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.
