The Ancient Library

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I. diophantus (AifywTos),1 of Alexandrca, is the only Greek writer on Algebra. His period is wholly unknown, which is not to be wondered at, if we consider that he stands quite alone as to the subject which he] treated. But, looking at the improbability of all mention of such a writer being omitted by Proclus and Pappus, modern inquirers have felt strong­ly inclined to place him toward the end of the fifth century of our era at the earliest. He wrote Arithmetica ('AptQwriKd), in thirteen books, of which only six are extant, and one book, De Multangulis Numeris, on polygonal numbers. These books contain a system of reasoning on num­bers by the aid of general symbols, and with some use of symbols of operation ; so that, though the demonstrations are very much conducted in words at length, and arranged so as to remind us of Euclid, there is no question that the work is algebraical ; not a treatise on algebra, but an algebraical treatise on the relations of integer numbers, and on the solu­tion, of equations of more than one variable in integers. The question whether Diophantus was an original inventor, or whether he received a hint from India, the only country we know of which could then have given one, is of great difficulty. The very great similarity, however, of the Diophantine and Hindu algebra (as far as the former goes) makes it almost certain that the two must have had a common origin, or have come one from the other, though it is clear that Diophantus, if a borrow­er, has completely recast the subject by the introduction of Euclid's form of demonstration.

The first Greek edition, with Latin version, and original notes (the scholia of the monk Maximus Planudes on the first two books being rejected as useless), is that of Bachet de Meziriac, Paris, 1621, fol. Fermat left materials for the second and best edi­tion (Greek and Latin), in which is preserved all that was good in Bachet, and, in par­ticular, his Latin version, with most valuable comments and additions of his own (it being peculiarly his subject).

II. pappus (naTnros),2 of Alexandrea, one of the later Greek geometers, is said by Suidas to have lived under Theodosius (A.D. 379-395). The writings mentioned as having come from the pen of Pappus are as fol­ lows : MaQijfjiaTiK&j' avyaywywv j8i/3Aia, the celebrated Mathematical Collec­ tions. This work, as we now have it in print, consists of the last six of eight books. Only portions of these books have been published in Greek. 2. Xopoypatyia oiKovfj.ej/tK'fj. 3. Els ret reffffapa /3ij8Aia tov TlTO\€(j.a(ov a.tjs 2wr dittos uTrtfyu/Tj/ua. 4. Tlora/J-obs robs & al^tltt). 5. The last four have not reached us. They are mentioned by Suidas, and just as here written down in continuous quotation, headed /3i/3Am 5e avrov. 1 De Morgan; Smith's Diet. "Bwgr^ s.v. 2 Id. ib.

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