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nence in astronomical studies. C. Sulpitius Gallus is mentioned by Cicero as an indefatigable calculator of eclipses*; and he is known to have predicted an eclipse of the moon on the night preceding a decisive battle between the Romans and the king of Macedonia t. On this occasion his science may be said to have rendered his countrymen an essential service; for, from the wellknown superstition of the ancients, the Roman soldiery would have been much terrified by what was supposed to be an unfavourable omen. At the celebrated siege of Syracuse an unexpected eclipse of the moon deterred the Athenian commanders from commencing their march at the proper time, and caused eventually the destruction of a fine army. Besides Sulpitius Gallus, we find the names of one or two Romans, who seem to have written on astronomical subjects (among whom is Varro); but their works are lost, and we have no means of judging of the extent of their scientific acquirements. Perhaps Cicero himself ought to be quoted here, as he has translated into Latin verse the Phenomena of Aratus, a poem which has been already noticed. One of the books of this translation is still extant, containing a description of the celestial sphere, and in particular of the constellations of the zodiac. Nothing is to be found in this poem beyond the most elementary doctrines of astronomy: the same may be said of the astronomical poem of Manilius, the date of which is a little later.

Of the last-mentioned poem a small part is devoted to the description of the sphere; by far the greater part being occupied with astrological precepts. This superstition, the influence of which has been so long and so widely felt, and the traces of which are not yet extinct in Europe, is in all probability of Chaldæan origin. It seems to have been unknown in Greece before the conquests of Alexander; and, indeed, it is but justice to the astronomers of that country, to say that in general no traces of belief in astrology are to be found in their writings. It is true that there exists an astrological treatise attributed to Ptolemy, but it may be doubted whether it is really one of his productions.

Cato Major de Senectute, c. 49. V. Also Pliny, ii., 12.

+ V. Liv. Hist., xliv., c. 37.

Thucydid., vii., c. 50.

His great and very complete work the μεγάλη Σύνταξις contains nothing which could lead us to believe that he was infected with these ideas. At Rome, under Augustus, and the succeeding emperors, the city was inundated with Syrians, Chaldæans, and other natives of the East; and numerous passages in ancient authors show that a belief in judicial astrology was extremely prevalent. From this time, down to the seventeenth century, the whole of the civilized world in the West as well as the East was enslaved by this childish superstition, against which philosophy and religion seem to have combated in vain. It is humiliating to know that some of the great restorers of astronomy in Europe, were not superior to the follies of their age; and that even the bold and acute Kepler could dispute on the best manner of drawing up a scheme of nativity. Our posterity will, perhaps, be equally astonished to think that in the nineteenth century, in the country of Newton and Bradley, almanacks in general circulation should contain predictions founded on the aspect of the planets, and all the mummery of an art, the existence of which is a disgrace to any nation possessing claims to civilization, or even common sense. It is difficult to imagine that there can still be persons who believe that the distances between Jupiter and Saturn can influence the fate of empires, or that on the sign of the ecliptic which is just rising, at the moment of a man's birth, depend the principal events of his life. But vain and futile as is this pretended art, it has exercised too great an influence on the cultivation of astronomy to be passed over here without an allusion. There can be no doubt that an attachment to astrology was at least one of the reasons that induced the Arabs to study with so much ardour the phenomena of the heavens; and it is quite certain that the encouragement given at the revival of letters by many European princes to astronomy, was entirely owing to their wish to read the future by means of the stars.


But to return to the Romans. calendar, in the time of the republic, fell as has been already noticed, into great confusion. This, Julius Cæsart, who

Jampridem Syrus in Tiberim defluxit Orontes. -Juv. Sat. iii.

This sign was called the horoscope; a term famliar to most persons, though perhaps at this day few are acquainted with its exact meaning.

It appears from Pliny, vii., 25, that Cæsar was himself an observer, and had composed some

was a man of extraordinary knowledge and universal genius, endeavoured to correct, with the assistance of a Greek astronomer, named Sosigenes. At this time, Hipparchus had already shown that the length of the solar year was something less than 365 days and a quarter, and Sosigenes could not have been ignorant of this fact: but, in all probability, he considered the difference too small to be worth taking into account. Be the reasons what they may, he proposed a method of intercalation which, to be quite rigorous, supposes the solar year to be 365 days and a quarter; namely, he proposed to make the civil year of 365 days, and every fourth year to insert an additional day. The year in which this intercalation took place was called bissextile, because the additional day inserted, bore the designation of bis sexto calendas Martii; the day named sext. calend. Mart. (corresponding to our 28th of February) being repeated. It is easy to see that this intercalation, and in general the Roman form of year is the same as that now in use; but it has been found necessary to introduce some modifications, the nature of which will be explained in a subsequent part of this treatise. But without going further at present, it may be noticed that the tropical year, not having the value supposed by this method, but being in fact, at the time of Cæsar, about ten minutes shorter, at the end of about a century and a half, the beginning of the civil year would be a day behind that of the astronomical; and this difference would, of course, go on increasing. We shall see that this was in reality what took place, and that ultimately the error became pretty


The great division of the Roman empire under the sons of Theodosius, probably exercised considerable influence on the fate of letters and science. The Greek language, which for a long time had been familiar to the Romans, ceased to be cultivated in the West; and this circumstance is of some importance in the history of astronomy; for we have seen that this science was almost completely neglected in Italy: those who wished to cultivate it were necessarily obliged to have recourse to Greek authors. But, during the middle ages, the little learning that existed in Western Europe was confined entirely to a knowledge of the

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Latin language: the works of Ptolemy were a sealed book for the few learned men (if they may deserve the name) of those days. However, the conquests of the Arabs having brought them into immediate contact with the Gothic nations in Spain, they began to impart to their neighbours some of their zeal for science; and the works of Euclid and Ptolemy became known in Europe, through the means of Arabic translations. Gerbert, a man of great talent and very superior to the age in which he lived, found himself obliged to attend the Moorish universities in Spain, to acquire some knowledge of mathematics and astronomy, which it was impossible at that time to study in any Christian country. On his return to France, he composed several treatises, which show a knowledge of geometry remarkable for that time, and a considerable familiarity with the works of Euclid and Archimedes.

At a later period the example of Gerbert was imitated by an English monk named Adhelard, who for the sake of acquiring scientific knowledge, travelled in Spain and Egypt, and having become acquainted with Arabic, turned it to account, by translating from that language into Latin the Elements of Euclid. This appears to be the first translation of Euclid executed in the west; but it seems to have been little known, and has remained in manuscript till the present day. The translation of Euclid by Campanus, who lived about a century later, was the first that acquired any popularity; and all the early editions were printed from his text, which was like that of Adelhard, a translation from the Arabic, a language apparently

known to several of the literati of that

day, while they still remained in profound ignorance of Greek.

In the thirteenth century many symptoms of a reviving love for letters and science began to show themselves; and knowledge which had been hitherto confined in monasteries, now spread into cities and courts. The barbarous monarchs of the middle ages were succeeded by princes who cultivated and protected letters; and though it is to be feared that the encouragement given by some of them to astronomy, was founded on a superstitious belief in the influence of the stars, we may view with some indulgence a weakness which led to such beneficial effects. The emperor Frederick the Second, a prince distinguished as well by a very cultivated mind, as a

generous protection of learned men, deserves particular mention here, as to his encouragement we owe the first translation into Latin of the Almagest of Ptolemy. This translation it is to be noticed was made from the Arabic, (Greek being still unknown in the west,) and consequently was a good deal disfigured; the Mahometan writers by no means piquing themselves on a scrupulous adherence to the text of the authors they translate: but still the service thus rendered was important; and no doubt had a favourable influence on the progress of science. The writer* who had executed the translation of the Almagest, added a translation of the commentary of Geber on the same work, and of the treatise of Alhazen on twilight. But in this latter respect he seems to have been anticipated by Vitellion, a Pole, whose voluminous treatise on optics is little more than a translation of Alhazen.

To Alphonso X., king of Castile, astronomy owes still more than to Frederick; and his reign will always form a memorable epoch in the annals of that science. His situation in a country bordering on the Arabs, who then occupied the south of the Spanish Peninsula, was very favourable for collecting about him able astronomers, who were then only to be found at the Moorish universities. Of this he profited to draw to his court a number of learned men, whom he employed for four years in constructing new and complete tables; those of Ptolemy having become in the lapse of time quite insufficient. These tables, generally called the Alphonsine, cost the prince an immense sum; and if they fell short of the degree of perfection that might have been expected, it was not from any want of munificence and zeal. Their principal defect was the introduction of an inequality in the motion of the fixed stars in longitude, by which this motion appeared to be sometimes accelerated and sometimes retarded: as the equinoctial point was supposed to describe the circumference of a small circle, the centre of which moved along the ecliptic according to the ordinary law of preces sion. This pretended inequality, known by the name of the trepidation of the fixed stars, or the motion of the eighth sphere, has been already noticed in speaking of the Arabs. It seems to have originated in Greece; but it was cer

Gerard of Cremona.

fainly not admitted by Ptolemy, or the most judicious of the oriental astronomers. The introduction of it into the Alphonsine tables seems owing to the Jews, who had a large share in their formation; at least this may be conjectured from the numbers 7000 and 49,000 years, in which the small circle above-mentioned and the ecliptic were respectively described. These are cabalistic numbers for which the Jews from fanciful ideas felt great veneration; and, indeed, the astronomers of that nation seem to have been singularly attached to the doctrine of trepidation, since the time of Thebit-ben-Corah, unjustly accused of being the inventor of the system. But it reflects little credit on the Alphonsine astronomers, to have admitted an inequality founded on no observations, and rejected by every author of eminence.

It seems but reasonable to suppose that Alphonso, who protected so zealously astronomy, was himself versed in the science. Of this we have no direct proof, but there is on record a saying of his, which has been accused of impiety, though it would be fairer to regard it as an expression of the disgust caused to a sound judgment, by the complication of the Ptolemaic system. "Iad the Deity," said Alphonso, "consulted me at the creation of the universe, I could have given him some good advice." If this exclamation may be justly blamed as irreverent in its expression, it certainly conveys a condemnation of the theories of his time, and the monstrous combination of

Cycle and epicycle, orb on orb,

then generally received as the system of the world.

On comparing the Alphonsine tables with those of Ptolemy, we see how little progress astronomy had made in eleven centuries. Some ameliorations in the elements of the syntaxis, are perhaps more than counterbalanced by the introduction of the imaginary inequality called trepidation; which continued to disfigure the best tables as late as the time of the celebrated Copernicus. Nor to judge from the slowness with which physical science recovered from its long torpor, could any one have guessed at the rapid progress it was about to make in the sixteenth and subsequent centuries. The real restoration of astronomy in Europe can scarcely be placed earlier than two hundred years subsequent to the publication of the Alphonsine tables. At this time Pur

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bach, professor of astronomy at Vienna, undertook to ameliorate the hypotheses and tables then existing. He felt the necessity of beginning by making an accurate translation of Ptolemy, the want of which was very sensibly felt, though in addition to numerous translations from the Arabic, George of Trebizond had published one from the original Greek. This, however, was very faulty; nor was it in the power of Purbach to remedy, the defect, as he was ignorant both of the Greek and Arabic languages. His anxiety to acquire the former of these, induced him to accept an invitation made by Cardinal Bessarion, to visit Rome; but death prevented the accomplishment of this design, and the translation of Ptolemy was left to be performed by his pupil Regiomontanus.

Purbach's theory of the planets is in all essential points the same as that of Ptolemy; but he has unfortunately introduced into his tables the imaginary trepidation of the fixed stars we have just spoken of. The most considerable service that he has rendered to science, was by calculating a table of trigono metrical sines, from ten to ten minutes throughout the quadrant, for a radius of 600,000 parts. Ptolemy had employed a sexagesimal division of the radius, which was singularly inconvenient for arithmetical computations; the decimal division introduced by Purbach was an important improvement.

The design entertained by Purbach of making a new translation of Ptolemy's great work, was executed by his pupil and successor John Müller of Königsberg, commonly called Regiomontanus*. He added to this a commentary, containing a number of problems, likely to be useful in astronomical calculations: and made very considerable ameliorations in the solution of plane and spherical triangles. Regiomontanus enjoyed for a long time the reputation of having been the first to introduce tangents into trigonometry. But we have seen that this had been previously done by the Arabs: however, he was certainly the first in Europe to calculate a table of tangents, which he did for every degree of the quadrant. Nor is this the only benefit of the kind that we owe him: he extended the table of sines calculated by Purbach for every ten minutes, to every minute of the quadrant, for a

• Regiomontanus means of Königsberg,' or 'King's Hill.'

radius of 1,000,000 parts; which was a second important improvement added to that of his predecessor. Indeed, the decimal division of the radius has been found so convenient, that it remains unaltered to the present day. It is, perhaps, to be regretted that he did not extend the decimal division to the quadrantal arc itself: such a reform, which, however useful, it has been found impossible to effectuate in the present day, might have been practicable in the infancy of astronomy. The great reputation of Regiomontanus induced Pope Sixtus IV. to request his assistance in the reformation of the calendar, an operation of which we shall say more shortly. For this purpose he proceeded to Rome, but had not been long engaged in the prosecution of this important work, when he was carried off either by an epidemic distemper, or as some have said, by poison, administered by the sons of George of Trebizond, to avenge the criticisms on the translation of Ptolemy, executed by their father.

The labours of Purbach and Regiomontanus form the link between modern astronomy and that of the middle ages. The end of the fifteenth century was not distinguished by any great discoveries; yet it is easy to see in the rise of a spirit of inquiry and investigation, the dawn of that light which was about to illuminate Europe with so much brilliancy. No doubt the progress of this spirit was at first slow and uncertain; but it may fairly be traced back as far as those who felt the necessity of establishing their theories upon observation alone, and who aspired to something beyond commenting Ptolemy. Among those who contributed most by assiduous observation was Bernard Walther, a rich citizen of Nuremberg; one of the earliest and certainly of the most zealous of modern astronomers. His observations, interesting on many accounts, are particularly remarkable for having been made with clocks regulated by wheels; which seem to have answered tolerably well for the division of time. We have seen what were the various and unsatisfactory contrivances of the Greeks and Arabs to accomplish this important point. Walther was one of the first, it appears, of the moderns who recognized the existence of refraction; of which it is true he formed a very incomplete idea; supposing it to exist only near the horizon. Albazen and Vitellion had both treated of

this subject, but Walther affirms that his discovery was made previously to becoming acquainted with the works of either of these philosophers.



THE limits of this treatise will not allow us to notice various meritorious astronomers of the early part of the sixteenth century, whose names are now little known, and whose writings can offer little interest. We shall proceed at once to a work which was destined to change forever the face of astronomical sciencethe Revolutions of Copernicus*. Struck with the complication of the Ptolemaic theory, and the weakness of the arguments by which it was supported, this great man had passed nearly forty years of his life in meditating on the true system of the world. He was led irresistibly to the conclusion that the system taught in Greece by the Pythagoreans, of the earth's motion on its own axis, and round the sun, was the only one consistent with the observed phenomena and the simplicity of nature. But to make this very interesting and important question fully understood, it will be better to refer to the opinions of preceding philosophers on the subject.

From a very early age in Greece, it had generally been recognized that the earth was of a spherical figure, and upon this point there was not, and indeed there scarcely could be, any difference of opinion. But this fact once conceded, the question naturally arose, was it suspended motionless in the universe, the centre of the heavenly motions, or did it of necessity, as some argued from the supposed impossibility of its remaining unsupported, revolve round another body? It is singular enough, that the philosophers who first taught in Greece the rudiments of science, generally advocated what we now know unquestionably to be the real system of the world, the revolution of the earth round the sun. This was taught by the followers of Pythagoras, and by those of Thales: and particularly by Philolaus and Anaximander. If we consider how contrary this theory apparently is to the evidence of the senses, and how unlikely to be one of the first truths discovered in the infancy of science,-if we consider the prediction of an eclipse by Thales (a most extraordinary fact for this early

A native of Thorn in Polish Prussia, was born in the year 1473; died in 1543,

age), his Phoenician origin, the travels of Pythagoras in the east,-if we compare these circumstances with the doctrines of Aryabhatta in India,-little doubt will remain that the motion of the earth was borrowed, with other truths, from one of the oriental nations. Unfortunately we know not much of the arguments by which these doctrines were supported in Greece; though we possess in sufficient detail the nugatory reasons urged against them by Aristotle, and in later times by Ptolemy*.

However, it was not difficult for Copernicus to conceive all the reasons which led the Pythagoreans to the doctrine of the earth's motion; and these he has expounded with singular judgment. It would be too much to expect him to be always superior to the erroneous physical ideas of his age; but his argument is in general equally distinguished by sound sense and moderation. He begins by remarking that if we suppose the distance from the earth to the fixed stars to be infinitely great, compared with its distance from the centre of the universe; but, on the contrary, this latter distance to be very considerable when compared with the orbits of the planets; all the phenomena may be just as well explained by supposing the earth to revolve on its axis from west to east in twenty-four hours, and to have besides this a motion of translation in the heavens; as by supposing the earth to be immoveable while the fixed stars and planets revolve round it in their different spherest. That the earth itself was a point compared with the distance of the heavens (meaning the fixed stars) was a point conceded on all sides; but as Copernicus very well remarks, it by no means follows from this that the earth is at rest in the centre of the universe: on the contrary, it seems the more extraordinary that such a vast circumference should revolve in twentyfour hours, rather than this infinitesimally small part of it, the earth*.

He then proceeds to consider the reasons urged by ancient philosophers against the earth's motion. The first argument he combats is a very futile and fanciful one urged by Aristotle. The earth according to him was the heaviest of the elements, and all heavy bodies tended to

Plutarch (Quæst. Plat.) tells us that the system of the earth's motion, which was proposed as an bypothesis by Aristarchus, was proved by Seleucus; but of the nature of this proof we are in ignorance. † Revolutionum, lib. i. cap. 5, Revol, lib. i. cap. 6,

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