metic, music, and astronomy, of great and lasting educational influence. His classification of these "seven liberal arts" maintained itself throughout the Middle Ages and is not yet wholly extinct. Gregory of Tours for example says:-"If thou wilt be a priest of God, then let our Martianus instruct thee first in the seven sciences."

BOETHIUS (480-524) born at Rome on the eve of its fall in 476 is the author not only of the famous Consolations of Philosophy but also of works on Music and on Arithmetic which long served to represent Greek mathematics to the medieval world. In the course of his public-spirited career, Boethius interested himself in the reform of the coinage and in the introduction of waterclocks and sun-dials. His geometry consists merely of some of the simpler propositions of Euclid, with proofs of the first three only, and with applications to mensuration. Yet the intellectual poverty of the age was such that this remained long the standard for mathematical teaching. Boethius' Arithmetic begins:

By all men of old reputation who following Pythagoras' reputation have distinguished themselves by pure intellect it has always been considered settled that no one can reach the highest perfection of philosophical doctrines, who does not seek the height of learning at a certain crossway - the quadrivium.

For him the things of the world are either discrete (multitudes), or continuous (magnitudes). Multitudes are represented by numbers, or in their ratios by music; magnitudes at rest are treated by geometry, those in motion by astronomy. These four of the seven liberal arts form the quadrivium; grammar, dialectics and rhetoric, the trivium. A Christian in faith, a pagan in culture, Boethius has been called the "bridge from antiquity to modern times." (See page 50.)

The scholars of the time were almost without exception men whose first interests were theological. Mathematics, having no direct moral significance, seemed to them in itself unworthy of attention. On the other hand, they attached exaggerated importance to all sorts of mystical attributes of numbers and to the

interpretation of scriptural numbers. Thus Augustine says the science of numbers is not created by men, but merely discovered, residing in the nature of things.

Whether numbers are regarded by themselves or their laws applied to figures, lines or other motions, they have always fixed rules, which have not been made by men at all, but only recognized by the keenness of shrewd people.

SCIENCE AND THE EARLY CHRISTIAN CHURCH. In the earlier centuries of our era the history of science gradually enters upon a new phase. The more highly developed civilization of Greece and Rome, weakened by corruption, has finally yielded to the attacks on the one hand of barbarous or semicivilized races, Goths, Vandals, Huns, and Arabs, and on the other hand to a moral revolution of humble Jewish origin. These changes were adverse to the development, or even the survival, of Greek science. The destructive relation of the northern barbarians to scientific progress may be easily imagined. The policy of official Christianity was based on antecedent antipathy for the unmoral intellectual attitude and the degenerate character which the early Christians found in close association with Greek learning, and on a too literal interpretation of the Jewish scriptures, with their primitive Chaldean theories of cosmogony and the world.

Justin Martyr, in the second century, says that what is true in the Greek philosophy can be learned much better from the Prophets. Clement of Alexandria (d. 227) calls the Greek philosophers robbers and thieves who have given out as their own what they have taken from the Hebrew prophets. Tertullian (160-220) insists that since Jesus Christ and his gospel, scientific research has become superfluous. Isidore of Seville in the seventh century declares it wrong for a Christian to occupy himself with heathen books, since the more one devotes himself to secular learning, the more is pride developed in his soul. Lactantius early in the fourth century includes in his "Divine Institutions" a section, 'On the false wisdom of the philosophers,' of which the 24th chapter is devoted to heaping ridicule on the doctrine of the spherical

figure of the earth and the existence of antipodes. It is unnecessary to enter into particulars as to his remarks about the absurdity of believing that there are people whose feet are above their heads, and places where rain and hail and snow fall upwards, while the wonder of the hanging gardens dwindles into nothing when compared with the fields, seas, towns, and mountains, supposed by philosophers to be hanging without support. He brushes aside the argument of philosophers that heavy bodies seek the centre of the earth, as unworthy of serious notice; and he adds that he could easily prove by many arguments that it is impossible for the heavens to be lower than the earth, but he refrains because he has nearly come to the end of his book, and it is sufficient to have counted up some errors, from which the quality of the rest may be imagined.

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It was natural that Augustine (354–430), . . . should express himself with ... moderation, as befitted a man who had been a student of Plato as well as of St. Paul in his younger days. With regard to antipodes, he says that there is no historical evidence of their existence, but people merely conclude that the opposite side of the earth, which is suspended in the convexity of heaven, cannot be devoid of inhabitants. But even if the earth is a sphere, it does not follow that that part is above water, or, even if this be the case, that it is inhabited; and it is too absurd to imagine that people from our parts could have navigated over the immense ocean to the other side, or that people over there could have sprung from Adam. With regard to the heavens, Augustine was, like his predecessors, bound hand and foot by the unfortunate water above the firmament. He says that those who defend the existence of this water point to Saturn being the coolest planet, though we might expect it to be much hotter than the sun, because it travels every day through a much greater orbit; but it is kept cool by the water above it. The water may be in a state of vapor, but in any case we must not doubt that it is there, for the authority of Scripture is greater than the capacity of the human mind. He devotes a special chapter to the figure of the heaven, but does not commit himself in any way though he seems to think that the allusions in Scripture to the heaven above us cannot be explained away by those who believe the world to be spherical. But anyhow Augustine did not, like Lactantius, treat Greek science with ignorant contempt; he appears to have had a wish to yield to it whenever Scripture did not pull him the

other way, and in times of bigotry and ignorance this is deserving of credit. Dreyer.

Arguing elsewhere that the soul perceives what the bodily eye cannot, Augustine avails himself of the geometrical analogy of the ideal straight line which shall have length without breadth or thickness, but he lapses into mysticism when he passes to the circle.

The biographer of St. Eligius (writing in 760 under Pepin) says 'What do we want with the so-called philosophies of Pythagoras, Socrates, Plato and Aristotle, or with the rubbish and nonsense of such shameless poets as Homer, Virgil and Menander? What service can be rendered to the servants of God by the writings of the heathen Sallust, Herodotus, Livy, Demosthenes or Cicero?' Fredegar . . . complains (about 600) that 'The world is in its decrepitude, intellectual activity is dead, and the ancient writers have no successors.'...-G. H. Putnam, Books of the Middle Ages.

The following is a broad survey of the whole period:

The soft autumnal calm. . . which lingered up to the Antonines over that wide expanse of empire from the Persian Gulf to the Pillars of Hercules and from the Nile to the Clyde. . . was only a misleading transition to that bitter winter which filled the half of the second and the whole of the third century, to be soon followed by the abiding dark and cold of the Middle Ages. The Empire was moribund when Christianity arose. Rome had practically slain the ancient world before the Empire replaced the Republic. The barbarous Roman soldier who killed Archimedes absorbed in a problem, is but an instance and a type of what Rome had done always and everywhere by Greek art, civilization and science. The Empire lived upon and consumed the capital of preceding ages, which it did not replace. Population, production, knowledge, all declined and slowly died.

The sun of ancient science, which had risen in such splendour from Thales to Hipparchus, was now sinking rapidly to the horizon; and when it at last disappeared, say, in the fifth century, the long night of the Middle Ages began. . . . The pursuit of knowledge for knowledge's sake was out of place. . . . All the outlets through which modern energy is chiefly expended were then closed; a man could not serve the state as a citizen, he could not serve knowledge

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There was only one thing left for him to J. C. Morison, The Service of Man.

THE EASTERN EMPIRE. EDICT OF JUSTINIAN.-Only half a century after the fall of Rome the Greek schools in Athens were closed, in 529 A.D., by order of the emperor Justinian, and intellectual darkness settled down over Eastern Europe. Theology became more than ever the chief pursuit of the educated, and Greek learning more than ever neglected. Many Greek manuscripts, however, were hidden away, and many Greek scholars, though scattered, kept alive the feeble spark of Greek learning.

THE DARK AGES. After the mighty Roman Empire of the West had come to its end, the peoples of Christian Europe and of the Graeco-Roman world descended into the great hollow which is roughly called the Middle Ages, extending from the fifth to the fifteenth century, a hollow in which many great and beautiful and heroic things were done and created, but in which knowledge, as we understand it and as Aristotle understood it, had no place. The revival of learning and the Renaissance are memorable as the first sturdy breasting by humanity of the hither slope of that great hollow which lies between us and the ancient world. The modern man, reformed and regenerated by knowledge, looks across it and recognizes on the opposite ridge, in the far-shining cities and stately porticoes, in the art, politics and science of antiquity, many more ties of kinship and sympathy than in the mighty concave between, wherein dwell his Christian ancestry in the dim light of scholasticism and theology. — Morison.

The "great hollow" here so graphically portrayed may be described as the Middle or Medieval Age (c. 450-1450 A.D.) and of these ten centuries the first three, or thereabouts, are often called the Dark as they certainly were the darkest - Ages.

The darkest time in the Dark Ages was from the end of the sixth century to the revival of learning under Charles the Great (Charle magne). Bad grammar was openly circulated and sometimes commended. St. Gregory the Great quoted the Bible in depreciation of the Humanities. (Ps. lxx. 15. 16.) The study of heathen authors was discouraged more and more. "Will the Latin grammar save an immortal soul?" "What profit is there in the record of pagan sages,