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The Almagest of Ptolemy.

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it maintained its ground until the era of Kepler and Newton, when the heliocentric doctrine, and that of elliptic motions, were incontestably established. Even Newton himself, in the thirty-fifth proposition of the third book of the Principia,' availed himself of its aid. Hipparchus also undertook to make a register of the stars by the method of alineations,—that is, by indicating those which were in the same apparent straight line. The number of stars catalogued by him was 1080. If he thus depicted the aspect of the sky for his times, he also endeavoured to do the same for the surface of the earth, by marking the position of towns and other places by lines of latitude and longitude.

Subsequently to Hipparchus, we find the astronomers Ge- The writings of minus and Cleomedes; their fame, however, is totally eclipsed Ptolemy. by that of Ptolemy, A.D. 138, the author of the great work theSyntaxis,' or the mathematical construction of the heavens, a work fully deserving the epithet which has been bestowed upon it, "a noble exposition of the mathematical theory of epicycles and eccentrics." It was translated by the Arabians after the Mohammedan conquest of Egypt; and, under the title of 'Almagest,' was received by them as the highest authority on the mechanism and phenomena of the universe. It maintained its ground in Europe in the same eminent position for nearly fifteen hundred years, justifying the encomium of Synesius on the institution which gave it birth, "the divine school of Alexandria." The 'Almagest' commences with the His great doctrine that the earth is globular and fixed in space; it de- mechanical scribes the construction of a table of chords and instruments tion of the for observing the solstices, and deduces the obliquity of the heavens. ecliptic. It finds terrestrial latitudes by the gnomon; describes climates; shows how ordinary may be converted into sidereal time; gives reasons for preferring the tropical to the sidereal year; furnishes the solar theory on the principle of the sun's orbit being a simple eccentric; explains the equation of time; advances to the discussion of the motions of the moon; treats of the first inequality, of her eclipses, and the motion of the node. It then gives Ptolemy's own great discovery, that which makes his name immortal,-the discovery

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His geography.

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The other Writings of Ptolemy.

of the moon's evection or second inequality, reducing it to the
epicyclic theory. It attempts the determination of the dis-
tances of the sun and moon from the earth, with, however,
only partial success, since it makes the sun's distance but one-
twentieth of the real amount. It considers the precision of
the equinoxes, the discovery of Hipparchus, the full period for
which is twenty-five thousand years. It gives a catalogue of
1022 stars; treats of the nature of the Milky Way; and dis-
cusses, in the most masterly manner, the motions of the pla-
nets. This point constitutes Ptolemy's second claim to scien-
tific fame. His determination of the planetary orbits was ac-
complished by comparing his own observations with those of
former astronomers, as those of Timochares on Venus.

To Ptolemy we are also indebted for a work on geography,
used in European schools so late as the fifteenth century. The
known world to him was from the Canary Islands eastward to
China, and from the equator northward to Caledonia. His
maps, however, are very erroneous; for, in the attempt to make
them correspond to the spherical figure of the earth, the lon-
gitudes are too much to the east; the Mediterranean Sea is
twenty degrees too long. Ptolemy's determinations are there-
fore inferior in accuracy to those of his illustrious predecessor
Eratosthenes, who made the distance from the Sacred Promon-
tory in Spain to the eastern mouth of the Ganges to be seven-
ty thousand stadia. Ptolemy also wrote on Optics, the Pla-
nisphere, and Astrology. It is not often given to an author
to endure for so many ages; perhaps, indeed, few deserve it.
The mechanism of the heavens, from his point of view, has,
however, been greatly misunderstood. Neither he nor Hip-
parchus ever intended that theory as anything more than a
geometrical fiction. It is not to be regarded as a representa-
tion of the actual celestial motions. And, as might be ex-
pected, for such is the destiny of all unreal abstractions, the
theory kept advancing in complexity as facts accumulated, and
was on the point of becoming altogether unmanageable, when
it was supplanted by the theory of universal gravitation, which
as ever exhibited that inalienable attribute of a true theory
—affording an explanation of every new fact as soon as it was

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discovered, without requiring to be burdened with new provisions, and prophetically foretelling phenomena which had not as yet been observed.

Alexandri

ters.

From the time of the Ptolemies the scientific spirit of the The later Alexandrian school declined; for though such mathematicians an geomeas Theodosius, whose work on Spherical Geometry was greatly valued by the Arab geometers; and Pappus, whose mathematical collections, in eight books, still for the most part remain; and Theon, doubly celebrated for his geometrical attainments, and as being the father of the unfortunate Hypatia, A.D. 415, lived in the next three centuries,-they were not men like their great predecessors. That mental strength which gives birth to original discovery had passed away. The commentator had succeeded to the philosopher. No new developement illustrated the physical sciences; they were destined long to remain stationary. Mechanics could boast of no trophy like the proposition of Archimedes on the equilibrium of the lever; no new and exact ideas like those of the same great man on statical and hydrostatical pressure; no novel and clear views like those developed in his treatise on floating bodies; no mechanical invention like the first of all steam-engines-that of Hero. Natural philosophy had come to a stop. Its great, Decline of and hitherto successfully cultivated department, Astronomy, age of reaexhibited no further advance. Men were content with what had been done, and continued to amuse themselves with reconciling the celestial phenomena to a combination of equable circular motions. To what are we to attribute this pause ? Something had occurred to enervate the spirit of science. A gloom had settled on the Museum.

the Greek

son.

that decline.

There is no difficulty in giving an explanation of this unfor- Causes of nate condition. Greek intellectual life had passed the period of its maturity, and was entering on old-age. Moreover, the talent which might have been devoted to the service of science was in part allured to another pursuit, and in part repressed. Alexandria had sapped Athens, and in her turn Alexandria was sapped by Rome. From metropolitan pre-eminence she had sunk to be a mere provincial town. The great prizes of life were not so likely to be met with in such a declining

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city as in Italy, or subsequently, in Constantinople. Whatever affected these chief centres of Roman activity necessarily influenced her; but, such is the fate of the conquered, she must await their decisions. In the very institutions by which she had once been glorified, success could only be attained by a conformity to the manner of thinking fashionable in the imperial metropolis, and the best that could be done was to seek distinction in the path so marked out. Yet even with all this restraint Alexandria asserted her intellectual power, leaving an indelible impress on the new theology of her conquerors. During three centuries the intellectual atmosphere of the Roman empire had been changing. Men were unable to resist the steadily increasing pressure. Tranquillity could only be secured by passiveness. Things had come to such a state that the thinking of men was to be done for them by others, or, if they thought at all, it must be in accordance with a prescribed formula or rule. Greek intellect was passing into decrepitude, and the moral condition of the European world was in antagonism to scientific progress.

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CHAPTER VII.

THE GREEK AGE OF INTELLECTUAL DECREPITUDE.

THE DEATH OF GREEK PHILOSOPHY.

I preis Chapter l

N this Chapter it is a melancholy picture that I have to Decline of

Greek phi

present the old-age and death of Greek philosophy, losophy The strong man of Aristotelism and Stoicism is sinking into the superannuated dotard; he is settling

"Into the lean and slipper'd pantaloon,

With spectacles on nose and pouch on side;
His youthful hose, well saved, a world too wide
For his shrunk shank; and his big manly voice,
Turning again toward childish treble, pipes
And whistles in his sound. Last scene of all,
That ends this strange, eventful history,

Is second childishness and mere oblivion

Sans teeth, sans eyes, sans taste, sans everything.”

He is full of admiration for the past and of contemptuous disgust at the present; his thoughts are wandering to the things that occupied him in his youth, and even in his infancy. Like those who are ready to die, he delivers himself up to religious preparation, without any further concern whether the things on which he is depending are intrinsically true or false.

In this, the closing scene, no more do we find the vivid faith of Plato, the mature intellect of Aristotle, the manly self-control of Zeno. Greek philosophy is ending in garrulity and mysticism. It is leaning for help on the conjuror, juggler, and high-priest of Nature.

There are also new-comers obtruding themselves on the stage. The Roman soldier is about to take the place of the Greek

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