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his successors, Anaximander, Anaximenes, and Anaxagoras; but most especially by , Pythagoras, who having resided a long time in Egypt, &c. brought thence the learning of the Egyptians, taught the same in Greece and Italy, and founded the sect of the Pythagoreans. He taught that the sun was in the centre of the universe; that the earth was round, and people had antipodes; that the moon reflected the rays of the sus, and was inhabited like the earth; that comets were a kind of wandering stars, disappearing in the farther parts of their orbits; that the white colour of the milky way was owing to the united brightness of a great multitude of small stars; and he supposed that the distances of the moon and planets from the earth, were in certain harmonic proportions to one another. Philolaus, a Pythagorean, who flourished about 450 years before Christ, asserted the annual motion of the earth about the sun; and not long after, the diurnal motion of the earth, on its own axis, was taught by Hicetus a Syracusian. About the same time, Meton and Euctemon flourished at Athens, where they observed the summer solstice 432 years before Christ; and observed the risings and settings of the stars, and to what seasons they answered. Meton also invented the cycle of nineteen years, which still bears his name. Eratosthenes, who was born at Cyrene in the year 271 before Christ, measured the circumference of the earth; and being invited from Athens to Alexandria, by Ptolemy Euergetes, and made keeper of the royal library there, he set up for that prince those armillary spheres, which Hipparchus and Ptolemy afterwards employed so successfully in observing the heavens. He also determined the distance between the tropics to be } of the whole meridian circle,

which makes the obliquity of the ecliptic, in his time, to be 23° 51%. The celebrated Archimedes also cultivated astronomy, as well as geometry and mechanics; and constructed a kind of planetarium, or orrery, to represent the pheuomena

. motions of the heavenly bo. 16se

Hipparchus, who flourished about 140 years before Christ, was the first who applied himself to the study of every part of this science; and, as we are informed by Ptolemy, made great improvements in it: he discovered that the orbits of the planets are eccentric, that the moon moved slower in the apogee than in her perigee, and that there was a motion of anticipation of the moon’s nodes; he constructed tables of the motions of the sun and moon, collected accounts of such eclipses, &c. as had been made by the Egyptians and Chaldeans, and calculated all that were to happen for 600 years to come: he discovered that the fixed stars changed their places, having a slow motion of their own from west to east : he corrected the Calippic period, and pointed out some errors in the method of Erastosthenes for measuring the circumference of the earth; he computed the sun’s distance more accurately than any of his predecessors: but his chief work is a catalogue which he made of the fixed stars, to the number of 1022, with their longitudes and latitudes, and apparent magnitudes; which, with most of his other observations, are preserved by Ptolemy in his Almagest.

But little progress was made in astronomy from the time of Hipparchus to that of Ptolemy, who was born at Pelusium in Egypt, in the first century of the Christian era, and who made the greatest part of his observations at the celebrated school of Alexandria in that country. Profiting by the observations of Hipparchus, and other ancient astronomers, he formed a system of his own, which, though erroneous, was followed for many ages by all nations: he compiled the Almagest, which contained the observations and collections of Hipparchus, and others of his predecessors in astronomy; a performance which will ever be valuable to the professors of that science. This work was preserved from the onflagration of the Alex andrian #. and translated out of Greek into Arabic, in the year 827, and again into Latin in 1230. From the year 800 till the begin. ning of the fourteenth century, the western parts of Europe were immersed in ignorance and barbarity, while the Arabians, profiting by the books they had preserved from the wreck of the Alexandrian Library, cultivated and improved all the sciences, and particularly astronomy, in which they had many able professors and authors; the caliph, Al Manor, first introduced a taste for the sciences into his empire; and his grandson, Al Mamon, who ascended the throne in 814, was a great encourager and improver of the sciences, and especially of astronomy. Having constructed proper instruments, he made many observations; determined the obliquity of the ecliptic to be 23° 35' ; and under his auspices, a degree of the circle of the earth was measured a second time, in the plain of Singar, on the border of the Red Sea. The settlement of the Moors in Spain introduced the sciences into Europe; from , which time they have continued to improve, and , to be communicated from one people to another, to the present time, when astronomy and all the sciences have arrived at a very eminent degree of perfection. The Emperor Frederick II. about 1230, first began to encourage learning, by restoring some decayed universities and founding a new one in Vienna: he also caused the works of Aristotle, and Ptolemy's Almagest, to be translated into Latin; and from the translation of this work we may date the revival of astronomy in Europe. Two years after this, John de Sacro Bosco, or John of Halifax, compiled from Ptolemy, Albategnius, Alferganus, and other Arabic astronomers, his work “De Sphaera,” which was held in the greatest estimation for 300 years after, and was honoured with commentaries by Clavius and other learned men. In 1240, Alphonso, King of Castile, not only cultivated astronomy himself, but greatly encouraged others; and by the assistance of several learned men he

corrected the tables of Ptolemy, and composed those which were denominated from him the Alphonsine Tables. About the sary- time also Roger Bacon, an English monk, wrote several tracts relative to astronomy, particularly of the lunar aspects, the solar rays, and the places of the fixed stars. And about the year 1270, Viteilo, a Polander, composed a treatise on optics, in which he showed the use of refraction in astronomy. Little other improvement was made in this science till the time of Purbach, who was born in 1423. He composed new tables of sines for every ten minutes, making the radius sixty, with four ciphers annexed. He constructed spheres and globes, and wrote several astronomical tracts, as a commentary on Ptolemy's Almagest; some ureatises on arithmetic and dialling, with tables for various climates; new tables of the fixed stars, reduced to the middle of that century; and he corrected the tables of the planets, making new equations to them where the Alphonsine tables were erroneous. He had just finished a theory of the planets, when he died in 1462, being only thirty-nine years of age. After Purbach, the subject of astronomy was cultivated by John Muller, commonly called Regiomontanus; by Bernard Walther, and John Werner; Copernicus was the next who made any considerable figure in astronomy. He very early conceived doubts of the Ptolemaic system, and entertained notions about the true one, which he gradually improved by a series of astronomical observations, and the contemplation of former authors. By these he formed new tables, and completed his work in the year 1530, containing these, and a renovation of the true system of the universe, in which all the planets are considered as revolv. ing about the sun, as their common Centre. After the death of Copernicus, the science and practice of astronomy were greatly improved by Schoner, Nonius, Appian, Gemma Frisius, Byrgius, &c.; and about the year 1561, William IV. Land

grave of Hesse-Cassel, made a great number of observations, published by Snelius in 1618, and preferred y Hevelius to those of Tycho Brahe. From these observations he formed a catalogue of 400 stars, with their latitudes and longitudes, and adapted them to the beginning of the year 1593. Tycho Brahe, a Dane, began his observations about the same time with the Landgrave of Hesse, and observed the great conjunction of Jupiter and Saturn: but finding the usual instruments very inaccurate, he constructed many others, much larger and more exact. In 1571, he discovered a new star in the chair of Cassiopeia; which induced him, like Hipparchus on a similar occasion, to make a new catalogue of the stars; which he composed to the number of 777, and adapted their places to the year 1600. Tycho invented a sysiem to account for the planetary motions; but he is more to be noted on account of his accurate observations, which tended much to the discovery of the real nature of the planetary orbits. While Tycho resided at Prague, with the emperor, he prevailed on Repler to leave the University of Glatz and to come to him ; and Tycho dying in 1601, Kepler enjoyed the title of mathematician to the emperor; who ordered him to finish the tables of Tycho Brahe, which he published in 1627, under the title of Rodolphine. He died about the year 1630, at Ratisbon, where he was soliciting the arrears of his pension. From his own observations, and those of Tycho, Kepler discovered several of the true laws of nature, by which the motions of the celestial bodies are regulated. He discovered that all the planets revolve about the sun, not in circular but in elliptical orbits, having the sun in one of the foci of the ellipse; that their motions are not equable, but varying quicker or slower, as they are near to the sun, or farther from him ; that the areas described by the variable line drawn from the planet to the sun are equal in equal times, and always proportional to the times % describing them. He also

discovered, by trials, that the cubes of the distances of the planets from the sun were in the same proportion as the squares of their periodical times of revolution. By observations also on comets, he concluded that they are freely carried about among the orbits of the planets, in paths that are nearly rectilinear; but which he could not then determine. See Dr. Small on the discoveries of Kepler. About this time much was done by Wright, Napier, Bayer, Mercator, Maurolycus, Magnius, Homelius, Schulter, Steven, Galileo, Thomas and Leonard Digges, John Dee, Robert Hood, Harriot, &c. The beginning of the seventeenth century was particularly distinguished by the invention of telescopes, and the application of them to the purposes of astronomy. Hevelius, from his own curious observations, furnished a catalogue of fixed stars, much more complete than Tycho's. Huygens and Cas: sini discovered the satellites of Saturn and his ring. And Gassendus, Horrox, Bullialdus, Ward, Ricciolus, Gascoign, &c. each contributed very considerably to the improvement of astronomy. Newton demonstrated, from physical consideration, the great law that regulates all the heavenly notions, sets bounds to the planetary orbs, determined their greatest excursions from the sun, and their nearest approaches to him. It was he who first discovered whence arose that constant and regular proportion, observed by both primary and secondary planets, in their circulation round their central Lodies; and their distances compared with their periods. He also gave a new theory of the moon, which accounts for all her." inequalities from the laws of gravity and mechanics. Mr. Flamstead was appointed the first astronomer royal at Greenwich in 1675. He observed, for forty-four years, all the celestial phenomena, the sun, moon, planets, and fixed stars; of all which he gave an improved theory and tables. Cassini also, the first French astronomer royal, very much distinguished himself, making many observations on the sun, moon, planets, and comets, and greatly improved the elements of their motions. He also erected the gnomon, and drew the celebrated meridian line in the church of Petronia, at Bologna. In 1719, Mr. Flamstead was succeeded by Dr. Halley, who had been sent, at the early age of 21, to the island of St. Helena, to observe the southern stars, a catalogue of which he published in 1679; and, a few years afterward, he gave to the public his “Synopsis Astronomiae Cometicae,” in which he ventured to predict the return of a comet in 1758, or 1759. He was the first who discovered the acceleration of the moon’s mean motion ; and is the author of a very ingenious method for finding her parallax, by three observed places of a solar eclipse: he also showed the use that might be made of the approaching transit of Venus, in 1761, in determining the distance of the sun from the earth ; and recommended the method of determining the longitude by the moon’s distance from the sun and certain fixed stars, which has since been carried into execution at the instance of the late Astronomer Royal., Dr. Halley also composed tables of the sun, moon, and planets, with which he compared the observations he made of the moon at Greenwich, amounting to near 1500, and noticed the differences. About this time, an attempt was Imade in France to measure a degree of the earth, which was the occasion of a warm dispute concerning its figure. M. Cassini concluded, from the measurement of Picard, that it was an oblong spheroid ; but Newton, from a conside- ration of the laws of gravity, and the diurnal motion of the earth, had determined its figure to be that of an oblate spheroid, flattened at the poles, and protuberant at the equator. To determine this point, Louis XV. ordered two degrees of the meridian to be measured ; one under or near the equator, and the other as mear as possible to the pole: the result of this arduous undertaking was a confirmausoof Newton's investigation.

It was found, by those who went to the south, that the attraction of the mountains of Peru had a sensible effect on the plumb-lines of their large instruments, which af. forded an experimental proof of the Newtonian doctrine of gravitation, that has since been completely verified by the observations of Dr. Maskelyne, made on the moun. tain Schehallien, in Scotland. On the death of Dr. Halley, in 1742, he was succeeded by Dr. Bradley, who has rendered himself celebrated by two of the finest discoveries that have ever been made in astronomy, the aberration of light, and the nutation of the earth's axis. Among other things he also formed new and accurate tables of the motions of Jupiter’s satellites, as well as the most correct table of refractions yet extant. Also, with a large transit instrument, and a new mural quadrant of eight feet radius, constructed by Bird, in 1750 he made an immense number of observations for settling the places of all the stars in the British catalogue, together with near 150 places of the moon, the greater part of which he compared with Mayer's tables. Dr. Bradley was succeeded in 1762, in his office of astronomer royal, by Mr. Bliss; but who died in 1765, and was succeeded by Nevil Maskelyne, D.D. who rendered very considerable services to the science, by his publication of the “Nautical Almamac,” the “Requisite Tables,” &c.; and more particularly by his great assiduity and zeal, in bringing the lunar method of determining the longitude at sea into general practice. In the mean time, many other eminent mathematicians were assiduously employed in endeavouring to promote the science of astronomy. Amongst these may be particularly distinguished, Clair. aut, d’Alembert, Euler, Simpson, Walmsley, Mayer, de la Callie, Manfredi, Lambert, &c. Such was the state of astronomy when Dr. Herschel, by augmenting the powers of telescopes be yond the most sanguine expectations, opened a scene altogether unlooked for, by the discovery of a new planet, 13th March, 1781, the Georgium Sidus, or Uranus. On the 1st of January, 1801, another new planet was discovered between Mars and Jupiter, by M. Piazzi, of Palermo, which is named Ceres; and since this time three others have been observed, revolving also between Mars and Jupiter, viz. Pallas, discovered by Dr. Olbers, March 28, 1802; Juno, first observed by Mr. Harding, at the observatory at Lilienthal, near Bremen, Sep. 1, 1804; and Wester, discovered by Dr. Olbers, 29th of March, 1807, being the second that we owe to this eminent astronomer. For the particular elements of these new planets, see the respective articles URANU's CE Res, PAL LAs, JUNO, and West ER. Hence it appears, that within a few years the number of planets in our system have been nearly doubled, and many other important and interesting discoveries have been made during the same period : yet it must be acknowledged, that we are still unacquainted with many particulars, and which therefore still remain to exercise the talents of modern astronomers. We have not yet determined the times of rotation, and the proper figures of some of the planets and their satellites; nor do we know, with sufficient precision, the masses of those bodies. The theory of their motions also consists in a series of approximations, of which the convergence depends both upon the perfection of the instruments and the progress of analysis, and which for that reason ought to acquire continually new degrees of exactness. ASTROSCOPE, an astronomical instrument, composed of two cones, on whose surfaces are exhibited the stars and constellations, by means of which they are both easily found in the heavens. ASYMPTOTE, a right line to which some curve continually approaches nearer, in such sort, that when they are both indefinitely produced, they are nearer together than by any assignable finite distance; or it may otherwise be conoldero,” a tangent to the curve,

when infinitely produced, or at an infinite distance. Two curves are also said to be asymptotical, when they, thus continually approach indefinitely to a coincidence : thus two parabolas, placed with their axis in the same right line, are assymptotes to each other. Of lines of the second kind, or curves of the first kind, that is, the conic sections, only the hyperbola has asymptotes, which are two in number. All curves of the second kind have at least one asymptote, but they may have three; and all curves of the third kind may have four asymptotes, and so on. The conchoid, cissoid, and logarithmic curve, though not geometrical curves, have each one asymptote; and the branch or leg of the curve that has an asymptote, is said to be of the hyperbolic kind. The nature of an asymptote is very difficult to be conceived, by persons who are not acquainted with the higher geometry: they cannot comprehend how two lines shon ld always continually approach each other, without the possibility of touching or coinciding; this mystery, however, may be elucidated, and the nature of these lines readily comprehended, by considering the generation of the conchoid of Nicomedes. See Conchoid. As YMPtot Es, by some are distinguished into various orders. The asymptote is said to be of the first order, when it coincides with the base of the curvilinear figure; of the 2d order, when it is a right line parallel to the base ; of the 3d order, when it is a right line oblique to the base; of the 4th order, when it is the common parabola, having its axis perpendicular to the base ; and, in general, of the n + 2 order, when it is a parabola whose ordinate is always as the n power of the base. The asymptote is oblique to the base, when the ratio of the first fluxion of the ordimate to the fluxion of the base, approaches to an assignable ratio, as its limit; but it is parallel to the base, or coincides, with it, when this limit is not *pable.

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