What, then, remains for us? Is it not this—the acquisition of knowledge, the cultivation of virtue and of friendship, the observance of faith and truth, an unrepining submission to whatever befalls us, a life led in accordance with reason?
PLATONISM IN THE MUSEUM. But, though the Alexandrian Museum was especially intended for the cultivation of the Aristotelian philosophy, it must not be supposed that other systems were excluded. Platonism was not only carried to its full development, but in the end it supplanted Peripateticism, and through the New Academy left a permanent impress on Christianity. The philosophical method of Plato was the inverse of that of Aristotle. Its starting-point was universals, the very existence of which was a matter of faith, and from these it descended to particulars, or details. Aristotle, on the contrary, rose from particulars to universals, advancing to them by inductions.
Plato, therefore, trusted to the imagination, Aristotle to reason. The former descended from the decomposition of a primitive idea into particulars, the latter united particulars into a general conception. Hence the method of Plato was capable of quickly producing what seemed to be splendid, though in reality unsubstantial results; that of Aristotle was more tardy in its operation, but much more solid. It implied endless labor in the collection of facts, a tedious resort to experiment and observation, the application of demonstration. The philosophy of Plato is a gorgeous castle in the air; that of Aristotle a solid structure, laboriously, and with many failures, founded on the solid rock.
An appeal to the imagination is much more alluring than the employment of reason. In the intellectual decline of Alexandria, indolent methods were preferred to laborious observation and severe mental exercise. The schools of Neo-Platonism were crowded with speculative mystics, such as Ammonius Saccas and Plotinus. These took the place of the severe geometers of the old Museum.
PHYSICAL SCIENCE IN THE MUSEUM. The Alexandrian school offers the first example of that system which, in the hands of modern physicists, has led to such wonderful results. It rejected imagination, and made its theories the expression of facts obtained by experiment and observation, aided by mathematical discussion. It enforced the principle that the true method of studying Nature is by experimental interrogation. The researches of Archimedes in specific gravity, and the works of Ptolemy on optics, resemble our present investigations in experimental philosophy, and stand in striking contrast with the speculative vagaries of the older writers. Laplace says that the only observation which the history of astronomy offers us, made by the Greeks before the school of Alexandria, is that of the summer solstice of the year B.C. 432. by Meton and Euctemon. We have, for the first time, in that school, a combined system of observations made with instruments for the measurement of angles, and calculated by trigonometrical methods. Astronomy then took a form which subsequent ages could only perfect.
It does not accord with the compass or the intention of this work to give a detailed account of the contributions of the Alexandrian Museum to the stock of human knowledge. It is sufficient that the reader should obtain a general impression of their character. For particulars, I may refer him to the sixth chapter of my "History of the Intellectual Development of Europe."
EUCLID—ARCHIMEDES. It has just been remarked that the Stoical philosophy doubted whether the mind can ascertain absolute truth. While Zeno was indulging in such doubts, Euclid was preparing his great work, destined to challenge contradiction from the whole human race. After more than twenty-two centuries it still survives, a model of accuracy, perspicuity, and a standard of exact demonstration. This great geometer not only wrote on other mathematical topics, such as Conic Sections and Prisms, but there are imputed to him treatises on Harmonics and Optics, the latter subject being discussed on the hypothesis of rays issuing from the eye to the object.
With the Alexandrian mathematicians and physicists must be classed Archimedes, though he eventually resided in Sicily. Among his mathematical works were two books on the Sphere and Cylinder, in which he gave the demonstration that the solid content of a sphere is two-thirds that of its circumscribing cylinder. So highly did he esteem this, that he directed the diagram to be engraved on his tombstone. He also treated of the quadrature of the circle and of the parabola; he wrote on Conoids and Spheroids, and on the spiral that bears his name, the genesis of which was suggested to him by his friend Conon the Alexandrian. As a mathematician, Europe produced no equal to him for nearly two thousand years. In physical science he laid the foundation of hydrostatics; invented a method for the determination of specific gravities; discussed the equilibrium of floating bodies; discovered the true theory of the lever, and invented a screw, which still bears his name, for raising the water of the Nile. To him also are to be attributed the endless screw, and a peculiar form of burning-mirror, by which, at the siege of Syracuse, it is said that he set the Roman fleet on fire.
ERATOSTHENES—APOLLONIUS—HIPPARCHUS. Eratosthenes, who at one time had charge of the library, was the author of many important works. Among them may be mentioned his determination of the interval between the tropics, and an attempt to ascertain the size of the earth. He considered the articulation and expansion of continents, the position of mountain-chains, the action of clouds, the geological submersion of lands, the elevation of ancient sea-beds, the opening of the Dardanelles and the straits of Gibraltar, and the relations of the Euxine Sea. He composed a complete system of the earth, in three books—physical, mathematical, historical—accompanied by a map of all the parts then known. It is only of late years that the fragments remaining of his "Chronicles of the Theban Kings" have been justly appreciated. For many centuries they were thrown into discredit by the authority of our existing absurd theological chronology.
It is unnecessary to adduce the arguments relied upon by the Alexandrians to prove the globular form of the earth. They had correct ideas respecting the doctrine of the sphere, its poles, axis, equator, arctic and antarctic circles, equinoctial points, solstices, the distribution of climates, etc. I cannot do more than merely allude to the treatises on Conic Sections and on Maxima and Minima by Apollonius, who is said to have been the first to introduce the words ellipse and hyperbola. In like manner I must pass the astronomical observations of Alistyllus and Timocharis. It was to those of the latter on Spica Virginis that Hipparchus was indebted for his great discovery of the precession of the eqninoxes. Hipparchus also determined the first inequality of the moon, the equation of the centre. He adopted the theory of epicycles and eccentrics, a geometrical conception for the purpose of resolving the apparent motions of the heavenly bodies on the principle of circular movement. He also undertook to make a catalogue of the stars by the method of alineations—that is, by indicating those that are in the same apparent straight line. The number of stars so catalogued was 1,080. If he thus attempted to depict the aspect of the sky, he endeavored 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. He was the first to construct tables of the sun and moon.
THE SYNTAXIS OF PTOLEMY. In the midst of such a brilliant constellation of geometers, astronomers, physicists, conspicuously shines forth Ptolemy, the author of the great work, "Syntaxis," "a Treatise on the Mathematical Construction of the Heavens." It maintained its ground for nearly fifteen hundred years, and indeed was only displaced by the immortal "Principia" of Newton. It commences with the doctrine that the earth is globular and fixed in space, it describes the construction of a table of chords, and instruments for observing the solstices, it deduces the obliquity of the 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 her nodes. It then gives Ptolemy's own great discovery—that which has made his name immortal—the discovery of the moon's evection or second inequality, reducing it to the epicyclic theory. It attempts the determination of the distances of the sun and moon from the earth—with, however, only partial success. It considers the precession of the equinoxes, the discovery of Hipparchus, the full period of which is twenty-five thousand years. It gives a catalogue of 1,022 stars, treats of the nature of the milky-way, and discusses in the most masterly manner the motions of the planets. This point constitutes another