S SCIENCE PROGRESS 



but written in 1691, John Bernoulli refers to previous lectures 

 on the differential calculus, which he would not publish as they 

 were contained in de I'Hospital's Analyse des infiniment petits, 

 i6g6. Bernoulli only advanced this claim after de I'Hospital's 

 death, and historians are divided with regard to its justice. 

 P. Schafheitlin (Verhl. Basel, 32, 1920-21, 230-35) has now dis- 

 covered at Basel the MSS. of Bernoulli's earlier lectures, which 

 agree very closely, except in matters of arrangement, with 

 much of de I'Hospital's book. 



In a review of Cajori's valuable History of Fluxions (see 

 Science Progress, January 1921, p. 486), J. M. Child (Math. 

 Gazelle, 11, 1922, 26-30) expresses the opinion that Newton's 

 definition of a fluxion is logically sound, involving the notion 

 of a section, and that there is in it no idea of an infinitesimal. 

 Cajori has iDcen misled by using an English translation instead 

 of the original Latin. 



F. Cajori (Bull. Amer. Math. Soc, 27, 192 1, 453-58) traces 

 the spread of the rival Newtonian and Leibnizian notations 

 of the Calculus. S. Wiesner [Jahresber. d. deut. Math. Verein, 

 29, 1920, 130-35) publishes new material for the life of Johann 

 Bolyai from the archives in Modling and Vienna ; and 

 L. Schlesinger {ibid., 28-40) prints correspondence between 

 Weierstrass and L. Fuchs. 



Logic and the Theory of Aggregates. — A notable new 

 mathematical periodical, of which the first two volumes have 

 appeared, is Fundamental Mathematicce, edited in Warsaw by S. 

 Mazurkiewicz and W. Sierpinski. It is to deal solely with the 

 theory of aggregates and allied questions (analysis situs, 

 mathematical logic) and contributions will be received in 

 French, German, English, or Italian (not Polish). The second 

 volume (192 1 ), 256-85 contains an article by H. Lebesgue 

 " Sur les correspondances entre les points de deux espaces." 



A. Schoenflies {Math. Ann., 83, 1921, 173-200) attempts to 

 apply the methods of Hilbert's Grundlagen der Geonietrie to the 

 theory of aggregates ; the terms are left undefined, only their 

 mutual relations being considered, and the axioms are divided 

 into groups — axioms of equivalence, of order, and so on. 



N. Wiener {Proc. Lond. Math. Soc, 20, 1921, 329-46) 

 develops a categorical theory of the structure of the line in 

 terms of bicontinuous, biunivocal transformations. 



Algebra and Analysis. — G. A. Miller {Bull. Amer. Math. Soc., 

 27, 1 92 1, 459-62) examines and criticises adversely the Group 

 Theory reviews which have appeared in the Jahrbuch ilber die 

 Fortschritte der Mathematik. 



W. Burnside {Proc. Camb. Phil. Soc, 20, 1921, 482-84) 

 proves a result conjectured in his Theory of Groups, viz. that a 

 simply-transitive permutation group containing a regular 



