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y years of Ptolemy's reign are probably those of Euclid's age, not of his youth; for had he been trained in the school of Alexandria formed by Ptolemy, who invited thither men of note, Proclus would probably have given us the name of his teacher: but tradition rather makes Euclid the founder of the Alexandrian mathematical school than its pupil. This point is very material to the foinnation of a just opinion of Euclid's writings; he was, we see, a younger contemporary of Aristotle (B. C. 384-322) if we suppose him to have been of mature age when Ptolemy began to patronise literature. and on this supposition it is not likely that Aristotle's writings, and his logic in particular, should have been read by Euclid in his youth, if at all. To us it seems almost certain, from the structure of Euclid's writings, that he had not read Aristotle: on this supposition, we pass over, as perfectly natural, things which, on the contrary one, would have seemed to shew great want of judgment. Eucli
To this it may be added, that there is hardly any book in our language in which the young scholar or the young mathematician can find all the information about this name which its celebrity would make him desire to have. Euclid has almost given his own name to the science of geometry, in every country in which his writings are studied; and yet all we know of his private history amounts to very little. He lived, according to Proclus (Comm. in Eucl. 2.4), in the time of the first Ptolemy, B. C. 323-283. The forty years of Ptolemy's reign are probably those of Euclid's age, not of his youth; for had he been trained in the school of Alexandria formed by Ptolemy, who invited thither men of note, Proclus would probably have given us the name of his teacher: but tradition rather makes Euclid the founder of the Alexandrian mathematical school than its pupil. This point is very material to the foinnation of a just opinion of Euclid's writings; he was, we see, a younger contemporary of Aris
d Mohammedan nation: our notice, therefore, must be but slight, and various points of it will be confirmed by the bibliographical account which will follow. In Greece, including Asia Minor, Alexandria, and the Italian colonies, the Elements soon became the universal study of geometers. Commentators were not wanting; Proclus mentions Heron and Pappus, and Aeneas of Hierapolis, who made an epitome of the whole. Theon the younger (of Alexandria) lived a little before Proclus (who died about A. D. 485). The latter has made his feeble commentary on the first book valuable by its historical information, and was something of a luminary in ages more dark than his own. But Theon was a light of another sort, and his name has played a conspicuous and singular part in the history of Euclid's writings. He gave a new edition of Euclid, with some slight additions and alterations: he tells us so himself, and uses the word e)/kdosis, as applied to his own edition, in his commentary on Ptolemy. He al
circumstances under which the first started, they should view the second systematically dispersing the remains of (Greek civilization, while the first were concentrating the geometry of Alexandria, the arithmetic and algebra of India, and the astronomy of both, to formn a nucleus for the present state of science. The Elements of Euclid were restored to Europe by translation from the Arabic. In connection With this restoration four Eastern editors may be mentioned. Honein ben Ishak (died A. D. 873) published an edition which was afterwards corrected by Thabet ben Corrah, a well-known astronomer. After him, according to D'Herbelot, Othman of Damascus (of uncertain date, but before the thirteenth century) saw at Rome a Greek manuscript containing many more propositions than he had been accustomed to find: he had been used to 190 diagrams, and the manuscript contained 40 more. If these numbers be correct, Honein could only have had the first six books; and the new translation which Oth
h, a well-known astronomer. After him, according to D'Herbelot, Othman of Damascus (of uncertain date, but before the thirteenth century) saw at Rome a Greek manuscript containing many more propositions than he had been accustomed to find: he had been used to 190 diagrams, and the manuscript contained 40 more. If these numbers be correct, Honein could only have had the first six books; and the new translation which Othman immediately made must have been afterwards augmented. A little after A. D. 1260, the astronomer Nasireddin gave another edition, which is now accessible, having been printed in Arabic at Rome in 1594. It is tolerably complete, but yet it is not the edition from which the earliest European translation was made, as Peyrard found by comparing the same proposition in the two. The first European who found Euclid in Arabic, and translated the Elements into Latin, was Athelard or Adelard, of Bath, who was certainly alive in 1130. (See "Adelard," in the Biogr. Dict. of the
he forty years of Ptolemy's reign are probably those of Euclid's age, not of his youth; for had he been trained in the school of Alexandria formed by Ptolemy, who invited thither men of note, Proclus would probably have given us the name of his teacher: but tradition rather makes Euclid the founder of the Alexandrian mathematical school than its pupil. This point is very material to the foinnation of a just opinion of Euclid's writings; he was, we see, a younger contemporary of Aristotle (B. C. 384-322) if we suppose him to have been of mature age when Ptolemy began to patronise literature. and on this supposition it is not likely that Aristotle's writings, and his logic in particular, should have been read by Euclid in his youth, if at all. To us it seems almost certain, from the structure of Euclid's writings, that he had not read Aristotle: on this supposition, we pass over, as perfectly natural, things which, on the contrary one, would have seemed to shew great want of judgment.
s it may be added, that there is hardly any book in our language in which the young scholar or the young mathematician can find all the information about this name which its celebrity would make him desire to have. Euclid has almost given his own name to the science of geometry, in every country in which his writings are studied; and yet all we know of his private history amounts to very little. He lived, according to Proclus (Comm. in Eucl. 2.4), in the time of the first Ptolemy, B. C. 323-283. The forty years of Ptolemy's reign are probably those of Euclid's age, not of his youth; for had he been trained in the school of Alexandria formed by Ptolemy, who invited thither men of note, Proclus would probably have given us the name of his teacher: but tradition rather makes Euclid the founder of the Alexandrian mathematical school than its pupil. This point is very material to the foinnation of a just opinion of Euclid's writings; he was, we see, a younger contemporary of Aristotle (