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was first suggested by Pythagoras, and afterwards filled up by Aristocle.
The mathematicians of whom we possess written monuments, may be arranged in the following order : Euclid (306) who studied the Platonic philosophy at Athens, and taught mathematics at Alexandria-his writings have been acknowledged, in all ages, as models of scientific completeness, profundity and clearness, not to be surpassed. Many of them, among which was the highly praised geometrical analysis, in 4 books, are lost. We possess of bim-Elements of pure Mathesis, in 15 books, viz. from 1 to 6, on pure geometry; from 7 to 9, on arithmetic; the 10th on irrational numbers; from 11 to 13, on stereometry; the 14th and 15th are, probably, composed by the Alexandrian Hypsicles, (160 after Ch.); the revision is by Theon, (390 after Christ) who also made some additions ; a commentary on the first book by Proclus of Lycia, (450 after Christ) has been preserved. Apollonius of Perge, (350) the celebrated mathematician, lived partly at Pergamus, partly at Alexandria, and left many works on the geometrical analysis, none of which have been completely preserved in their original forın. Of Bito, (235) we possess a treatise on the construction of machines of war. Heron, (220) disciple of the renowned hydraulist and artist, Ctesebius, (250) and like him also, inventor of many mechanical and artificial works, wrote on Pneumatics, on the construction of automata, and of some martial machines. Archimedes (b. 287, d. 212) formed himself in the Alexandrian school, under the learned Conon of Samos, (260) whose doctrine of the spiral line be perfected, and lived afterwards at Syracuse, wholly devoted, until his death, to science and examination. He acquired great merit in all the branches of mathematics, especially of geometry, in which he made the most important discoveries, as well as in mechanics, wherein he composed with scientific profundity.*
Astronoiny gained, during this period, especially at Rhodes and Alexandria, the seat of mathematical studies, a more solid foundation and extensive scientific enrichment. The observatory which was erected in the museum at Alexandria (283) loy Ptolemy Philadelphus, was provided with very fine instruments for that purpose. Aristillus and Timocharis observed for twenty-six years the fixed stars and planets, and made notes and records, which were improved and made use of by their successors, and C. Ptolemeus. Aristarchus observed (279; the solstices. Eratosthenes was
Mem. de De Lambre sur l'arithm: des Grecs. Compare Fab. Bib. gr. 4, 170.
the first who nttempted an astronomico-geometrical measure of the world, which was repeated by the Rhodian Posidonius, (70.) Hipparchus fixed the space of the solar year at 365 days and 6 hours, (entirely agreeing with Tycho de Brahe) calculated the course of the sun from the vernal equinox to the autumnal, as well as the motion of the fixed stars, and the sun and moon, corrected many of the calculations of Aristarchus, ordered the astronomical calculus, and applied astronomy to scientific geography. It is not probable that the Alexandrians made use of older Ægyptian preparatory works: we may sooner suppose that they might have borrowed somewhat from the Persians, for they had very early (312) a fixed solar year (sol chodai) and a' cycle of 1440 astronomical years, each consisting of 365 days, 5 hours, and 49 minutes. · The most remarkable among the astronomical authors are, Aristarchus of Samos, (264 who taught the motion of the earth around the immoveable sun, calculated the distance of the sun from the earth by the dichotomy of the moon, and developed the finest principles of astronomy. We possess only one of his writings-of the size and distance of the sun and moon. Hipparchus of Nicæa, (d. 125) who lived first at Rhodes, and afterwards at Alexandria, surpassed very far bis predecessors in the precision of his observations and calculations, and obtained important results from his scientific experiments. He calculated the length of the solar year by means of more strict observations of the equinoxes, froin the monthly course of the moon, and from the eccentricity of the sun from one-twenty-fourth of the radius of his course, arranged the first solar and lunar tables, and fixed, after his own method, (diagramma Hipparchi) the distance of the planets from one another, as well as the size of our globe. His name is celebrated in all later compositions of important astronomical observations and examinatione, and the most profound astronomers of modern times do full justice to his merits. Of the many writings of the Rhodian Geminus, (70) only the elements of astronomy have been preserved.*
Physics retained, in the philosophical systems into which they were incorporated as essential parts, their hypothetical form. The ingenious Aristotle enriched them with many scientific views, which were derived from repeated, though not always complete and sufficiently exact observations. The Epicureans and Stoics also, although their researches often depended on systematical prejudices, acquired some merit in this science.
• Fabr. Bib. gr. 4, 128.
Natural history was elevated to a science by Aristotle and Theophrastus ; to the former it is indebted for zoology, as much as to the latter for botany and mineralogy. But they found no emulators or travellers of the road which they had laid out with successful efforts. It is true, that at Alexandria and Pergamus, rich collections of natural curiosities were accumulated and much augmented by travellers—but study had taken too entirely a pedantically literary turn, to permit the careful observation of natural life and its various relations to be much attended to. The most fruitful knowledge is seen in the poems of Nicander and some of their commentators. The majority, yielding to the predominant taste of a commercial city, which always looks for amusement, were chiefly occupied with all that was marvellous and adventurous. Of this kind is the compilation of Antigonus Carystius, (280) under the title of “Collection of strange accounts."
The medical theory was treated dialectically, and at Alexandria sophistically. The more studious observation of nature led to materialism, and gave occasion to the neglect of psychological medicine. By Aristotle, who first noticed the diseases of beasts, was anatomy much advanced, and psychology by Theophrastus. On these, as well as on pathology, the stoic writers had no little influence. At Alexandria, the progress of medicine was chiefly promoted by its library, and chiefly by a more precise knowledge of the human body. Ptolemy II. and his successor, gave permission to dissect human bodies. Herophilus of Chalcedon, (280) scholar of Praxagoras, and a studious composer of the semiotic system, is supposed to have made many anatomical discoveries. To his contemporary, Erasistratus of lulis, on the island Cos, a grandson of Aristotle, and disciple of Theophrastus, who was distinguished for remarkable peculiarities in the praxis, who appears to have anticipated the reaction of the bodily strength, and who spent his latter days at Alexandria entirely in scientific researches, are attributed, perhaps not without exageration, the finest anatomical observations on the nerves and the brain. The perfection of medicine is manifest by the poem of Nicander. Whether the old Egyptian systems, or the variety of diseases in so large a city, together with the consequences of a profligate life and various bodily excitements, had given rise to the separation of medical disciplines, is uncertain. Chirurgy and pharmacy formed separate sciences. Of the writings of the Alexandrian physicians, nothing bas been preserved—we only know of their views and efforts by traditions and later quotations. Ptolemæus Physcon banisbed (135)
the physicians together with the philosophers and grammarians from Alexandria. The disciples of Erasistratus then settled themselves at Smyrna, and those of Herophilus at Laodicea. Medical studies were thus again transferred to Greece, especially to Athens. The empiric system which became predominant at Alexandria, had based itself more firmly upon the dialectic and scepticism, and was opposed to dogmatism-it was founded solely on individual experience, observation and inductive proof. Philinus of Cos, (250) disciple of Herophilus, is supposed to be the founder of this school--it attained its riper cultivation under Serapion of Alexandria, and Heraclides of Tarentum. Asclepiades of Prusa, in Bithynia, (75) who studied at Alexandria and Athens, and was the first successful pbysician at Rome, where the Peloponnesian Archagathus had, at an earlier date, (220) introduced chirurgy, which was hated and despised as the business of a hangman, approached to the principles of the methodic school, which deduced all diseases from constriction and relaxation, and which obtained its perfection under Themison of Laodicea.
Art.V.-A Comparative View of the Social Life of England and
France, from the Restoration of Charles II. to the French
This is a tolerably good collection of anecdotes and remarks, as to the modes of living, habits and manners of the courts of these two countries, and of the grades of society who would be immediately and directly influenced in consequence of their connexion with courts and courtiers. To persons who regard these classes of society as pre-eminently " the world,” the characters of the principal actors during the reigns of Louis XIV,
the Regent, Duc d'Orleans, Louis XV, and Louis XVI.--those of Charles II. James II. and the three Georges of Englandthe men and the women of distinction, so far as they contributed to improve or demoralize society, so far as they contributed to mould or modify the practical ethics of the upper classes-must be interesting; and for such readers this book seems principally designed. But the information here presented, of the modes of thinking, the modes of living, the dress, the habits and manners of the great mass of society, from the class of wealthy men of leisure, without title, at the upper end of the scale, to the respectable and opulent mechanic at the lower end-comprehending fully what may be called the middle classes—is very meagre. It may be said that the manners of the court and courtiers gave the tone of fashion in both countries to all the classes below them: but this is not the fact; the separation of the middle classes in England from those of titular dignity, until after the French revolution, was marked and complete; nor was there any obliteration of the line that separated in France the bourgeoisie from the titled noblesse, even of the most inferior orders. The literary men of eminence were, indeed, seen in the saloons of the noblesse, speciali gratiâ, but they were visitors only; there was no amalgamation.
Nor is there in the present volume a sufficient elucidation of the effects of the religion of the two countries, compared as to its influence on the manners of the population in each. Indeed, the whole subject embraced, is so extensive, that it can be barely touched upon in a single volume. When we inquire, for instance,
What was the influence of the court on the metropolis, and of the metropolis and the nobility on the manners and morals of the great mass of the people, during the reign of Louis XIV. particularly on married life and domestic habits ?
What was the influence of the clergy on the same mass of population during that reign? What the effect of the substitution of rites and ceremonies for practical morality, and the permission or prohibition of sabbath-day amusements on the temper of the people, distinguishing the deism or atheism of the upper classes, always dressed out in the costume of orthodoxy, from the honest fides carbonaria of the vulgar?
What was the influence of literature during the same period ? The literature of amusement, that is to say ; for of scientific literature, there was hardly any.
What were the domestic habits, dress, modes of living, and amusements, during that period ? Not sufficiently elucidated