[Sidenote: Astronomy of Eratosthenes.]

[Sidenote: Attempts of Aristarchus to find the distance of the sun.]

At the time of which we are speaking--the time of Eratosthenes--general ideas had been attained to respecting the doctrine of the sphere, its poles, axis, the equator, arctic and antarctic circles, equinoctial points, solstices, colures, horizon, etc. No one competent to form an opinion any longer entertained a doubt respecting the globular form of the earth, the arguments adduced in support of that fact being such as are still popularly resorted to--the different positions of the horizon at different places, the changes in elevation of the pole, the phenomena of eclipses, and the gradual disappearance of ships as they sail from us. As to eclipses, once looked upon with superst.i.tious awe, their true causes had not only been a.s.signed, but their periodicities so well ascertained that predictions of their occurrence could be made. The Babylonians had thus long known that after a cycle of 223 lunations the eclipses of the moon return. The mechanism of the phases of that satellite was clearly understood. Indeed, Aristarchus of Samos attempted to ascertain the distance of the sun from the earth on the principle of observing the moon when she is dichotomized, a method quite significant of the knowledge of the time, though in practice untrustworthy; Aristarchus thus finding that the sun's distance is eighteen times that of the moon, whereas it is in reality 400. In like manner, in a general way, pretty clear notions were entertained of the climatic distribution of heat upon the earth, exaggerated, however, in this respect, that the torrid zone was believed to be too hot for human life, and the frigid too cold. Observations, as good as could be made by simple instruments, had not only demonstrated in a general manner the progressions, retrogradations and stations of the planets, but attempts had been made to account for, or rather to represent them, by the aid of epicycles.

[Sidenote: Biography of the Ptolemies.]

It was thus in Alexandria, under the Ptolemies, that modern astronomy arose. Ptolemy Soter, the founder of this line of kings, was not only a patron of science, but likewise an author. He composed a history of the campaigns of Alexander. Under him the collection of the library was commenced, probably soon after the defeat of Antigonus at the battle of Ipsus, B.C. 301. The museum is due to his son Ptolemy Philadelphus, who not only patronized learning in his own dominions, but likewise endeavoured to extend the boundaries of human knowledge in other quarters. Thus he sent an expedition under his admiral Timosthenes as far as Madagascar. Of the succeeding Ptolemies, Euergetes and Philopator were both very able men, though the later was a bad one; he murdered his father, and perpetrated many horrors in Alexandria. Epiphanes, succeeding his father when only five years old, was placed by his guardians under the protection of Rome, thus furnishing to the ambitious republic a pretence for interfering in the affairs of Egypt. The same policy was continued during the reign of his son Philometor, who, upon the whole, was an able and good king. Even Physcon, who succeeded in B.C. 146, and who is described as sensual, corpulent, and cruel--cruel, for he cut off the head, hands, and feet of his son, and sent them to Cleopatra his wife--could not resist the inspirations to which the policy of his ancestors, continued for nearly two centuries, had given birth, but was an effective promoter of literature and the arts, and himself the author of an historical work. A like inclination was displayed by his successors, Lathyrus and Auletes, the name of the latter indicating his proficiency in music. The surnames under which all these Ptolemies pa.s.s were nicknames, or t.i.tles of derision imposed upon them by their giddy and satirical Alexandrian subjects. The political state of Alexandria was significantly said to be a tyranny tempered by ridicule. The dynasty ended in the person of the celebrated Cleopatra, who, after the battle of Actium, caused herself, as is related in the legends, to be bitten by an asp. She took poison that she might not fall captive to Octavia.n.u.s, and be led in his triumph through the streets of Rome.

If we possessed a complete and unbiased history of these Greek kings, it would doubtless uphold their t.i.tle to be regarded as the most ill.u.s.trious of all ancient sovereigns. Even after their political power had pa.s.sed into the hands of the Romans--a nation who had no regard to truth and to right--and philosophy, in its old age, had become extinguished or eclipsed by the faith of the later Caesars, enforced by an unscrupulous use of their power, so strong was the vitality of the intellectual germ they had fostered, that, though compelled to lie dormant for centuries, it shot up vigorously on the first occasion that favouring circ.u.mstances allowed.

[Sidenote: They patronize literature as well as science.]

This Egyptian dynasty extended its protection and patronage to literature as well as to science. Thus Philadelphus did not consider it beneath him to count among his personal friends the poet Callimachus, who had written a treatise on birds, and honourably maintained himself by keeping a school in Alexandria. The court of that sovereign was, moreover, adorned by a constellation of seven poets, to which the gay Alexandrians gave the nickname of the Pleiades. They are said to have been Lycophron, Theocritus, Callimachus, Aratus, Apollonius Rhodius, Nicander, and Homer the son of Macro. Among them may be distinguished Lycophron, whose work, ent.i.tled Ca.s.sandra, still remains; and Theocritus, whose exquisite bucolics prove how sweet a poet he was.

[Sidenote: The writings of Apollonius.]

To return to the scientific movement. The school of Euclid was worthily represented in the time of Euergetes by Apollonius Pergaeus, forty years later than Archimedes. He excelled both in the mathematical and physical department. His chief work was a treatise on Conic Sections. It is said that he was the first to introduce the words ellipse and hyperbola. So late as the eleventh century his complete works were extant in Arabic.

Modern geometers describe him as handling his subjects with less power than his great predecessor Archimedes, but nevertheless displaying extreme precision and beauty in his methods. His fifth book, on Maxima and Minima, is to be regarded as one of the highest efforts of Greek geometry. As an example of his physical inquiries may be mentioned his invention of a clock.

[Sidenote: The writings of Hipparchus.]

[Sidenote: The theory of epicycles and eccentrics.]

Fifty years after Apollonius, B.C. 160-125, we meet with the great astronomer Hipparchus. He does not appear to have made observations himself in Alexandria, but he uses those of Aristyllus and Timochares of that place. Indeed, his great discovery of the precession of the equinoxes was essentially founded on the discussion of the Alexandrian observations on Spica Virginis made by Timochares. In pure mathematics he gave methods for solving all triangles plane and spherical: he also constructed a table of chords. In astronomy, besides his capital discovery of the precession of the equinoxes just mentioned, he also determined the first inequality of the moon, the equation of the centre, and all but antic.i.p.ated Ptolemy in the discovery of the evection. To him also must be attributed the establishment of 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. In the case of the sun and moon, Hipparchus succeeded in the application of that theory, and indicated that it might be adapted to the planets. Though never intended as a representation of the actual motions of the heavenly bodies, 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 37th 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 1,080. 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 lat.i.tude and longitude.

[Sidenote: The writings of Ptolemy.]

[Sidenote: His great work: the mechanical construction of the heavens.]

Subsequently to Hipparchus, we find the astronomers Geminus and Cleomedes; their fame, however, is totally eclipsed by that of Ptolemy, A.D. 138, the author of the great work "Syntaxis," or the mathematical construction of the heavens--a work fully deserving the epithet which has been bestowed upon it, "a n.o.ble exposition of the mathematical theory of epicycles and eccentrics." It was translated by the Arabians after the Mohammedan conquest of Egypt; and, under the t.i.tle 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 inst.i.tution which gave it birth, "the divine school of Alexandria." The Almagest commences with the doctrine that the earth is globular and fixed in s.p.a.ce; it describes the construction of a table of chords and instruments for observing the solstices, and deduces the obliquity of the ecliptic. It finds terrestrial lat.i.tudes 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...o...b..t 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 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, since it makes the sun's distance but one-twentieth of the real amount. It considers the precession of the equinoxes, the discovery of Hipparchus, the full period for 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 const.i.tutes Ptolemy's second claim to scientific fame. His determination of the planetary orbits was accomplished by comparing his own observations with those of former astronomers, especially with those of Timochares on Venus.

[Sidenote: His geography.]

To Ptolemy we are also indebted for a work on Geography used in European schools as 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 longitudes are too much to the east; the Mediterranean Sea is twenty degrees too long. Ptolemy's determinations are, therefore, inferior in accuracy to those of his ill.u.s.trious predecessor Eratosthenes, who made the distance from the sacred promontory in Spain to the eastern mouth of the Ganges to be seventy thousand stadia.

Ptolemy also wrote on Optics, the Planisphere, 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 Hipparchus ever intended that theory as anything more than a geometrical fiction. It is not to be regarded as a representation of the actual celestial motions.

And, as might be expected, for such is the destiny of all unreal abstractions, the theory kept advancing in complexity as facts acc.u.mulated, and was on the point of becoming altogether unmanageable, when it was supplanted by the theory of universal gravitation, which has ever exhibited the inalienable attribute of a true theory--affording an explanation of every new fact as soon as it was discovered, without requiring to be burdened with new provisions, and prophetically foretelling phenomena which had not as yet been observed.

[Sidenote: The later Alexandrian geometers.]

[Sidenote: Decline of the Greek age of Reason.]

From the time of the Ptolemies the scientific spirit of the Alexandrian school declined; for though such mathematicians as 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 pa.s.sed away. The commentator had succeeded to the philosopher. No new development ill.u.s.trated 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, and hitherto successfully cultivated department, Astronomy, exhibited no farther 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.

[Sidenote: Causes of that decline.]

There is no difficulty in giving an explanation of this unfortunate condition. Greek intellectual life had pa.s.sed 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 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 inst.i.tutions 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 a.s.serted 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 pa.s.siveness. 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 pa.s.sing into decrepitude, and the moral condition of the European world was in antagonism to scientific progress.

CHAPTER VII.

THE GREEK AGE OF INTELLECTUAL DECREPITUDE.

THE DEATH OF GREEK PHILOSOPHY.

_Decline of Greek Philosophy: it becomes Retrospective, and in Philo the Jew and Apollonius of Tyana leans on Inspiration, Mysticism, Miracles._

NEO-PLATONISM _founded by Ammonius Saccas, followed by Plotinus, Porphyry, Iamblicus, Proclus.--The Alexandrian Trinity.--Ecstasy.--Alliance with Magic, Necromancy._

_The Emperor Justinian closes the philosophical Schools._

_Summary of Greek Philosophy.--Its four Problems: 1. Origin of the World; 2. Nature of the Soul; 3. Existence of G.o.d; 4.

Criterion of Truth.--Solution of these Problems in the Age of Inquiry--in that of Faith--in that of Reason--in that of Decrepitude._

_Determination of the Law of Variation of Greek Opinion.--The Development of National Intellect is the same as that of Individual._

_Determination of the final Conclusions of Greek Philosophy as to G.o.d, the World, the Soul, the Criterion of Truth.--Ill.u.s.trations and Criticisms on each of these Points._

[Sidenote: Decline of Greek philosophy.]

In this chapter it is a melancholy picture that I have to present--the old age and death of Greek philosophy. 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 farther 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 conjurer, 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 thinker, and a.s.sert his claim to the effects of the intestate--to keep what suits him, and to destroy what he pleases. The Romans, advancing towards their age of Faith, are about to force their ideas on the European world.

Under the shadow of the Pyramids Greek philosophy was born; after many wanderings for a thousand years round the sh.o.r.es of the Mediterranean, it came back to its native place, and under the shadow of the Pyramids it died.

[Sidenote: It becomes retrospective.]

[Sidenote: Has arrived at Oriental ideas.]

From the period of the New Academy the decline of Greek philosophy was uninterrupted. Inventive genius no longer existed; its place was occupied by the commentator. Instead of troubling themselves with inquiries after absolute truth, philosophers sought support in the opinions of the ancient times, and the real or imputed views of Pythagoras, Plato, or Aristotle were received as a criterion. In this, the old age of philosophy, men began to act as though there had never been such things as original investigation and discovery among the human race, and that whatever truth there was in the world was not the product of thought, but the remains of an ancient and now all but forgotten revelation from heaven--forgotten through the guilt and fall of man.

There is something very melancholy in this total cessation of inquiry.

The mental impetus, which one would have expected to continue for a season by reason of the momentum that had been gathered in so many ages, seems to have been all at once abruptly lost. So complete a pause is surprising: the arrow still flies on after it has parted from the bow; the potter's wheel runs round though all the vessels are finished.

In producing this sudden stoppage, the policy of the early Caesars greatly a.s.sisted. The principle of liberty of thought, which the very existence of the divers philosophical schools necessarily implied, was too liable to make itself manifest in aspirations for political liberty.

While through the emperors the schools of Greece, of Alexandria, and Rome were depressed from that supremacy to which they might have aspired, and those of the provinces, as Ma.r.s.eilles and Rhodes, were relatively exalted, the former, in a silent and private way, were commencing those rivalries, the forerunners of the great theological struggles between them in after ages for political power. Christianity in its dawn was attended by a general belief that in the East there had been preserved a purer recollection of the ancient revelation, and that hence from that quarter the light would presently shine forth. Under the favouring influence of such an expectation, Orientalism, to which, as we have seen, Grecian thought had spontaneously arrived, was greatly re-enforced.

[Sidenote: Philo the Jew thinks he is inspired.]