speculation. The very name of the science, however, indicates a culture almost as ancient and geometry, properly so called, could alone offer an adequate field for arithmetical, and yet more for algebraic pursuit; which could not at first be separated. Thence Thales derived the first true geometry, which he presented in his fundamental theory of rectilinear figures, soon extended by the immortal discovery of Pythagoras, which might indeed have been derived from the theorems of Thales on proportional lines, if the power of abstract deduction had been sufficiently advanced, but which proceeded from the distinct principle of the direct study of areas. The well-known fact of Thales teaching the Egyptian priests to measure the height of their pyramids by the length of their shadows is, to the thoughtful, a symptom of vast significance, disclosing the true state of science, still absurdly exaggerated in favour of ancient theocracy, while it exhibits the intellectual progress already made when human progress began to deal, for purposes of scientific utility, with an order of phenomena which had hitherto been merely a subject of superstitious terror. From that date geometry rose, by the aid of the invention of conic sections, to the perfection which it exhibited in the genius of Archimedes, in whom we recognize the eternal type of the true geometer, and the originator of the fundamental methods to which we owe all subsequent progress. After him, I need specify (except perhaps Apollonius) only Hipparchus, the founder of trigonometry (after the preparation made by Archimedes), the inventor of the chief methods of celestial geometry, and the indicator of its practical relations, in regard to the ascertainment of time and place. Mathematical speculation then offered the only field for scientific activity, for reasons exhibited in the whole course of this work, and illustrated by the very name of the science indicating its exclusive positivity at that period. The study of life by the physician Hippocrates, and the works of Aristotle on animals, meritorious as they are, could not so affect the human mind as to render it adequate to sciences of such complexity as to require a systematic creation in a remote future.

With this advent of rational positivity came in that spirit of special research which at once distinguished the

new order of speculations from the indeterminate contemplations of the ancient philosophy. Our modern need is of new generalities; but the case of the ancients was very different. The pursuit of specialities then involved no political disadvantages; and it was the only means by which, independently of the common need of division of employments, the human mind could learn to penetrate the depths of any subject whatever. In short, the scientific spirit was not, under the theological régime, the chief ulterior element of the positive régime, but only destined for its remote preparation; and it must therefore be special in its character, or fail altogether: and there is, in fact, no doubt that men of science, properly so called, began to appear as a separate class from the philosophers, at the memorable epoch distinguished under this point of view by the foundation of the museum of Alexandria, directly adapted to satisfy this new intellectual need, when progressive polytheism had achieved its final triumph over the stationary.

As for the purely philosophical developPhilosophy. ment, it had for some time before its separation from the scientific, been influenced by the nascent positivity. This is shown by the marked intervention of metaphysics. Before astronomical study had begun to disclose the existence of natural laws, the human mind, eager to escape from the exclusively theological régime, was searching among rudimentary mathematical conceptions for universal ideas of order and fitness, which, confused and illusory as they were, were a genuine first presentiment of the subjection of all phenomena to natural laws. This original loan of science to philosophy was the basis of the whole Greek metaphysics; and the metaphysical spirit followed upon mathematical discovery, passing from the mysteries of numbers to those of forms, as science proceeded from arithmetic to geometry, and at length comprehended both classes of ideas. Aristotle's mighty work will always be the most admirable monument of this philosophy, and an immortal testimony to the intrinsic power of human reason in a period of extreme speculative imperfection, passing sagacious judgment on the sciences and fine arts, and omitting from his range of

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conceptions only the industrial arts, which were then thought beneath the notice of free citizens. When the Alexandrian establishment had separated philosophy into natural and moral, it obtained a more and more active social existence, and strove for ever-increasing influence upon the government of mankind. Notwithstanding the strange extravagances of this new phase, it was as necessary as the first in preparation for the monotheistic régime, not only as precipitating the decline of polytheism, but as unconsciously supplying, as we shall see, a germ of spiritual re-organization. If we made a thorough examination into the series of speculations on the supreme good, we should discover a tendency to conceive of social economy in complete independence of all theological philosophy. But such a hope could have none but a critical influence, like all that sprang from this philosophy, which was the active organ of an intellectual and moral anarchy very like our own. Its radical unfitness to be a basis of even mental, and much more social organization, is unquestionable, at the time of its chief spiritual activity, as we see by the continuous progress of universal and systematic doubt, leading every school from Socrates to Pyrrho and Epicurus to a denial of all external existence. This strange issue, directly incompatible with any idea of natural law, discloses the radical antipathy between the metaphysical spirit and the positive, from the time of the separation of philosophy from science; a separation which the good sense of Socrates saw to be impending, but without suspecting either the limits or the dangers involved. Its distinctive social action throughout its whole course, reprobated as it will ever be by posterity, was well represented by the noble Fabricius, when, speaking of Epicureanism, he regretted that such a moral philosophy as that did not prevail among the Samnites and the other enemies of Rome, because it would then be so easy to conquer them. Its intellectual action was scarcely more favourable; as we may judge by the fact that when the separation between philosophy and science had gone sufficiently far, the most eminent philosophers were ignorant of knowledge which was popularized in the school of Alexandria; as when the philosophy of Epicurus put forth those strange astronomical absurdities

which the poet Lucretius piously repeated, half a century after the time of Hipparchus. In short, metaphysics desired to be so independent and absolute as to be emancipated from the only two powers that can organize,theology and science.

The Roman

The Roman civilization will not detain us or Military. so long as the Greek. It is more simple and marked; and its influence on modern society is more complete and evident. I may point out here, that in assigning the names Greek and Roman to certain phases of civilization, I am not deserting my abstract method of research, but rendering those names abstract, by making them the representatives of certain collective conditions. Antiquity presents many populations animated by military activity, but prevented by circumstances from fulfilling a career of conquest; and, on the other hand, inverse influences have favoured an opposite state. Each case must, in its extreme, furnish an instance of preponderant political or intellectual superiority. The system of conquest could not be completely carried out by more than one power: and the spiritual action which was compatible with the age, must operate from a single centre first, whatever the ulterior propagation might amount to. The further we examine, the more we shall see that there has been nothing fortuitous about this double process of human advancement, even in the places and times indicated by these representative names. As to the places, it is obvious that the two movements, political and intellectual, go forward in scenes sufficiently but not too remote, so that at the outset the one should not be absorbed or perverted by the other, while yet they should be able, after a certain progress had been made, to penetrate each other, so as to conduce and converge equally to the monotheistic régime of the Middle Ages, which we shall soon see to have issued from this memorable combination. As to the time, it is obvious that the mental progression of Greece must precede by some centuries the extension of the Roman dominion, the premature establishment of which would have radically impeded it by crushing the independent activity from which it arose and if the interval had, on the other hand, been too great, the universal propagation and social use would have failed, because the original

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movement, which could not be of any great duration, would have become too much weakened at the time of contact. On the other hand, when the first Cato insisted on the expulsion of the philosophers, the political danger from metaphysical contagion was pretty nearly gone by, since the Roman impulsion was by that time too decided to be really liable to such adulteration: but if a permanent contact had been possible two or three centuries earlier, it would certainly have been incompatible with the free and unmixed course of the spirit of conquest.

The more we study the Roman people, the more we see that it was indeed destined to universal empire, as its own poet said, and as every citizen perseveringly and exclusively desired. The nation freed itself from its theocratic beginning by the expulsion of its kings, but securing its own organization by means of the senatorial caste, in which the sacerdotal was subordinated to the military power. When this wise and energetic corporation of hereditary captains failed to yield to the people or the army such influence as might attach them to the system of conquest, the natural march of events had the needed effect. Generally speaking, the formation and improvement of the internal constitution, and the gradual extension of external dominion, depended on each other much more than on any mysterious superiority of design and conduct in the chiefs, whatever may have been the influence of individual political genius, to which a vast career was thus opened. The first cause of success was the convergence of all the means of education, direction, and execution towards one homogeneous and permanent end, more accessible than any other to all minds, and even to all hearts. The next cause was the gradual course of the progression. When we see this noble republic devoting three or four centuries to the solid establishment of its power in a radius of under a hundred miles, about the same time that Alexander was spreading out his marvellous empire in the course of a few years, it is not difficult to foresee the fate of the two empires, though the one usefully prepared the East for the succession of the other. Another cause of success was the course Conquest.

of conduct steadily pursued towards the conquered nations; the principle being that of progressive in