his remain, which prove him to have been an eminent mathematician; the first, a treatise "On the Spheres;" the second, a treatise "On the rising and setting of the Planets."

PYTHEAS, an ancient mathematician, astronomer, and geographer, was a native of the Greek colony of Marseilles, in Gaul, and flourished in the time of Aristotle and Alexander the Great. He contributed to the improvement of science by accounts which he wrote of his travels and voyages, and other works. To him is attributed a work, entitled, The Circuit of the Earth; and in the abridgment of Artemidorus the Ephesian, he is placed in the number of those who have written a Periplus of the World ;" and he is supposed to have written a treatise " De Oceano." None of these pieces have reached modern times, though some of them were extant in the fourth century. From fragments collected out of Strabo, it appears that Pytheas introduced into them, as the testimony of others, a number of marvellous and incredible circumstances, which drew on him the censure of that author and Polybius. The last named author maintained it to be utterly impossible for a private person, who was ever in want, to have travelled so far as he pretended to have done by sea and land. He, however, probably visited all the countries of Europe that are situated upon the ocean, discovered the island of Thule, or Iceland, and penetrated a considerable distance into the Baltic. This fact has been proved by Gassendi, who shows that Pytheas was well acquainted with the northern countries, and accurately marked the distinction of climates, by the difference which he observed in the length of the days and nights in different latitudes. He also attempts to prove that Eratosthenes and Hipparchus improved their geographical works by availing themselves of the labours of Pytheas, without due acknowledgments of their obligations. There is no doubt that Pytheas was a skilful observer of the heavens; for he taught that there is no star in the precise situation of the pole, and he rendered himself famous among astronomers, by being the first calculator of the meridian altitude of the sun at the summer solstice, at Marseilles. This fact he ascertained by erecting a gnomon of a given height, and finding the proportion between that height and the length of the meridian shadow. The result was found to correspond exactly with that of an observation made by Gassendi, at the same place, in the year 1636. To obviate such objections as those advanced by Polybius against the reality of Pytheas's voyages, it has been said that he probably was furnished with the means of prosecuting them at the public expense; for as the republic of Marseilles was then powerful at sea, largely engaged in commercial pursuits, and sent Euthimenes to make such discoveries in the southern parts of the world, as might lead to the extension of its trade, it seems very

probable that Pytheas was despatched on the public account into the northern regions for the same purposes.

ARCHELAUS, a geographer, was the author of a treatise on all the countries conquered by Alexander, in whose time he lived. Stobæus quotes also another book, on rivers, written by one Archelaus. HERO. There were two celebrated mathematicians of antiquity of this name, who are usually distinguished by the epithets, Hero the Elder, and Hero the Younger. The first was a native of Alexandria, and the disciple of Ctesias, who flourished in the reign of Ptolemy Philadelphus, and Euergetes I. He was distinguished by his great skill in mechanics, and particularly in the construction of machinery; as a moralist, he was inclined to the tenets of Epicurus. The younger Hero is supposed to have flourished under the reign of the emperor Heraclitus.

CLEOSTRATUS, a celebrated astronomer, born in Tenedos, who, according to Pliny, was the first who discovered the signs of the zodiac; others say, that he only discovered the signs Aries and Sagittarius. He also corrected the errors of the Grecian years. He lived about B. C. 306.

TIMOCHARIS, an astronomer of Alexandria. He observed, B. C. 294, on the 9th of March, four hours before midnight, a conjunction of the moon with the Spica Virginis, the star being then, according to him, eight degrees West from the equinoxial point.

EUCLID, the celebrated mathematician, according to the account of Pappus and Proclus, was born at Alexandria, in Egypt, where he flourished, and taught mathematics with great applause, under the reign of Ptolemy Lagus, about B. C. 280. And here, from his time, till the conquest of Alexandria by the Saracens, all the eminent mathematicians were either born or studied; and it is to Euclid and his scholars we are indebted for Eratosthenes, Archimedes, Apollonius, Ptolemy, Theon, &c. &c. He reduced into regularity and order all the fundamental principles of pure mathematics, which had been delivered down by Thales, Pythagoras, Eudoxus, and other mathematicians before him, and added many others of his own discovering; on which account, it is said he was the first who reduced arithmetic and geometry into the form of a science. He likewise applied himself to the study of mixed mathematics, particularly to astronomy and optics.

His works, as we learn from Pappus, and Proclus, are, the Elements, Data, Introduction to Harmony, Phenomena, Optics, Catoprics, Treatises on the Division of Superficies, Porisms, Loci and Superficies, Fallacies, and four books of Conics.

The most celebrated of these is the first work, "The Ele

ments of Geometry;" of which there have been numberless editions, in all languages; and a fine edition of all his works now extant was printed in 1703, by David Gregory, Savilian Professor of Astronomy at Oxford.

The "Elements," as commonly published, consist of fifteen books, of which the two last, it is suspected, are not Euclid's, but a comment of Hypsicles of Alexandria, who lived two hundred years after Euclid. They are divided into three parts; viz. The Contemplation of Superficies, Numbers, and Solids; the first four books treat of planes only; the fifth, of the proportions of magnitudes in general; the sixth, of the proportion of plane figures; the seventh, eighth, and ninth, give us the fundamental properties of numbers; the tenth contains the theory of commensurable and incommensurable lines and spaces; the eleventh, twelfth, thirteenth, fourteenth, and fifteenth, treat of the doctrine of solids.

There is no doubt, that before Euclid's time, Elements of Geometry were compiled by Hippocrates of Chius, Eudoxus, Leon, and many others, mentioned by Proclus, in the beginning of his second book; for he affirms, that Euclid new ordered many things in the Elements of Eudoxus, completed many things in those of Theatetus, and, besides, strengthened such propositions as before were too slightly, or but superficially established, with the most firm and convincing demonstrations.

History is silent as to the time of Euclid's death, or his age. He is represented as a person of a courteous and agreeable behaviour, and in great esteem and familiarity with king Ptolemy, who once asking him whether there was any shorter way of coming at geometry than by his Elements, Euclid, as Proclus testifies, made answer, that there was no royal way, or path, to geometry.

ARISTARCHUS, a celebrated Greek astronomer and philosopher, and a native of the city of Samos; but at what period he flourished is not certain. It must have been before the time of Archimedes, as some parts of his writings and opinions are cited by that author. He held the doctrine of Pythagoras as to the system of the world. He maintained that the sun and stars were fixed in the heavens, and that the earth moved in a circle about the sun at the same time that it revolved about its own axis. He determined that the annual orbit of the earth, compared with the distance of the fixed stars, is but as a point. For these, his opinions, which time has proved to be undeniably true, he was censured by his contemporaries, some of whom went about to prove that Greece ought to have punished Aristarchus for his heresy. This philosopher invented a peculiar kind of sun-dial, mentioned by Vitruvius. There is now extant only a treatise upon the magnitude and distance of the sun and moon, which was trans

lated into Latin, and commented upon, by Commandine, who published it, with Pappus's explanations, in 1572.

PAINTING.

CIDEAS, an ancient Greek painter, contemporary with Euphranor, about the hundred and fourth olympiad. Amongst other works, he painted a picture of the Argonauts, which was afterwards bought by Hortensius for the sum of forty-four thousand sesterces, about fourteen thousand four hundred florins, and placed it in a small temple, built on purpose to receive it, in his villa at Tivoli. It was afterwards removed by M. Agrippa to the portico of Neptune, which he had fabricated in Rome.

EUPHRANOR, an eminent painter and sculptor, who flourished about B. C. 362. He wrote several volumes on symmetry and the art of colouring, and was the first who signalized himself by representing the majesty of heroes.

CTESİDEMO, an ancient painter, who is celebrated for his picture representing Hercules taking Echalia, a city of Boeotia; and for another of Laodæmia ascending the funeral pile.

PAUSIAS, a famous ancient painter, the inventor of ENCAUSTIC PAINTING, was a native of Sicyon. He was a disciple of Pamphylus, and flourished about B. C. 352. He drew a beautiful picture of his mistress, Glycere, for which Lucullus gave two talents. The Sicyonians being obliged to sell his pictures, to clear an enormous debt, they were all purchased by M. Scaurus, the Roman.

PAMPHYLUS, a celebrated painter of Macedonia, in the age of Philip II. He was founder of the school for painting at Sicyon; and he made a law, which was observed, not only in Sicyon, but all over Greece, that none but the children of noble and dignified persons should be permitted to learn painting. Apelles was one of his pupils.

TIMANTHUS, a famous painter of Sicyon, who lived in the reign of Philip II. of Macedon. His painting of the Sacrifice of Iphigenia was much and justly admired, wherein he represented all the spectators in extreme grief, but covered the face of Agamemnon, as esteeming the father's grief impossible to be expressed by the pencil. This painting carried off the prize.

NICIAS, a celebrated painter of Athens, who flourished about B. C. 322, and was universally extolled for the great variety and noble choice of his subject; the force and relievo of his figures; his skill in the distribution of the lights and shades; and his dexterity in representing all sorts of four

footed animals, beyond any master of his time. His most celebrated piece was that of Tartarus, or Hell, as described by Homer, for which king Ptolemy I. offered him sixty talents, or eleven thousand two hundred and fifty pounds, which he refused, and generously presented it to his own country. He was much esteemed likewise by his contemporaries, for his excellent talent in sculpture.

APELLES, an ancient Greek painter, born in the isle of Cos, and lived in the time of Alexander the Great. He is called the prince of painters, and was so highly esteemed by Alexander, that he would not permit any other person to paint his portrait; and gave him Campaspa, one of his mistresses, with whom Apelles fell in love, while taking her likeness, for a wife. The following reply of the painter to Alexander, or, according to some authors, to a Persian nobleman, who often visited his study, contains a sentiment so apposite as to deserve transcribing. The great man, endeavouring to display his taste on the subject of Apelles's art, and talking very absurdly on the subject, the indignant painter replied, "While you were silent, the boys in my study were lost in admiration of your magnificence; but the moment you began to talk of what you did not understand, they laughed."

CTESILOCO, the scholar of Apelles, was known by his picture representing the birth of the Egyptian Bacchus, where Jupiter seemed to moan effeminately in the midst of the goddesses, assisting at the labour. Pliny speaks of this painting as highly indecent.

PROTOGENES, a celebrated ancient painter, born at Caunas, a city of Caria, subject to the Rhodians, who flourished about B. Č. 300. He was at first employed in the lowest use of the brush, as in painting ships, &c.; but soon acquired the highest fame for historical pieces. His most celebrated piece was Jalysus, the founder of Jalysus, a city of Rhodes, which saved Rhodes from destruction; for Demetrius Poliorcetes, who intended to burn the town, raised the siege rather than risk the loss of so valuable a painting. Apelles did great justice to his merits; for he gave him fifty talents (about ten thousand pounds) for one picture, which the Rhodians purchased back from him at a still higher price. He lived very abstemiously.

ARISTIDES, a painter, contemporary with Apelles, flourished at Thebes about B. C. 288. He was the first, according to Pliny, who expressed character and passion, the human mind, and its several emotions; but he was not remarkable for softness of colouring. His most celebrated picture was of an infant, on the taking of a town, at the mother's breast, who is wounded and expiring. The sensations of the mother were clearly marked; and her fear lest the child, upon failure of the