riches having led the national institute of France, to wish for an inspection of the Leyden manuscript, the Batavian Republic has entrusted it to it's care, and transmitted it through the hands of it's ambassador at Paris. It has been carefully examined; but no observations, except those I have mentioned, have been found in it. It gives us none of the information, that was hoped for, respecting the instruments of the arabs, and their manner of observing: but it has afforded some interesting corrections of the fragment, of which Delisle had obtained a copy, at present in the possession of citizen Messire, member of the national institute; and of which citizen Caussin, professor of arabic in the national college of France, has made a translation, now printing with the original on the opposite page. Ibn Ionis likewise constructed some astronomical tables, which were long celebrated and useful in the East.

The arabs established in Spain, of which they had Conquered the greater part in the eighth century, cultivated the sciences there with the same ardour, and the same success, as in the East. Astronomy was the principal object of their labours; and they built observatories in several cities in Spain. Arsachel, who was one of the most distinguished of their astronomers, improved the theory of the Sun. A. D. 1020. By a method also, more simple, and more capable of accuracy, than those which Hipparchus and Ptolemy employed, he made some happy alterations in the dimensions they had assigned to the solar orbit. He is likewise believed to have discovered certain inequaLities in the Sun's motion, the existence of which has since

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since been confirmed both by observations and the newtonian theory; whence he has been considered as a very accurate and attentive astronomer. He composed a collection of Tables, entitled Tabula Toledanæ, from the name of the city of Toledo, where he resided.

Alhazen, another celebrated arab settled in Spain, has left us a treatise on optics, which contains the first attempt we have at a theory of refraction and the twilight. A. D. 1100. He makes them depend, not on vapours accumulated in the vicinity of the horizon, but on the difference of transparency, that exists between the air of the atmosphere and an ethereal matter placed beyond it. He even teaches, how we may ascertain by observation the difference between the true and apparent place of a star produced by refraction. According to him the cause of the extraordinary size of the Sun and Moon near the horizon is not to be sought in refraction, but rather a contrary effect. Malebranche has since employed and enlarged upon the same doctrine; and as he does not quote Alhazen, we may presume he was unacquainted with his works. Some authors assert, that Alhazen only translated and commented on a work, which Ptolemy had composed on the same subject; and which is quoted by other arabian writers, though how lost but this we may venture to contradict, since the ancient astronomers, and Ptolemy himself, paid no regard to the effect of refraction in their astronomical observations. To Alhazen at least must be ascribed the honour of having clearly pointed out

this effect, and made astronomers sensible of the necessity of taking it into account.

Several other arabian mathematicians are recorded in Spain about the same period: as Geber, mistakenly considered, on account of his name, as the inventor of algebra; but in reality the author of a translation of the Almagest, and of two theorems in spherical trigonometry very commodious for the resolution of rightangled triangles: Almansor, or Almaon, who made a very good observation of the obliquity of the ecliptic Averroes, a celebrated physician of Cordova, who abridged and commented on Ptolemy, and who was very learned for his time both in natural philo sophy and the mathematics: &c.

Some of these learned arabs were prompted by inclination to remove into more northern parts of Europe, where the knowledge they brought with them is so confounded with that of their scholars, that it is impossible at present, to assign to each their just share.

СНАР.

CHAP. IV.

State of the Sciences among the Persians.

THE persians, who till the middle of the eleventh century made but one people with the arabs, having then shaken off the yoke of the khalifs, did not relinquish the study of the sciences amid the troubles of war. They had algebraists, geometricians, and particularly astronomers, who were highly distinguished.

Loggia Nassir, or doctor Nassir, composed several works of great reputation in their time. We have a commentary of his on Euclid, printed in 1590, in his native tongue, the arabic. Nassir Eddin, another geometrician better known, has given several very ingenious demonstrations of the forty-seventh proposition of the first book of Euclid, which are recited by Clavius. They proceed by a simple transposition of parts, with which Nassir Eddin composes either the square of the hypothenuse, or the squares of the other two sides of the right angled triangle. He also made an accurate translation of the Conics of Apollonius, and added a commentary, of which Halley availed himself with advantage in translating the fifth, sixth, and seventh books of this important work.

We find at the same period another very celebrated persian geometrician, Maimon Rashid. He commented upon Euclid, and his passion for geometry was

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so great, that he always wore some favourite geometrical figures on the sleeves of his garment.

All these ancient persian geometricians had carefully collected the works of the greeks, and were thoroughly acquainted with their doctrines. It is even said, that several grecian works, which we do not possess, are still preserved in Persia.

CHAP.