The Chinese are well known to have observed the hea vens from the most remote ages, yet they appear to have made little progress in geometry. When the Europeans came among them, it consisted of little more than the rules of mensuration it is true, they have long known the famous property of a right angled triangle, and in this they have even gone before the Greeks; but this property, which, on account of its various applications, well deserv ed the sacrifice said to have been offered by Pythagoras to the Muses, has remained sterile in their hands. They did not become acquainted with spherical trigonometry before the 13th century ; and then they probably learned it from the Arabs or Persians.
The Romans fell far short of the Greeks in their atten tion to the sciences. The mathematics, in particular, were greatly neglected at Rome; so that geometry, hardly known, went little beyond the measuring of land and the fixing of boundaries. The celebrated Varro, although no mathema tician, had some knowledge of geometry, and wrote a trea tise on the science, which has been cited by Frontinus and Priscianus under the title of Mensuralia. Cicero was not unacquainted with mathematics ; although he did not write on the subject, his works contain expressions of esteem for the science. The pains he took to discover the tomb of Ar chimedes, in Sicily, was a proof that he could estimate the high merit of that illustrious man.
Vitruvius has displayed considerable knowledge in ma thematics, particularly in the ninth book of his architec ture. We owe to him many notices relating to the me chanics and gnomonics of his time.
The fifth, sixth, and seventh centuries, present hardly any mathematicians. The senator and Roman consul Boetius, so well known by his misfortunes and his Conso lations of Philosophy, was, in regard to the time, one of the most versed in mathematics. It was by his care that the Greek authors, as Nicomachus, Ptolemy, Euclid, &c. begin to be a little known in the Latin tongue. His geome try is a kind of free translation of Euclid.
The beginning of the eighth century was brightened by the learning of Beda; he understood all the branches of mathematics, then so little known, but he attended chiefly to astronomy. It is a curious fact, that at this period mathe matics were more cultivated in Britain than in any other part of Europe. This country produced Alcuin, who stu died under Beda ; he was well skilled in mathematics, and master to Charlemagne. The exertions of Alcuin and his exalted pupil to revive the sciences were unavailing : the light of science was almost extinguished, and the human mind enveloped in the darkness of ignorance ; insomuch, that there is no trace of a single mathematician to be found during a period of 150 years preceding the middle of the tenth century. However, about that period a few scatter
ed rays shot across the gloom. The monk Abbo, a man eminently endowed with a taste for knowledge, and in par ticular for mathematics, then hardly known, had made the monastery of Fleuri a school celebrated for its learning. Among his scholars was Gerbert, afterwards elevated to the pontificate by the name of Silvester II. His desire for learning could not be gratified by what was known among the Christians ; he therefore travelled into Spain, and studied among the Arabs, in their celebrated schools of Cordova and Grenada. He soon went beyond his mas ters in mathematics, and on his return to France he wrote a book on geometry, which has been published by the learned authors of Thesaurus ?necdotorum Novissimus, and from which it appears that he was acquainted with the geometry of Euclid and Archimedes. It is a work on practical geometry, in which he gives rules for measur ing heights and distances, by means of an instrument which he calls Horoscopes.
Gerbert had imitators in his own age, and in that which followed it. Among the first was Adelbold, who wrote a small treatise on the solidity of the sphere. It appears he knew what had been done in this matter by Archimedes, but his own reasoning is vague and ungeometrical. About the year 1050, Hermann Contractus wrote several treatises on mathematics, and in particular one on the quadrature bf the circle.
The twelfth century, notwithstanding the ignorance of the period, presents some mathematicians. The English monk Adhelard travelled into Spain and Egypt ; and on his return he translated Euclid from Arabic into Latin. lle appears to have been the first that made author known in the West; but his work exists only in the libra ries. Adhelard had vatiotis imitators among his country men, as Daniel Morlay, Robert of Reading, William Shell, Clement Langtown: They lived towards the end of this cen tury, as did also Robert, bishop of Lincoln, called Grots head, the author of a short treatise on the sphere, and his brother Adam Marsh. Roger Bacon, himself a mathema tician, and their cotemporary in his youth, speaks highly of did! skill in geometry. Passing over yam ious writers on astronomy, we shall only farther mention Plato of Ti voli, who, about the year 1120, translated the Spherics of Theodosius from the Arabic into barbarous Latin.