So a library is begun by Soter, and organised and completed by Philadelphus; or rather two libraries, for while one part was kept at the Serapeium, that vast temple on the inland rising ground, of which, as far as we can discover, Pompey’s Pillar alone remains, one column out of four hundred, the rest was in the Brucheion adjoining the Palace and the Museum.  Philadelphus buys Aristotle’s collection to add to the stock, and Euergetes cheats the Athenians out of the original MSS. of Æschylus, Sophocles, and Euripides, and adds largely to it by more honest methods.  Eumenes, King of Pergamus in Asia Minor, fired with emulation, commences a similar collection, and is so successful, that the reigning Ptolemy has to cut off his rival’s supplies by prohibiting the exportation of papyrus; and the Pergamenian books are henceforth transcribed on parchment, parchemin, Pergamene, which thus has its name to this day, from Pergamus.  That collection, too, found its way at last to Alexandria.  For Antony having become possessor of it by right of the stronger, gave it to Cleopatra; and it remained at Alexandria for seven hundred years.  But we must not anticipate events.

Then there must be besides a Mouseion, a Temple of the Muses, with all due appliances, in a vast building adjoining the palace itself, under the very wing of royalty; and it must have porticos, wherein sages may converse; lecture-rooms, where they may display themselves at their will to their rapt scholars, each like a turkey-cock before his brood; and a large dining-hall, where they may enjoy themselves in moderation, as befits sages, not without puns and repartees, epigrams, anagrams, and Attic salt, to be fatal, alas, to poor Diodorus the dialectician.  For Stilpo, prince of sophists, having silenced him by some quibbling puzzle of logic, Ptolemy surnamed him Chronos the Slow.  Poor Diodorus went home, took pen and ink, wrote a treatise on the awful nothing, and died in despair, leaving five “dialectical daughters” behind him, to be thorns in the sides of some five hapless men of Macedonia, as “emancipated women;” a class but too common in the later days of Greece, as they will always be, perhaps, in civilisations which are decaying and crumbling to pieces, leaving their members to seek in bewilderment what they are, and what bonds connect them with their fellow-beings.  But to return: funds shall be provided for the Museum from the treasury; a priest of rank, appointed by royalty, shall be curator; botanical and zoological gardens shall be attached; collections of wonders made.  In all things the presiding genius of Aristotle shall be worshipped; for these, like Alexander, were his pupils.  Had he not mapped out all heaven and earth, things seen and unseen, with his entelechies, and energies, and dunameis, and put every created and uncreated thing henceforth into its proper place, from the ascidians and polypes of the sea to the virtues and the vices—yea, to that Great Deity and Prime Cause (which indeed was all things), Noesis Noeseon, “the Thought of Thoughts,” whom he discovered by irrefragable processes of logic, and in whom the philosophers believe privately, leaving Serapis to the women and the sailors?  All they had to do was to follow in his steps; to take each of them a branch, of science or literature, or as many branches as one man conveniently can; and working them out on the approved methods, end in a few years, as Alexander did, by weeping on the utmost shore of creation that there are no more worlds left to conquer.

Alas! the Muses are shy and wild; and though they will haunt, like skylarks, on the bleakest northern moor as cheerfully as on the sunny hills of Greece, and rise thence singing into the heaven of heavens, yet they are hard to tempt into a gilded cage, however amusingly made and plentifully stored with comforts.  Royal societies, associations of savants, and the like, are good for many things, but not for the breeding of art and genius: for they are things which cannot be bred.  Such institutions are excellent for physical science, when, as among us now, physical science is going on the right method: but where, as in Alexandria, it was going on an utterly wrong method, they stereotype the errors of the age, and invest them with the prestige of authority, and produce mere Sorbonnes, and schools of pedants.  To literature, too, they do some good, that is, in a literary age—an age of reflection rather than of production, of antiquarian research, criticism, imitation, when book-making has become an easy and respectable pursuit for the many who cannot dig, and are ashamed to beg.  And yet, by adding that same prestige of authority, not to mention of good society and Court favour, to the popular mania for literature, they help on the growing evil, and increase the multitude of prophets who prophesy out of their own heart and have seen nothing.

And this was, it must be said, the outcome of all the Ptolemæan appliances.

In Physics they did little.  In Art nothing.  In Metaphysics less than nothing.

We will first examine, as the more pleasant spectacle of the two, that branch of thought in which some progress was really made, and in which the Ptolemaic schools helped forward the development of men who have become world-famous, and will remain so, I suppose, until the end of time.

Four names at once attract us: Euclid, Aristarchus, Eratosthenes, Hipparchus.  Archimedes, also, should be included in the list, for he was a pupil of the Alexandrian school, having studied (if Proclus is to be trusted) in Egypt, under Conon the Samian, during the reigns of two Ptolemies, Philadelphus and Euergetes.

Of Euclid, as the founder (according to Proclus) of the Alexandrian Mathematical school, I must of course speak first.  Those who wish to attain to a juster conception of the man and his work than they can do from any other source, will do well to read Professor De Morgan’s admirable article on him in “Smith’s Classical Dictionary;” which includes, also, a valuable little sketch of the rise of Geometric science, from Pythagoras and Plato, of whose school Euclid was, to the great master himself.

I shall confine myself to one observation on Euclid’s genius, and on the immense influence which it exerted on after generations.  It seems to me, speaking under correction, that it exerted this, because it was so complete a type of the general tendency of the Greek mind, deductive, rather than inductive; of unrivalled subtlety in obtaining results from principles, and results again from them ad infinitum: deficient in that sturdy moral patience which is required for the examination of facts, and which has made Britain at once a land of practical craftsmen, and of earnest scientific discoverers.

Volatile, restless, “always children longing for something new,” as the Egyptian priest said of them, they were too ready to believe that they had attained laws, and then, tired with their toy, throw away those hastily assumed laws, and wander off in search of others.  Gifted, beyond all the sons of men, with the most exquisite perception of form, both physical and metaphysical, they could become geometers and logicians as they became sculptors and artists; beyond that they could hardly rise.  The were conscious of their power to build; and it made them ashamed to dig.

Four men only among them seem, as far as I can judge, to have had a great inductive power: Socrates and Plato in Metaphysics; Archimedes and Hipparchus in Physics.  But these men ran so far counter to the national genius, that their examples were not followed.  As you will hear presently, the discoveries of Archimedes and Hipparchus were allowed to remain where they were for centuries.  The Dialectic of Plato and Socrates was degraded into a mere art for making anything appear alternately true and false, and among the Megaric school, for undermining the ground of all science, and paving the way for scepticism, by denying the natural world to be the object of certain knowledge.  The only element of Plato’s thought to which they clung was, as we shall find from the Neoplatonists, his physical speculations; in which, deserting his inductive method, he has fallen below himself into the popular cacoethes, and Pythagorean deductive dreams about the mysterious powers of numbers, and of the regular solids.

Such a people, when they took to studying physical science, would be, and in fact were, incapable of Chemistry, Geognosy, Comparative Anatomy, or any of that noble choir of sister sciences, which are now building up the material as well as the intellectual glory of Britain.

To Astronomy, on the other hand, the pupils of Euclid turned naturally, as to the science which required the greatest amount of their favourite geometry: but even that they were content to let pass from its inductive to its deductive stage—not as we have done now, after two centuries of inductive search for the true laws, and their final discovery by Kepler and Newton: but as soon as Hipparchus had propounded any theory which would do instead of the true laws, content there to stop their experiments, and return to their favourite work of commenting, deducing, spinning notion out of notion, ad infinitum.

Still, they were not all of this temper.  Had they been, they would have discovered, not merely a little, but absolutely nothing.  For after all, if we will consider, induction being the right path to knowledge, every man, whether he knows it or not, uses induction, more or less, by the mere fact of his having a human reason, and knowing anything at all; as M. Jourdain talked prose all his life without being aware of it.

Aristarchus is principally famous for his attempt to discover the distance of the sun as compared with that of the moon.  His method was ingenious enough, but too rough for success, as it depended principally on the belief that the line bounding the bright part of the moon was an exact straight line.  The result was of course erroneous.  He concluded that the sun was 18 times as far as the moon, and not, as we now know, 400; but his conclusion, like his conception of the vast extent of the sphere of the fixed stars, was far enough in advance of the popular doctrine to subject him, according to Plutarch, to a charge of impiety.

Eratosthenes, again, contributed his mite to the treasure of human science—his one mite; and yet by that he is better known than by all the volumes which he seems to have poured out, on Ethics, Chronology, Criticism on the Old Attic Comedy, and what not, spun out of his weary brain during a long life of research and meditation.  They have all perished,—like ninety-nine hundredths of the labours of that great literary age; and perhaps the world is no poorer for the loss.  But one thing, which he attempted on a sound and practical philosophic method, stands, and will stand for ever.  And after all, is not that enough to have lived for? to have found out one true thing, and, therefore, one imperishable thing, in one’s life?  If each one of us could but say when he died: “This one thing I have found out; this one thing I have proved to be possible; this one eternal fact I have rescued from Hela, the realm of the formless and unknown,” how rich one such generation might make the world for ever!

But such is not the appointed method.  The finders are few and far between, because the true seekers are few and far between; and a whole generation has often nothing to show for its existence but one solitary gem which some one man—often unnoticed in his time—has picked up for them, and so given them “a local habitation and a name.”

Eratosthenes had heard that in Syene, in Upper Egypt, deep wells were enlightened to the bottom on the day of the summer solstice, and that vertical objects cast no shadows.

He had before suggested, as is supposed, to Ptolemy Euergetes, to make him the two great copper armillæ, or circles for determining the equinox, which stood for centuries in “that which is called the Square Porch”—probably somewhere in the Museum.  By these he had calculated the obliquity of the ecliptic, closely enough to serve for a thousand years after.  That was one work done.  But what had the Syene shadows to do with that?  Syene must be under that ecliptic.  On the edge of it.  In short, just under the tropic.  Now he had ascertained exactly the latitude of one place on the earth’s surface.  He had his known point from whence to start on a world-journey, and he would use it; he would calculate the circumference of the earth—and he did it.  By observations made at Alexandria, he ascertained its latitude compared with that of Syene; and so ascertained what proportion to the whole circumference was borne by the 5000 stadia between Alexandria and Syene.  He fell into an error, by supposing Alexandria and Syene to be under the same meridians of longitude: but that did not prevent his arriving at a fair rough result of 252,000 stadia—31,500 Roman miles; considerably too much; but still, before him, I suppose, none knew whether it was 10,000, or 10,000,000.  The right method having once been found, nothing remained but to employ it more accurately.

One other great merit of Eratosthenes is, that he first raised Geography to the rank of a science.  His Geographica were an organic collection, the first the world had ever seen, of all the travels and books of earth-description heaped together in the Great Library, of which he was for many years the keeper.  He began with a geognostic book, touched on the traces of Cataclysms and Change visible on the earth’s surface; followed by two books, one a mathematical book, the other on political geography, and completed by a map—which one would like to see: but—not a trace of all remains, save a few quoted fragments—

 
            We are such stuff
As dreams are made of.
 

But if Eratosthenes had hold of eternal fact and law on one point, there was a contemporary who had hold of it in more than one.  I mean Archimedes; of whom, as I have said, we must speak as of an Alexandrian.  It was as a mechanician, rather than as an astronomer, that he gained his reputation.  The stories of his Hydraulic Screw, the Great Ship which he built for Hiero, and launched by means of machinery, his crane, his war-engines, above all his somewhat mythical arrangement of mirrors, by which he set fire to ships in the harbour—all these, like the story of his detecting the alloy in Hiero’s crown, while he himself was in the bath, and running home undressed shouting εὕρηκα—all these are schoolboys’ tales.  To the thoughtful person it is the method of the man which constitutes his real greatness, that power of insight by which he solved the two great problems of the nature of the lever and of hydrostatic pressure, which form the basis of all static and hydrostatic science to this day.  And yet on that very question of the lever the great mind of Aristotle babbles—neither sees the thing itself, nor the way towards seeing it.  But since Archimedes spoke, the thing seems self-evident to every schoolboy.  There is something to me very solemn in such a fact as this.  It brings us down to some of the very deepest questions of metaphysic.  This mental insight of which we boast so much, what is it?  Is it altogether a process of our own brain and will?  If it be, why have so few the power, even among men of power, and they so seldom?  If brain alone were what was wanted, what could not Aristotle have discovered?  Or is it that no man can see a thing unless God shows it him?  Is it that in each separate act of induction, that mysterious and transcendental process which cannot, let logicians try as they will, be expressed by any merely logical formula, Aristotelian or other—is it I say, that in each separate act of induction we do not find the law, but the law is shown to us, by Him who made the law? Bacon thought so.  Of that you may find clear proof in his writings.  May not Bacon be right?  May it not be true that God does in science, as well as in ethics, hide things from the wise and prudent, from the proud, complete, self-contained systematiser like Aristotle, who must needs explain all things in heaven and earth by his own formulæ, and his entelechies and energies, and the rest of the notions which he has made for himself out of his own brain, and then pack each thing away in its proper niche in his great cloud-universe of conceptions?  Is it that God hides things from such men many a time, and reveals them to babes, to gentle, affectionate, simple-hearted men, such as we know Archimedes to have been, who do not try to give an explanation for a fact, but feel how awful and divine it is, and wrestle reverently and stedfastly with it, as Jacob with the Angel, and will not let it go, until it bless them?  Sure I am, from what I have seen of scientific men, that there is an intimate connection between the health of the moral faculties and the health of the inductive ones; and that the proud, self-conceited, and passionate man will see nothing: perhaps because nothing will be shown him.

But we must leave Archimedes for a man not perhaps so well known, but to whom we owe as much as to the great Syracusan—Hipparchus the astronomer.  To his case much which I have just said applies.  In him astronomic science seemed to awaken suddenly to a true inductive method, and after him to fall into its old slumber for 300 years.  In the meantime Timocharis, Aristyllus, and Conon had each added their mites to the discoveries of Eratosthenes: but to Hipparchus we owe that theory of the heavens, commonly called the Ptolemaic system, which, starting from the assumption that the earth was the centre of the universe, attempted to explain the motions of the heavenly bodies by a complex system of supposed eccentrics and epicycles.  This has of course now vanished before modern discoveries.  But its value as a scientific attempt lies in this: that the method being a correct one, correct results were obtained, though starting from a false assumption; and Hipparchus and his successors were enabled by it to calculate and predict the changes of the heavens, in spite of their clumsy instruments, with almost as much accuracy as we do now.