ON MATHEMATICAL TABLES. 35 



is merely necessary to form the miiltiples of 2, 3, 5 . . up to the extent of the 

 table, the numbers that do not occur being of course primes. The manner 

 in which the formation of these multiples is best effected, and other practi- 

 cal details, are explained by Bueckhaedt in his preface to the second 

 million. The following is a Hst of tables of divisors and of primes, abridged 

 from an elaborate account prefixed to Cheriiac : — 



1657. Francis Schooten : table of primes to 9997. 



1668. Pell (in Branker's translation of Rhonius's ' Algebra,' iniblished at 

 London) : least divisors of odd numbers not ending in 5 to 100,U00. 



1728. Poetius. An ' anatome' of numbers to 10,000. 



1746. KEtJGEE. Primes to 100,999. 



1767. Anjema. All divisors (simple and compound) of numbers to 

 10,000. 



1770. Lambeet. Least divisors of numbers to 102,000 (multiples of 2, 3, 

 and 5 omitted). 



1772. Marci. Extension of Lambert's table by the addition of primes to 

 400,000. 



1785. Neumann. Simple divisors (Pell only gave the least) of numbers 

 to 100,100 (multiples of 2, 3, 5 omitted). 



1797. Vega. Simple factors to 102,000, and 'primes to 400,000 (seo 

 Yega, ' Tabula;,' 1797, Vol. II. T. I.). 



1804. Krause. Factor table to 100,000. 



From the above list Chernac has omitted Rahn (1659), giving factors to 

 24,000, and Pigri (1758) to 10,000, which are described below. A more 

 important omission. is that of Felkel, whose table is noticed at length 

 further on. 



The titles of Anjema's, Neumann's, and Krause's works are given in the 

 Babbage Catalogue as follows : — " Anjema (Henricus), Tabula divisorum 

 omnium numerorum naturalium ab 1 usque ad 10000. 4to, Lugd. Bat. 

 1707 ; " " Neumann (Jobann), TabcUen der Prim-Zahlen- und der Factoren 

 der Zahlen, welche unter 100100, und durch 2, 3, oderS nicht theilbar sind ; 

 herausgegoben durch J. N. 4to, Dessau, 1785 ; " and " Krause (Karl C. F.), 

 Factoren- und Primzahlen-Tafel von 1 bis 100000 neu berechnet. Fol. 

 Leipzig, 1804." 



The same catalogue also contains the title, " Snell (F. W. D.), Ueber cine 

 neue und bequeme Art, die Faktorentafeln einzurichten, nebst einer Kup- 

 fcrtafel der einfachen Faktoren von 1 bis 30000. 4to. Giessen und Darm- 

 stadt, 1800." 



The following are accounts of tables we have seen : — 



Rahn, 1659. On pp. 37-48 is given a table of divisors; viz. the least 

 divisor of every number, not divisible by 2 or 5, is tabulated from 1 to 24,000, 

 the primes being marked with a p. 



Pigri, 1758. All the simple factors (so that if multiplied together they 

 give the number) are given of all numbers from 1 to 10,000. When the 

 number is a power, letters are used instead of numbers (a = 2,b = 3,c = 5, 

 &c., as explained on p. 11 of the book) ; thus, answering to 25 Ave have cc, 

 to 27 hhh, to 225 bh, cc, &c. 



Kriiger, 1746. At the end of the ' Algebra ' is a list of primes to 100,999, 

 arranged consecutively in pages of six columns, and occupying 47 pp. The 

 titlepage runs ' Primzahlcn von 1 bis 1000000' ; but the limit is as above 

 stated ; and there is no possibility that the copy before us is incomplete, as the 

 last page is a short one, and there is no printing on the back. 



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