Maboh 17, 1916] 



SCIENCE 



391 



ago. To be sure there was the Libri transcrip- 

 tion of the translation attributed to Gherardo 

 to help in reading the manuscript, and there 

 was Eosen's translation from the Arabic 

 (1831), but neither of these has the same 

 wording, and neither could render much assist- 

 ance in the difficult task. 



The translation can best be described by the 

 word sensible. It is fortunately not literal, 

 for a literal translation of, say, " substantise 

 radices cosequant " or " De substantia et 

 drachmis res cosequantibus " would be unin- 

 telligible. Even such an expression as " et 

 etiam si dicas " is better rendered by " another 

 exampje " than by a verbatim translation. To 

 be sure this freedom leads to inconsistencies, 

 as when " Tria igitur huius substantia sunt 

 radix ; et substantia nouem " appears as 

 " Therefore three (spelled) is the root of this 

 x^ (symbol), and x- is-9 (symbol) "; while the 

 sentence " Substantia et 21 drachmse 10 

 rebus sequiparantur," which follows, appears 

 as " A square (word) and 21 units are equal 

 to ten (spelled) unknowns " instead of, say, 

 " x^ -\- 21 =■ lOx." These variations in style 

 are not at all confusing, however, because the 

 student always has the original on the facing 

 page. 



The style of the problems of Al-Khowarizmi 

 shows the Greek influence, that is, the ques- 

 tions are generally abstract; for example, 

 " From a square I subtract three of its roots 

 and multiply the remainder by itself; the sinn 

 total of this multiplication equals the square "; 

 or, in the shorthand of modern algebra, 

 (x^ — 3x)-^x-. There are, however, a few 

 questions in the rule of three, apparently a 

 product of the Orient, but all are so simple as 

 to deserve no place in algebra. 



Al-Khowarizmi can not be said to have 

 made any discovery in algebra. He was essen- 

 tially a compiler of problems which he solved 

 by methods already known. He invented no 

 symbolism as Diophantus apparently did, nor 

 did he show the remarkable genius of this last 

 great representative of the dying mathematics 

 of a dying Greek civilization. He contributed 

 nothing to the solution of the quadratic that 

 the Alexandrian school had not known, and 



even the special cases of the cubic equation 

 were as a sealed book to him. His problems 

 lack the delicious imagery to be found in the 

 Hindu schools of his time, and the same is 

 true, oddly enough, of those of the great 

 Persian algebraist and poet Omar Khayyam. 



Whatever may be said, however, of the de- 

 tails of the work itself, it is evident that Al- 

 Khowarizmi will always occupy a prominent 

 place in the history of mathematics, and that 

 Dr. Karpinski's publication will rank as the 

 first noteworthy effort in our country in the 

 editing of a renaissance manuscript on the 

 subject of algebra. The thanks of all scholars 

 are due to him for his careful work and to the 

 University of Michigan for publishing the re- 

 sult in such a satisfactory style. 



David Eugene Smith 



Fungoid Diseases. An English-American 



Book. London, Longmans, Green and Co. 



118 pp. Price 65c. 



The latest book on fungi to come to hand is 

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