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How aptly does Horace's description of the young man apply to the people! Imberbis juvenis, tandem custode remoto Gaudet equis, canibusque et aprici gramine campi; Cereus in vitium flecti, monitoribus asper, Utilium tardus provisor, prodigus æris, Sublimis, cupidusque et amata relinquere pernix.
The Pythagorean arithmetic as a whole, with the developments made after the time of Pythagoras himself, is mainly known to us through Nicomachus's Introductio arithmetica, Iamblichus's commentary on the same, and Theon of Smyrna's work Expositio rerum mathematicarum ad legendum Platonem utilium. The things in these books most deserving of notice are the following.
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