Archimedes in a later age imitated and surpassed Archytas. But even Archimedes was not free from the prevailing notion that geometry was degraded by being employed to produce any thing useful. It was with difficulty that he was induced to stoop from speculation to practice. He was half ashamed of those inventions which were the wonder of hostile nations, and always spoke of them slightingly as mere amusements, as trifles in which a mathematician might be suffered to relax his mind after intense application to the higher parts of his science.

The opinion of Bacon on this subject was diametrically opposed to that of the ancient philosophers. He valued geometry chiefly, if not solely, on account of those uses, which to Plato appeared so base. And it is remarkable that the longer Bacon lived the stronger this feeling became. When in 1605 he wrote the two books on the Advancement of Learning, he dwelt on the advantages which mankind derived from mixed mathematics; but he at the same time admitted that the beneficial effect produced by mathematical study on the intellect, though a collateral advantage, was “no less worthy than that which was principal and intended.” But it is evident that his views underwent a change. When, near twenty years later, he published the De Augmentis, which is the Treatise on the Advancement of Learning, greatly expanded and carefully corrected, he made important alterations in the part which related to mathematics. He condemned with severity the high pretensions of the mathematicians, “delicias et fastum mathemati-corum.” Assuming the well-being of the human race to be the end of knowledge, (1) he pronounced that mathematical science could claim no higher rank than that of an appendage or an auxiliary to other sciences. Mathematical science, he says, is the handmaid of natural philosophy; she ought to demean herself as such; and he declares that he cannot conceive by what ill chance it has happened that she presumes to claim precedence over her mistress. He predicts—a prediction which would have made Plato shudder—that as more and more discoveries are made in physics, there will be more and more branches of mixed mathematics. Of that collateral advantage the value of which, twenty years before, he rated so highly, he says not one word. This omission cannot have been the effect of mere inadvertence. His own treatise was before him. From that treatise he deliberately expunged whatever was favourable to the study of pure mathematics, and inserted several keen reflections on the ardent votaries of that study. This fact, in our opinion, admits of only one explanation. Bacon’s love of those pursuits which directly tend to improve the condition of mankind, and his jealousy of all pursuits merely curious, had grown upon him, and had, it may be, become immoderate. He was afraid of using any expression which might have the effect of inducing any man of talents to employ in speculations, useful only to the mind of the speculator, a single hour which might be employed in extending the empire of man over matter. (2) If Bacon erred here, we

(1) Usui et commodis hominum consulirems.
(2) Compare the passage relating to mathematics in the
Second Book of the Advancement of Learning, with the De
Augmeniis, Lib. 3. Cap. 6.

must acknowledge that we greatly prefer his error to the opposite error of Plato. We have no patience with a philosophy which, like those Roman matrons who swallowed abortives in order to preserve their shapes, takes pains to be barren for fear of being homely.

Let us pass to astronomy. This was one of the sciences which Plato exhorted his disciples to learn, but for reasons for removed from common habits of thinking. “Shall we set down astronomy,” says Socrates, “among the subjects of study?” (1) “I think so,” answers his young friend Glaucon: “to know something about the seasons, the months, and the years is of use for military purposes, as well as for agriculture and navigation.”

“It amuses me,” says Socrates, “to see how afraid you are, lest the common herd of people should accuse you of recommending useless studies.” He then proceeds, in that pure and magnificent diction which, as Cicero said, Jupiter would use if Jupiter spoke Greek, to explain that the use of astronomy is not to add to the vulgar comforts of life, but to assist in raising the mind to the contemplation of things which are to be perceived by the pure intellect alone. The knowledge of the actual motions of the heavenly bodies Socrates considers as of little value. The appearances which make the sky beautiful at night are, he tells us, like the figures which a geometrician draws on the sand, mere examples, mere helps to feeble minds. We must get beyond them; we must neglect them; we must attain to an astronomy which is as independent of the actual stars as geometrical truth is independent of the lines of an ill-drawn diagram. This is, we imagine, very nearly, if not exactly, the astronomy which Bacon

(1) Plato’s Republic, Book 7.

compared to the ox of Prometheus, (1) a sleek, wellshaped hide, stuffed with rubbish, goodly to look at, but containing nothing to eat. He complained that astronomy had, to its great injury, been separated from natural philosophy, of which it was one of the noblest provinces, and annexed to the domain of mathematics. The world stood in need, he said, of a very different astronomy, of a living astronomy, (2) of an astronomy which should set forth the nature, the motion, and the influences of the heavenly bodies, as they really are. (3)

On the greatest and most useful of all human inventions, the invention of alphabetical writing, Plato did not look with much complacency. He seems to have thought that the use of letters had operated on the human mind as the use of the go-cart in learning to walk, or of corks in learning to swim, is said to operate on the human body. It was a support which, in his opinion, soon became indispensable to those who used it, which made vigorous exertion first unnecessary and then impossible. The powers of the intellect would, he conceived, have been more fully developed without this delusive aid. Men would have been compelled to exercise? the understanding and the memory, and, by deep and assiduous meditation, to make truth thoroughly their own. Now, on the contrary, much knowledge is traced on paper, but little is engraved in the soul. A man is certain that he can find information at a moment’s notice when he wants it. He therefore suffers it to fade from his mind. Such a man cannot in strictness

(1) De Augmentis, Lib. 3. Cap. 4.
(2) Astronomia viva.
(3) “Quæ substantiam et motum et influxum colestium, prout
re vera flint proponat.” Compare this language with Plato’s,
“[Greek]”