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SCIENCE 



[N. S. Vol. XLUI. No. 1107 



and the other domains of human activity, 

 there are a few gTeat classics which stand out 

 as monuments to the world's progress. Such 

 are the " Elements " of Euclid, the work of 

 Apollonius on conies, the " Arithmetic " of 

 Diophantus, " La Geometric " of Descartes, 

 and others of their kind, works upon which 

 rest the great structure of modern mathe- 

 matics. Among these classics stands and must 

 always stand the first work which bore the 

 name of algebra, the algehr tv'al muquabala 

 of Al-Khowarizmi, a scholar working at the 

 court of the caliphs at Bagdad although bear- 

 ing the name of his native state, Kharezm, the 

 country about the modern Khiva. This treatise 

 was written about the year 825 of our era, and 

 although the world had an algebra of one kind 

 or another for many centuries before the era 

 of the "Arabian Nights Tales," it was Al- 

 Khowarizmi who first set forth the science in 

 a treatise bearing the name with which we are 

 familiar. 



Like so many Arab productions, the works 

 of Al-Khorwarizmi attracted the attention of 

 scholars in that remarkable period of the 

 awakening of Europe from a long intellectual 

 slumber, the twelfth century. First there was 

 his arithmetic, which was translated by John 

 of Seville as the " Liber algorismi " (Book of 

 Al-Khowarizmi), a title from which we have 

 such words as algorism (algorithm) and 

 augrim. This work did^ much to make the 

 Hindu-Arabic numerals known in Europe, 

 and to it is due the name given to the algorists 

 (algoristi), those who computed by these num- 

 erals instead of using the medieval counters. 

 In the nature of things, the algebra was a less 

 popular work, although it was more or less 

 familiar to scholars from and after the middle 

 of the twelfth century. Of the translators who 

 assisted in making known the science of the 

 Arabs to the scholars of the West, Gherardo 

 of Cremona and Eobertus Cestrensis (Robert 

 of Chester) are among the best known, and 

 each appears to have translated the algebra of 

 Al-Khowarizmi. There seems also to have 

 been another translator of this work, not to 

 speak of Leonardo Fibonacci who has a chapter 

 upon " Aljebra et almuchabala " in his " Liber 



abaci" (1202). This translator was William 

 of Luna, and it is possible, as Professor Kar- 

 pinski points out, that it is his version which 

 was found by this reviewer some years ago in 

 a manuscript in the library of Gteorge A. 

 Plimpton, Esq., of New York. 



Of these translations one had appeared in 

 print before Professor Karpinski imdertook his 

 work. This is the translation attributed to 

 Gherardo of Cremona, published about eighty 

 years ago in the appendix to Libri's " Histoire 

 des sciences mathematiques." Eobert of 

 Chester's translation, which has now been 

 made available for us, had been described by 

 Wappler from two codices (Dresden and 

 Vienna), but only these two copies had come 

 to light until the present writer happened upon 

 a third one about a dozen years ago and pur- 

 chased it for the Columbia University Library. 

 This last-mentioned codex turned out to be in 

 the handwriting of Johann Scheybl, a Tiibin- 

 gen professor who lived in the first three quar- 

 ters of the sixteenth century. It is this manu- 

 script which Professor Karpinski has trans- 

 lated and annotated with rare pains and with 

 a scholarship which is very gratifying to 

 American workers in this field. 



The arrangement of the material is very 

 convenient. The original work, transcribed 

 with care, appears upon the left-hand page 

 while a translation faces it from the opposite 

 page, thus making it possible to compare the 

 two with a minimum of trouble. At the foot 

 of each page of text are notes relating to such 

 matters as the variants in the three codices, 

 while at the foot of each page of translation 

 are notes explanatory of the text. We have 

 nowhere a translation of a mathematical work 

 in any language that is so conveniently ar- 

 ranged. 



The task which Professor Karpinski set for 

 himself was not an easy one. Scheybl VTTote 

 a hand which looks legible at first sight 

 but which is difficult to read, as witness the 

 facsimile inserted in this edition. Indeed it 

 was no doubt due to the very fact that the 

 handwriting was so illegible that we owe its 

 acquisition by Colmnbia, since otherwise its 

 value would have been recognized many years 



