RECENT ADVANCES IN SCIENCE 177 



On Growth and Form (Cambridge, 191 7) is suggestive in this 

 connection (cf. the learned review in Bull. Amer. Math. Soc. 

 191 8, 24, 403-7), and on allied subjects we have excellent notes 

 in the last three of the following list of suggestions that have 

 been made : Rhind papyrus, geometrography, arithmetical 

 prodigies, Ptolemy's theorem, paper folding, women as mathe- 

 maticians and astronomers, binary arithmetic, the logarithmic 

 spiral, " golden section," and a Fibonacci series (Amer. Math. 

 Monthly, 191 8, 25, 6-8, 91-6, 136-42, 189-93, 232-8). Here 

 also may be mentioned the useful account by G. W. Evans 

 (ibid. 447-51) of Cavalieri's theorem on the mensuration of 

 solids. 



Articles of interest in the teaching of various parts of 

 geometry are those by D. M. Y. Sommerville (Math. Gaz. 



191 7, 9, 153-5), W. H. Roever (Amer. Math. Monthly, 191 8, 25, 

 145-59), and E. B. Stouffer (ibid. 159-67). 



History. — G. Milhaud (Rev. de Metaphys. 191 8, 25, 163-75) 

 inquires what was the discovery to which referred the date 

 of November 11, 1620, written on the margin of Descartes' 

 manuscript called " Olympica." It is, of course, known that 

 this date has been taken to be that of the discovery of the 

 method of co-ordinate geometry, but Milhaud gives good 

 reasons, chiefly based on the " Journal " of Beeckmann printed 

 in the tenth volume of Adam and Tannery's CEuvres of Des- 

 cartes, that the marginal note refers to the discovery of the 

 theory of telescopes. This paper is yet another result of 

 Milhaud 's important researches on the early scientific work of 

 Descartes (cf. Science Progress, 191 8, 13, 1-2). 



F. Cajori (Amer. Math. Monthly, 191 8, 25, 179-201) gives 

 a useful set of references to early uses of the process of " mathe- 

 matical induction " (cf. W. H. Bussey, Science Progress, 



191 8, 12, 362), and then inquires how it came to be called by 

 that rather ambiguous name. Wallis (1656) used the name 

 for a process used by him, which was very like the usual pro- 

 cess of induction from isolated facts ; but the first use of the 

 term for the process of deduction it now denotes seems to 

 have been made by De Morgan in 1838. 



There is an excellent and thorough review by A. Dresden 

 (Bull. Amer. Math. Soc. 191 8, 24, 454-6) of J. M. Child's short- 

 ened and striking edition of The Geometrical Lectures of Isaac 

 Barrow (Chicago and London), 191 6. "It seems not at all 



