190 SCIENCE PROGRESS 



in Nature of June 14, to an article in Science Progress for 

 April, to recent numbers of the Revue generate des Sciences, and 

 to the account of a recent meeting of the Italian Association 

 for the Advancement of Science in Scientia for June. 



History. — A. E.Taylor (Proc. Aristot. Soc. 1916, 16, 234-89) 

 makes a most learned and important contribution to the history 

 of Greek logical theory, by discussing the use made in Plato's 

 Parmenides of the appeal to an infinite regress. 



J. H. Weaver (Bull. Amer. Math. Soc. 191 7, 23, 357-65) 

 gives a short historical sketch of the development of the pro- 

 perties of conies connected with the foci, and also some of the 

 theorems from Pappus which have a bearing on foci and 

 tangents. 



F. Cajori (Science, 191 6, 44, 714-7) calls attention to the 

 early use of a symbol for zero and the principle of local 

 value by the Maya of Central America and Southern Mexico, 

 which probably dates back to about the beginning of the 

 Christian era, and was thus apparently the very earliest. The 

 unit of that number system of theirs which is of the greatest 

 interest was 20, for which a special symbol, which looks some- 

 thing like a half-closed eye (the symbol for zero) with a dot 

 above it, was used, and separate symbols composed of dots 

 and bars represented the numbers from 1 to 19, each dot 

 representing a unit and each bar five units . 



J. Ginsburg (Bull. Amer. Math. Soc. 191 7, 23, 366-9) gives 

 an account of the evidence discovered by F. Nau and described 

 in the Journal Asiatique of 1910 that the Hindu numerals 

 reached Arab lands much earlier than was formerly supposed, 

 since they were known to and justly appreciated by the Syrian 

 writer Severus Sebokht, who lived in the second half of the 

 seventh century. This is, then, about a hundred years before 

 the date of the first definite trace that we have hitherto had 

 of the introduction of the system into Bagdad. Also Nau's 

 work shows that the zero was probably not in this system 

 (cf. ibid. 467). 



A critical review by F. E. Robbins of George Johnson's dis- 

 sertation on The Arithmetical Philosophy of Nicomachus of 

 Gerasa (Lancaster, Pa., 1916), which presents a partial transla- 

 tion of and a short commentary on the Introduction to Arithmetic 

 of Nicomachus, is given in the Amer. Math. Monthly (191 7, 24, 

 121-3). 



