flourished about A. D. 50) contributed, in some degree, to the advancement of astronomy, by applying the principles of spherical trigonometry to determine the motions and distances of the heavenly bodies.

88. A considerable interval elapsed before another astronomer of eminence appeared in any part of the civilized world. During the Imperial government of Rome, poetry, sculpture, painting, oratory-all the ornamental arts and sciences, were cultivated, and attained a high degree of excellence; but the abstract sciences, amidst the luxuries of that degenerate age, languished, and gradually fell into decay. Before, however, their complete dissolution and abandonment, an attempt was made to revive them in the Alexandrian school of philosophy, by the celebrated PTOLEMY, whose name is identified with the whole system of ancient astronomy. It is not known whether Ptolemy was a native of Pelusium or of Alexandria, but he flourished during the reigns of Adrian and Antoninus, about a. D. 140. The celebrity of this astronomer is founded not so much on new and brilliant discoveries, (for in this respect he is far inferior to many who had preceded him,) as on his vast and almost incredible labours, his patience, perseverance, and unwearied industry in collecting and augmenting the stores of astronomical knowledge which had been accumulating in former ages. His principal work, entitled Almagest, (an Arabic word, denoting" the great Collection,") contains a digest of all the observations, discoveries, and opinions of former astronomers; to which his own researches being added, (which were by no

means inconsiderable,) the whole forms the most complete system of ancient astronomy that has ever appeared. The well-known theory of this astronomer relative to the solar system was, that the earth is fixed immoveably in the centre of the system, and that all the celestial luminaries revolve round it in their respective orbits. All the explanations given by him of the motions of the planets rest on this hypothesis, to which his authority as the first of astronomers insured an universal reception, and which still continues to bear his name, being usually designated the Ptolemaic System. The greatest difficulty with which Ptolemy had to contend was, to reconcile actual phænomena, of which he could not be ignorant, with this hypothesis; and for this purpose, he was under the necessity of framing theories and conjectures wholly unsubstantiated by evidence.

89. To the discoveries already mentioned, which were more fully demonstrated by Ptolemy, may be added some, the merit of which is exclusively his own, particularly those which relate to the inequality in the motion of the moon, known to modern astronomers by the term evection; a phænomenon which he both demonstrated and explained.* Following up the design of Hipparchus, he enlarged the catalogue of the fixed stars, and assigned distinct positions to no less than 1022; whilst he applied himself with no less diligence to the phænomena of the planets, calculating their distances, determining

See Playfair's Elements, Vol. II. pp. 129, 130.

their motions, and observing all their phænomena, as far as they could be discovered, by the means of observation then possessed. After Ptolemy, no astronomer is known to have flourished during the period under review, who can claim distinct notice, if we except Theon, author of a scientific commentary on Potolemy's "Almagest," and his renowned but unfortunate daughter Hypatia, who, after having presided with distinguished reputation over the astronomical and mathematical school of Alexandria, fell a victim to intolerance and superstition, in the disguise and under the name of Christian zeal.

SECTION III.

ON THE ORIGIN AND PROGRESS OF MECHANICAL SCIENCE.

90. THE practice of the mechanical arts was well understood by the ancients, long before the theory and general laws of that department of physical science were discovered. Necessity, the mother of inventions, prompted the Greeks at an early period of their history, as it had previously stimulated the Assyrians, Egyptians, and other oriental nations, to raise and transport large masses of matter and ponderous substances, by means not unlike those still in use: for without some such inventions, it would have been impossible to rear those massy fabrics, or to construct those splendid temples and forums, some of which are known to

have been erected from remote antiquity, and even the ruins of which are so magnificent. But it was not till a period much later than the known date of their erection, that the mechanical forces were theoretically understood, and mathematical reasonings employed to demonstrate their general principles and laws. Ctesiphon, for example, who is said to have built the celebrated temple of Diana at Ephesus, adopted the simplest and most strictly philosophical methods, by which to raise and fix the masses of stone employed in the construction of that farfamed edifice-in which were included the action of the lever and the inclined plane, and which implied a practical knowledge of the centre of gravity; but neither he nor any of the Grecian architects who succeeded him, down to the age of Archimedes, knew the principles of mechanical science, and still less were they capable of reducing them to a system. Even Aristotle himself, (who flourished as late as A. c. 320,) had most confused notions relative to the equilibrium and motion of heavenly bodies; and those who preceded him must necessarily have been still more destitute of science in these subjects.

91. The true theory of mechanical philosophy dates no higher than the æra of ARCHIMEDES. He is the first of the ancient philosophers who wrote systematically and scientifically on the principles and laws of mechanics. In his treatise on " Equilibria," he distinctly lays down, as the data of his mathematical reasonings, the general principles which modern science has fully established, relative to the lever, the balance, and the centre of gravity,

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confirming those principles by facts which he had previously discovered by " à priori" reasonings. Thus was he led onward, by a yet untrodden track, to a great variety of important deductions, which were subsequently illustrated by experiment, and reduced to practice. How little progress had been previously made in this department of science may be inferred, from the astonishment which Hiero, king of Syracuse, and his courtiers, are said to have expressed, when that philosopher said, "Give me but a place on which to stand, and I will move the globe." This proposition, daring as it may appear to persons ignorant of the fundamental principles of mechanics, is, however, but a simple consequence of the well-known laws of equilibria, and the action of the lever. By the combined influence of mathematical and practical science, Archimedes demonstrated, that there exists in every assemblage of small bodies, and in every large mass of matter considered as such an assemblage, one general point of pressure, which moderns have termed the centre of gravity. Having established the fact, he proceeded to apply it to particular cases, and determined geometrically the precise situation of this centre of gravity in bodies of all shapes and dimensions, whether parallelograms, triangles, trapezia, or parabolas.

92. The mechanical inventions that are specifically attributed to this great mechanician are, the inclined plane, the pulley, and the screw: not, indeed, that no machines acting on these principles were ever before employed, but because he first