Thcon, the associate of Pappus in the Alexandrian school, wrote Scholia, or Notes on Euclid, which Commandinus has given in one of his Latin editions of that author. He is supposed, however, to have greatly vitiated the text ; and Dr Simson, trle learned editor of Euclid, has bestowed great labour in freeing it from what he supposed to be Theon's interpolations.
Theon had a beautiful and accomplished daughter. named Hypatia, who cultivated geometry ; and so learned was she in the science, that she was judged worthy to suc ceed her father in the Alexandrian school. She wrote com mentaries on Apollonius and Diophantus, which are now lost. It is infinitely to be lamented that so exalted a being should have had so tragical a fate. This woman, the orna ment of her sex and of human nature, fell a sacrifice to the blind fury of a fanatical mob, about the beginning of the fifth century.
The philosopher Proclus, the chief of the Platonics at Athens, transferred thither, in some degree, the seat of the mathematical sciences, towards the middle of the fifth cen tury ; although he did not extend geometry, yet he held it in esteem. His very prolix commentary on the first book of Euclid, has made us acquainted with many traits in the history of the ancient geometry, and excited a regret that he did not extend it to the remaining books. Proclus was succeeded in his school by Marinus of Neapolis, who form ed, with Isidore of Miletus and Eutocius of Ascalon, a kind of succession, which brings the history of geometry down to the reign of Justinian. Marinus wrote a preface to Eu clid's book of Data, which Dr Simson has rejected in his edition as of no use. Isidore is said, by Eutocius, to have invented an instrument for describing a parabola, by conti nued motion.
It would appear that Diodes lived about this period ; he was the inventor of the cissoid, a curve contrived for the purpose of finding two mean proportionals. Eutocius also attributes to this geometer a solution of the Archi medean problem concerning the division of a sphere, which we have already noticed ; it is highly creditable to him, and shows that he was skilful in the ancient analysis. We may place Sporus, and his master Philo, about this period ; the former gave a solution of the problem of two mean proportionals, and the lattel^ extended Archimedes' ap proximation of the ratio of the diameter to the circumfer ence of a circle, as far as 10,000th parts.
The labours of Proclus, and the geometers that follow ed him, were the last rays which the ancient mathematics scattered upon Greece. The long night of ignorance which elapsed from this time, until the destruction of the Greek empire, produced merely elementary writers, such as in better times would scarce have deserved the name of ma thematicians. The school of Alexandria, however, yet existed, and the brilliant times of Euclid and Apollonius might have been renewed, had it not been for the troubles which agitated the East. The taking of Alexandria by the Saracens, gave a mortal blow to the sciences, not only in that celebrated capital, but also throughout the Greek em pire. This happened in the year 640 A. D. The Alex andrian library, a treasure of inestimable value, was de livered to destruction, and the finest monument of human genius, the accumulated store of knowledge produced by the exertion of the most enlightened minds in many ages, was expended in heating the public baths of the city. See ALEXANDRIA.
It is consoling to reflect, that although the followers of Mohammed, at this period, destroyed the sciences, yet they afterwards were entitled to the gratitude of posterity, for the care with which they cherished them. Within less than a century, we find the Arabs cultivating astro nomy and geometry. Many of the Greek mathematicians, chiefly such as treat of astronomy, as Euclid, Theodosius, Hypsicles, Menelaus, were translated into Arabic in the reign of Almamon, or soon after ; they even then began to study the more sublime geometry, for the four first ,books of the conics of ApoHoning were translated by or der of that enlightened prince. At a later period, thc re maining books were translated, also Archimedes' treatise on the sphere and cylinder, and probably his other works; and it deserves to be remarked, that the Arabs cite seve ral works of the Greek geometers, concerning which we know nothing ; as a treatise on parallel lines, another on triangles, and a third on the division of the circle. We are indebted to the Arabs for the form, under which tri gonometry is now known. Ptolemy had greatly simplified the theory of Menelaus, yet he employed a laborious rule, called the rule of six quantities.