Mathematics 33 



These tables give the result directly and to the nearest unit. Instead of having 

 to find the required product at the intersection of a line and a column, as in other 

 tables in using these tables the eye has to travel only in one direction at a time, 

 first in a column, stopping at the second factor or the nearest number less than 

 the second factor, and then along this line to one of the outside columns where the 

 required product is found. 



There is a great economy of space which makes the tables very much easver 

 and more rapid in use. They omit all unnecessary numbers of a series of consecu- 

 tive numbers which gives the same product. The great economy of space can be 

 judged from the fact that only fourteen pages, instead of the one hundred pages 

 in Crelle's tables, are required for the 200 tables from 0.001 to 0.200. 



These tables are more convenient and more accurate than a slide-rule of the 

 same capacity. 



The two-place tables (three pages) are printed separately on heavy paper. 



No. 256. DICKSON, L. E. History of the Theory of Numbers. Octavo. 



Vol. I. Divisibility and Primality. xn+486 pages. Published 1919. Price $7.50. 

 Vol. II. Diophantine Analysis. In press. 



The history of mathematics from the earliest times to 1800 has been the life- 

 long investigation of various writers. There remains the enormous task of treating 

 adequately the past century; the vastness of the material would seem to require 

 the separate treatment of the various branches of mathematics. The present history 

 of the theory of numbers aims to portray the development in historical sequence 

 of each topic from the early Greeks to date and to provide a source-book, taking 

 account of every article and book bearing on the subject. Certain material, not 

 accessible in America, was collected in the libraries of England, France, and Ger- 

 many. The aim has been to present a brief, but adequate, account of the results of 

 each article and, in certain cases, also of the proof when that was necessary to differ- 

 entiate the article from others on the same topic. It was borne in mind that 

 most readers would have access to only a small proportion of the journals and 

 books cited. 



Volume I treats of perfect and amicable numbers, Fermat's and Wilson's 

 theorems and their generalizations and converses, symmetric functions modulo P, 

 residue of (uP~ l 1) /p modulo p, Euler's < function and generalizations, Farey 

 series, periodic fractions, primitive roots, congruences, factorials, sum and number 

 of divisors, criteria for divisibility, factoring, tables, Fermat's numbers, factors 

 of o=t b n , recurring series, Lucas' , v n < theory of primes, inversion of functions, 

 numerical integrals and derivatives, and properties of digits. Report has been 

 made on more than 3,000 papers on these topics. 



Volume II treats of polygonal, pyramidal, and figurate numbers, linear equa- 

 tions, congruences and forms, partition analysis, rational right and oblique tri- 

 angles, quadrilaterals, polygons, and pyramids, representation of numbers as sums 

 of squares, relations between squares, quadratic congruences in unknowns, two 

 or more linear functions made equal to squares, Diophantine equations and systems 

 of equations of degrees 2, 3. 4, n (classified in eleven chapters with various sub- 

 divisions), sets of numbers with equal sums of like powers, Waring's problem, and 

 Fermat's last theorem. Report has been made on approximately 5,000 papers and 

 books on these topics. The ratio of this number to the corresponding number, 

 3,000 for Volume I, is roughly equal to the ratio of the length of Volume II to 

 the length of Volume I. 



The author plans a concluding volume, which will treat of quadratic and higher 

 forms, residues, and reciprocity laws. 



