prove a warning. Wallis thus opens on Hobbes :-" It seems, Mr. Hobbes, that you have a mind to say your lesson, and that the mathematic professors of Oxford should hear you. You are too old to learn, though you have as much need as those that be younger, and yet will think much to be whipped.

"What moved you to say your lessons in English, when the books against which you do chiefly intend them were written in Latin? Was it chiefly for the perfecting your natural rhetoric whenever you thought it convenient to repair to Billingsgate ?--You found that the oyster-women could not

H H

In the following year the campaign was opened by Hobbes with "TITMAI; or, marks of the absurd Geometry, rural Language, Scottish Church-politics, and Barbarisms, of John Wallis." Quick was the routing of these fresh forces; not one was to escape alive! for Wallis now took the field with "Hobbiani Puncti dispunctio! or, the undoing of Mr. Hobbes's Points; in answer to Mr. Hobbes's ΣTITMAI, id est, Stigmata Hobbii." Hobbes seems now to have been reduced to great straits; perhaps he wondered at the obstinacy of his adver sary. It seems that Hobbes, who had been used to other studies, and who confesses all the algebraists were against him, could not conceive a point to exist without quantity; or a line could be drawn without latitude; or a superficies be without depth or thickness; but mathematicians conceive them without these qualities, when they exist abstractedly in the mind; though, when for the purposes of science they are produced to the senses, they necessarily have all the qualities. It was understanding these figures, in the vulgar way, which led Hobbes into a labyrinth of confusions and absurdities.* They appear to have nearly maddened the clear and vigorous intellect of our philosopher; for he exclaims, in one of these writings:

"I alone am mad, or they are all out of their senses: so that no third opinion can be taken, unless any will say that we are all mad."

Four years of truce were allowed to intervene between the next battle; when the irrefutable Hobbes, once more collecting his weak and his incoherent forces, arranged them, as well as he was able, into "Six Dialogues," 1661. The utter annihilation he intended for his antagonist fell on himself. Wallis borrowing the character of "The Self-tormentor" from Terence, produced "Hobbius Heauton-timorumenos (Hobbes

teach you to rail in Latin. Now you can, upon all occasion, or without occasion, give the titles of fool, beast, ass, dog, &c., which I take to be but barking; and they are no better than a man might have at Billingsgate for a box o' the ear.

"You tell us, though the beasts that think our railing to be roaring have for a time admired us; yet now you have showed them our ears, they will be less affrighted.' Sir, those persons (the professors themselves) needed not the sight of your ears, but could tell by the voice what kind of creature brayed in your books: you dared not have said this to their faces."—He bitterly says of Hobbes, that "he is a man who is always writing what was answered before he had written."

* Dr. Campbell's art. on Hobbes, in "Biog. Brit." p. 2619.

the Self-tormentor); or, a Consideration of Mr. Hobbes's Dialogues; addressed to Robert Boyle," 1662.

This attack of Wallis is of a very opposite character to the arid discussion of abstract blunders in geometry. He who began with points, and doubling the cube, and squaring the circle, now assumes a loftier tone, and carrying his personal and moral feelings into a mere controversy between two idle mathematicians, he has formed a solemn invective, and edged it with irony. I hope the reader has experienced sufficient interest in the character of Hobbes to read the long, but curious extract I shall now transcribe, with that awe and reverence which the old man claims. It will show how even the greatest genius may be disguised, when viewed through the coloured medium of an adversary. One is, however, surprised to find such a passage in a mathematical work.

"He doth much improve; I mean he doth, proficere in pejus; more, indeed, than I could reasonably have expected he would have done;-insomuch, that I cannot but profess some relenting thoughts (though I had formerly occasion to use him somewhat coarsely), to see an old man thus fret and torment himself to no purpose. You, too, should pity your antagonist; not as if he did deserve it, but because he needs it; and as Chremes, in Terence, of his Senex, his self-tormenting Menedemus—

Cum videam miserum hunc tam excruciarier

Miseret me ejus. Quod potero adjutabo senem.

"Consider the temper of the man, to move your pity; a person extremely passionate and peevish, and wholly impatient of contradiction. A temper which, whether it be a greater fault or torment (to one who must so often meet with what he is so ill able to bear), is hard to say.

"And to this fretful humour you must add another as bad, which feeds it. You are therefore next to consider him as one highly opinionative and magisterial. Fanciful in his conceptions, and deeply enamoured with those phantasmes, without a rival. He doth not spare to profess, upon all occasions, how incomparably he thinks himself to have surpassed all, ancient, modern, schools, academies, persons, societies, philosophers, divines, heathens, Christians; how despicable he thinks all their writings in comparison of his; and what hopes he hath, that, by the sovereign command of some absolute prince, all other doctrines being exploded, his new dictates should be