RECENT ADVANCES IN SCIENCE 615 



tioned that Prof. Florian Cajori has brought to a conclusion 

 his painstaking and valuable researches (Amer. Math. Monthly, 

 191 5, 22) on the history up to modern times of Zeno's argu- 

 ments on motion, referred to in Science Progress for July, 

 1915 (10, 116). Cajori (Monist, 191 5, 25, 495) continues his 

 valuable paper describing the work of William Oughtred (cf. 

 Science Progress, 191 6, 10, 431). In this concluding part 

 the influence of Oughtred on the teaching of mathematics is 

 investigated in great detail. Another welcome example of a 

 detailed historical paper is a study of the geometrical work of 

 Colin Maclaurin by C. Tweedie (Math. Gaz. 191 5, 8, 133). 

 Tweedie gave a presentation in modern form of Maclaurin 's 

 Geometria organica in a paper read to the Royal Society of 

 Edinburgh on December 6, 191 5. 



Pierre Boutroux (Rev. de Metaphys. et de Morale, 1914, 22, 

 814; published in November 191 5) makes a study of the 

 historical significance of Descartes' Geometric It is well 

 known that Fermat seems to have been led in his invention of a 

 method of co-ordinates by a method sometimes used by Apollo- 

 nius ; but the repetition of this fact is the only thing which 

 appears of value in Boutroux's paper. 



At the end of a review by Prof. R. C. Archibald (Bull. 

 Amer. Math. Soc. 191 5, 22, 125) of some books on the life and 

 work of the late Henri Poincare\ there is a valuable list of 

 recent memoirs on Poincare. 



Logic and Principles of Mathematics. — One of the pioneers 

 of the science of symbolic logic, who has not been generally 

 known in this connection, is Bernard Bolzano, the first volume 

 of whose Wissenschaftslehre was reprinted at Leipzig in 1914. 

 Philip E. B. Jourdain (Monist, 191 5, 26, 633) attempts a 

 contrast between mathematicians and philosophers in their 

 ways of regarding logic. The comparison is not always favour- 

 able to the mathematicians, as the name of George Berkeley 

 reminds us. 



A translation of part of Gottlob Frege's Grundgesetze der 

 Arithmetik is given in the same number of the Monist (191 5, 

 25, 481) and prefaced by a short account of Frege's other work 

 on logic and the principles of mathematics. This translation 

 is to be continued by translations of other parts of the same 

 book which can be put into ordinary language. 



C. D. Broad (Mind, 191 5, 24, 464) gives a very able dis- 



