346 SCIENCE PROGRESS 



An account of the work of Theodore Reye (183 8-19 19) is 

 given by F. Schur {Math. Annalen, 82, 192 1, 165) ; he is perhaps 

 best known by his book Geometfie der Lage, first pubhshed in 

 1866-8, and by his work on the tetrahedral complex, obtained 

 as the locus of the intersections of corresponding planes of two 

 collinear spaces. 



H. G. Zeuthen (i 839-1920) of Copenhagen is associated with 

 Enumerative Geometry, with the Zeuthen-Segre invariant of 

 an algebraic surface, and with books on the history of mathe- 

 matics, notably Die Lehre von den Kegelschnitten im Altertum, 

 1886. Notices of his work are given by C. Juel {Bull, de I'acad. 

 roy. de Danemark, 1919-20, 6^), and by H. W. Richmond 

 {Proc. Lond. Math. Soc, 19, 192 1, xxxvi.). 



Karl Rohn (185 5-1 920) made important contributions to 

 our knowledge of quartic surfaces, in particular of ruled 

 quartics and quartics with a triple point. He also showed 

 that the maximum number of separated ovals possible for a 

 quartic surface is ten. A list of his papers and an account of 

 his work is given by O. Holder {Berichte d. Sachs. Akad., 78, 



1920, 109) 



An extremely interesting biography of S. Ramanujan 

 ( 1 887-1920) is given by G. H. Hardy {Proc. Lond. Math. Soc, 

 19, 1 92 1, xL), together with a list of his papers. 



For Martin Krause (1851-1920) and his work on the theory 

 of hyperelliptic functions see a notice by G. Herglotz {Berichte 

 d. Sachs. Akad., 72, 1920, 105). 



A Memorial Volume to Henri Poincare {Acta Mathematica, 

 88, 1 921) contains valuable analyses of his work by Poincar6 

 himself and by J. Hadamard, biographical notices by P. Appell 

 and by P. Boutroux, and correspondence with Mittag-Leffler 

 and L. Fuchs. 



History. — G. A. Miller {Amer. Math. Monthly, 28, 1921, 256) 

 has a note on the remarkably inaccurate formula \a {a + 1) for 

 the area of an equilateral triangle of side a, which is to be found 

 in Boethius and Gerbert. Hankel called the letter in which 

 Gerbert discusses the formula " the first mathematical paper 

 of the Middle Ages which deserves this name," but Miller 

 endeavours to show that this praise is not merited. 



J. W. L. Glaisher {Mess. Math., 51, 1921, i) writes on the 

 early history of the signs + and -, which first occur in Widman's 

 Rechenung, printed at Leipzig in 1489. He comes to the con- 

 clusion that they are derived from algebra and not from com- 

 merce, as was thought by De Morgan and Gerhardt. 



An account of the first work on mathematics printed in the 

 New World is given by D. E. Smith {Amer. Math. Monthly, 28, 



1 92 1, 10) ; it was a commercial arithmetic entitled Sumario 

 Compendioso by Juan Diez, and was printed in the City of 



