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ties of the compounds must resemble those of the elements which determine them; and their loose notions of contrariety never approached the form of those ideas of polarity, which, in modern times, regulate many parts of physics and chemistry.

If this statement should seem to any one to be technical or arbitrary, we must refer, for the justification of it, to the philosophy of science, of which we hope hereafter to treat. But it will appear, even from what has been here said, that there are certain ideas or forms of mental apprehension, which may be applied to facts in such a manner as to bring into view fundamental principles of science; while the same facts, however arrayed or reasoned about, so long as these appropriate ideas are not employed, cannot give rise to any exact or substantial knowledge.

We shall, in the next book, see the influence of the appropriate general ideas, in the formation of various sciences. It need only be observed, before we proceed, that, in order to do full justice to the physical knowledge of the Greek schools of philosophy, it is not necessary to study their course after the time of their founders. Their fortunes, in respect of such acquisitions as we are now considering, were not progressive. The later chiefs of the schools followed the earlier masters; and though they varied much, they added little. The Romans adopted the philosophy of their Greek subjects; but they were always, and, indeed, acknowledged themselves to be,

inferior to their teachers. They were as arbitrary and loose in their ideas as the Greeks, without possessing their invention, acuteness, and spirit of system. In addition to the vagueness which was combined with the more elevated trains of philosophical speculation among the Greeks, the Romans introduced into their treatises a kind of declamatory rhetoric, which arose probably from their forensic and political habits, and which still further obscured the waning gleams of truth. Yet we may also trace, in the Roman philosophers to whom this charge mostly applies (Lucretius, Pliny, Seneca), the national vigour and ambition. There is something Roman in the public spirit and anticipation of universal empire which they display, as citizens of the intellectual republic. Though they speak sadly or slightingly of the achievements of their own generation, they betray a more abiding and vivid belief in the dignity and destined advance of human knowledge as a whole, than is obvious among the Greeks.

We must, however, turn back, in order to describe steps of more definite value to the progress of science than those which we have hitherto noticed.

Ναρθηκοπλήρωτον δὲ θηρῶμαι πυρὸς
Πηγὴν κλοπαίαν, ἣ διδάσκαλος τέχνης
Πάσης βροτοῖς πεφῆνε καὶ μέγας πόρος.

Prom. Vinct. 109.

I brought to earth the spark of heavenly fire,
Concealed at first, and small, but spreading soon
Among the sons of men, and burning on,
Teacher of art and use, and fount of power.

BOOK II.

HISTORY OF PHYSICAL SCIENCES IN ANCIENT

GREECE.

INTRODUCTION.

In order to the acquisition of any such exact and real knowledge of nature as that which we properly call physical science, it is requisite, as has already been said, that men should possess ideas both distinct and appropriate, and should apply them to ascertained facts. They are thus led to propositions of a general character, which are obtained by induction, as will elsewhere be more fully explained. We proceed now to trace the formation of sciences among the Greeks by such processes. The provinces of knowledge which thus demand our attention are, Astronomy, Mechanics and Hydrostatics, Optics and Harmonics; of which I must relate, first, the earliest stages, and next, the subsequent progress.

Of these portions of human knowledge, astronomy is, beyond doubt or comparison, much the most ancient and the most remarkable; and probably existed, in somewhat of a scientific form, in Chaldea and Egypt, and other countries, before the period of

the intellectual activity of the Greeks. But I will give a brief account of some of the other sciences before I proceed to astronomy, for two reasons; first, because the origin of astronomy is lost in the obscurity of a remote antiquity; and therefore we cannot exemplify the conditions of the first rise of science so well in that subject as we can in others which assumed their scientific form at known periods; and next, in order that I may not have to interrupt, after I have once begun it, the history of the only progressive science which the ancient world produced.

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