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,[381] 465 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 Geometriæ 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 published 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[382] 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.[383]

466

In the following year the campaign was opened by Hobbes with “ΣΤΙΓΜΑΙ; 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 ΣΤΙΓΜΑΙ, id est, Stigmata Hobbii.” Hobbes seems now to have been reduced to great straits; perhaps he wondered at the obstinacy of his adversary. 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.[384] 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 467 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.