flutes at Athens, may be conceived from a circumstance mentioned by Plutarch, in his life of the orator. His father, says, he, acquired wealth sufficient by his business, not only to educate his children in a liberal manner, but also to bear one of the heaviest burdens to which an Athenian citizen was liable, of furnishing a choir or chorus for his tribe, or ward, at festivals and religious ceremonies.

MATHEMATICS, ASTRONOMY, &c.

MENELAUS, a celebrated mathematician, who flourished under the reign of the emperor Trajan, was of Grecian extraction, but a native of Alexandria. He is called by Ptolemy a geometrician, as having made astronomical observations at Rome, in the year 98, of the Christian era. He is supposed to have been the Menelaus referred to by Plutarch, in his dialogue, "De Facie quæ in orbe Lunæ apparet." He was author of " three books on Spherics," which have come down to the present times, through the medium of the Arabian lanA Latin version of this work was published at Paris, by father Mersenue, in 1664, with corrections, restorations, and additional illustrative propositions.

AQUILA, a mathematician of Pontus, who was employed by Adrian to rebuild Jerusalem, where he embraced the Christian religion, and was baptised; but being excommunicated for practising astrology, he turned Jew. He translated the Old Testament into Greek, of which only a few fragments remain. HELIODORUS, an eminent mathematician of Larissa in

Greece.

AGRIPPA, an astronomer, was a native of Bithynia. He was a very accurate observer.

THEON, a mathematician of the Platonic school, was a native of Smyrna, and flourished under the emperor Trajan and Adrian. His mathematical treatises are said to have been written for the purpose of elucidating the philosophy of Plato, and his discourses, treating of geometry, arithmetic, music, astronomy, and the harmony of the universe, may serve to throw some light upon the Pythagorean system.

BABILIUS, an astrologer in the time of Nero, who advised the emperor to put all the leading men of Rome to death, that he might avert the danger which seemed to hang over his head, from the appearance of a hairy comet. Nero strictly followed

this advice.

CLAUDIUS PTOLEMY, a very celebrated geographer, astronomer and mathematician, among the ancients, was born at Pelusium, in Egypt, about the seventieth year of the Christian era, and died, it has been said, in the seventy-eighth year

of his age, and in the year of Christ, 147. He taught astronomy at Alexandria, in Egypt, where he made many astronomical observations, and composed his other works. It is certain that he flourished in the reigns of Marcus Antoninus and Adrian, for it is noted in his Canon, that Antoninus Pius reigned twenty-three years, which shows that he himself survived him; he also tells us in one place, that he made a great many observations upon the fixed stars, at Alexandria, in the second year of Antoninus Pius; and in another, that he observed an eclipse of the moon in the ninth year of Adrian; from which it is reasonable to conclude, that this astronomer's observations upon the heavens, were many of them made between the year 125 and 140. Ptolemy has always been reckoned the prince of astronomers, among the ancients, and in his works has left us an entire body of that science. He has preserved and transmitted to us the observations, and principal discoveries of the ancients, and at the same time augmented and enriched them with his own. He corrected Hipparchus's catalogue of the fixed stars; and formed tables, by which the motions of the sun, moon, and planets might be calculated and regulated. He was, indeed, the first who collected the scattered and detached observations of the ancients, and digested them into a system, which he set forth in his "sive Magna Constructio," divided into thirteen books. He adopts and exhibits here, the ancient system of the world, which placed the earth in the centre of the universe; and this has been called, from him, the Ptolemaic system, to distinguish it from those of Copernicus and Tycho Brahe.

About the year 78, this work was translated by the Arabians into their language, in which it was called "Almagestum," by order of one of their kings; and from Arabic into Latin, about 1230, by the encouragement of the emperor Frederic II. There were also other versions from the Arabic into Latin; and a manuscript of one, done by Girardus Cremonensis, who flourished about the middle of the fourteenth century; Fabricius says, it is still extant, in the library of All Souls' College, in Oxford. The Greek text of this work, began to be read in Europe in the fifteenth century, and was first published by Simon Grynæus, at Basil, 1538, in folio, with the eleven books of Commentaries by Theon, who flourished at Alexandria, in the reign of the Elder Theodosius. In 1541, it was reprinted at Basil, with a Latin version, by George Trapizond; and again at the same place in 1551, with the addition of other works of Ptolemy, and Latin versions by Camerarius. We learn from Kepler, that this last edition was used by Tycho Brahe.

Of this principal work of the ancient astronomers, it may not be improper to give here a more particular account. In general it may be observed, that the work is founded upon the hy

pothesis of the earth, being at rest in the centre of the universe, and that the heavenly bodies, the stars and planets, all move round it in solid orbs, whose motions are all directed by one, which Ptolemy calls the primum mobile, or first mover, of which he discourses at large. But, to be more particular, this great work is divided into thirteen books.

In the first book, Ptolemy shows that the earth is in the centre of those orbs, and of the universe itself, as he understood it; he represents the earth as of a spherical figure and but as a point in comparison of the rest of the heavenly bodies; he treats concerning the several circles of the earth and their distances from the equator; as also of the right and oblique ascension of the heavenly bodies in a right sphere.

In the second book, he treats of the habitable parts of the earth, and of the elevation of the pole in an oblique sphere, and the various angles which the several circles make with the horizon, according to the different latitude of places; also of the phenomena of the heavenly bodies depending on the same.

In the third book he treats of the quantity of the year, and of the unequal motion of the sun through the zodiac; he here gives the method of computing the motion of the sun, with tables of the same; and likewise treats of the inequality of days and nights.

In the fourth book he treats of the lunar motions, and their various phenomena; he gives tables for finding the moon's mean motions, with her latitude and longitude; he discourses largely concerning lunar epicycles; and by comparing the times of a great number of eclipses, mentioned by Hipparchus, Calippus, and others, he has computed the places of the sun and moon, according to their mean motions, from the first year of Nabonassar, king of Egypt, to his own time.

In the fifth book he treats of the instrument called the astrolabe; he treats also of the eccentricity of the lunar orbit, and the inequality of the moon's motion according to her distance from the sun; he also gives tables, and an universal canon for the inequality of the lunar motions; he then treats of the different aspects or phases of the moon, and gives a computation of the diameter of the sun and moon, with the magnitude of the sun, moon, and earth, compared together; he states also the different measures of the distance of the sun and moon, according as they are determined by ancient mathematicians and philosophers.

In the sixth Book he treats of the conjunctions and oppositions of the sun and moon, with tables for computing the mean time when they happen; of the boundaries of solar and lunar eclipses; of the tables and methods of computing the eclipses of the sun and moon, with many other particulars.

In the seventh Book he treats of the fixed stars, and shows

the method of describing them in their various constellations, on the surface of an artificial sphere or globe; he rectifies the places of the stars to his own time, and shows how different those places were then, from what they had been in the times of Timocharis, Hipparchus, Aristillus, Colippus, and others, he then lays down a catalogue of the stars in each of the northern constellations, with their latitude, longitude, and magnitude.

In the eighth Book he gives a like catalogue of the stars in the constellations of the southern hemisphere, and in the twelve signs or constellations of the zodiac. This is the first catalogue of the stars now extant, and forms the most valuable part of Ptolemy's works. He then treats of the galaxy, or milky-way; also of the planetary aspects, with the rising and setting of the sun, moon, and stars.

In the ninth Book he treats of the order of the sun, moon, and planets, with the periodical revolutions of the five planets; then he gives tables of the mean motions, beginning with the theory of Mercury, and showing its various phenomena with respect to the earth.

The tenth Book begins with the theory of the planet Venus, treating of its greatest distance from the sun; of its epicycle, eccentricity, and periodical motions; it then treats of the same particulars in the planet Mars.

The eleventh Book treats of the same circumstances in the theory of the planets Jupiter and Saturn. It also corrects all the planetary motions, from observations made from the time of Nabonassar to his own.

The twelfth book treats of the retrogressive motion of the several planets, giving also tables of their stations, and of the greatest distances of Venus and Mercury from the sun.

The thirteenth Book treats of the several hypotheses of the latitude of the five planets; of the greatest latitude or inclination of the orbits of the five planets which are computed and disposed in tables; of the rising and setting of the planets, with tables of them. Then follows a conclusion or winding up of the whole work.

This great work of Ptolemy will always be valuable on account of the observations he gives of the places of the stars and planets in former times, and according to ancient philosophers and astronomers that were then extant; but principally on account of the large and curious catalogue of the stars, which being compared with their places at present, we thence deduce the true quantity of their slow progressive motion according to the order of the signs, or of the precession of the equinoxes.

Another great and important work of Ptolemy, was his Geography, in seven Books, in which, with his usual sagacity, he searches out and marks the situation of places according to their latitudes and longitudes; and he was the first that did so.

Though this work must needs fall far short of perfection, through the want of necessary observations, yet it is of considerable merit, and has been very useful to modern geographers. Cellarius indeed suspects, and he was a very competent judge, that Ptolemy did not use all the care and application which the nature of his works required; and his reason is, that the author delivers himself with the same fluency and appearance of certainty concerning things and places at the remotest distances, which it was impossible he could know any thing of, that he does concerning those which lay the nearest to him, and fall the most under his cognizance. Salmasius had before made some remarks to the same purpose upon this work, which was first published by himself at Basil, in 1533, in quarto; afterwards with a Latin version, and notes, by Gerard Mercator, at Amsterdam, 1605; which last edition was reprinted at the same place, 1618, in folio, with neat geographical tables by Bertices.

Other works of Ptolemy, though less considerable than these two, are still extant, as "Fabri quatuor de judiciis Astrorum," upon the first two books of which Cardan wrote a commentary, "Fructus librorum suorum," a kind of supplement to the former work, "Recentio Chronologica Regum;" this, with another work of Ptolemy, "De Hypothesibus Planetarum," was published in 1620, 4to. by John Bainbridge, the Savilian Professor of Astronomy at Oxford, and Scaliger, Palavius, Dodwell, and the other chronological writers have made great use of it. "Apparentia Stellarum Inerrantium;" this was published at Paris by Petavius, with a Latin version, 1630, in folio; but from a mutilated copy, the defects of which have since been supplied from a perfect one, which Sir Henry Saville had communicated to archbishop Usher, by Fabricius, in the third volume of his Bibliotheca Græca, "Elementarum Harmonicarum libri tres," published in Greek and Latin, with a commentary, by Porphyry, the philosopher, by Dr. Wallis, at Oxford, 1682, in 4to.; and afterwards reprinted there, and inserted in the third volume of Wallis's works, 1699, in folio.

Marbillon exhibits, in his German Travels, an effigy of Ptolemy looking at the stars through an optical tube; which effigy, he says, he found in a manuscript of the thirteenth century, made by Conradus, a monk. Hence, some have fancied, that the use of the telescope was known to Conradus. But this is only matter of mere conjecture, there being no facts or testimonies, nor even probabilities, to support such an opinion.

It is likely that the tube was nothing more than a plain open one, employed to strengthen and defend the eyesight, when looking at particular stars, by excluding adventitious rays from other stars and objects, a contrivance which no observer of the heavens can ever be supposed to have been without.