124 3Ir Glaisher, On factor tables. [Feb. 11; 



In tlie preface Chernac speaks of the work as one not of 

 months, but of years. There is an introduction, containing brief 

 notices of the previous tables and writings ; a list of these has 

 been given in § 3. The notices seem to be very accurate : all 

 the statements that I have verified I have found to be quite 

 correct. It is very remarkable that, although the preface and 

 introduction occupy 21 pages, Chernac does not say a word as to 

 the way in which he calculated the table, and he only alludes in 

 very vague terms to the mode of formation of factor tables\ 



With regard to the title of the work, Chernac prints on the 

 back of the title-page the following explanation : "Celeber. J. Alb. 

 Fabricius, in Biblioth. Gr. Vol. III. c. 18. scripta Eratosthenis de- 

 perdita, sed passim ab antiquis laudata recenset, quibus annumerat 

 etiam K.6(rKtvov, Cribrum Arithmeticum, de quo hsec verba profert : 

 'Nee aliud quicquam est, (cribrum arithmeticum) quam tabella 

 numeros impares complectens, adscriptis ad composites numeros 

 communibus divisoribus, ut compositi a simplicibus distinguantur, 

 et statim constet de compositorum divisore.' Hsec apponere volui, 

 ne quern offendat operis inscriptio. De cribro Eratosthenis plura 

 dicam, suo loco." 



At the beginning of his historical account he writes, "Inter prisci 

 8Bvi mathematicos, Eratosthenes fertur viam monstrasse indi- 

 rectam, ad numeros simplices a compositis secernendos. Cujus 

 rei testes sunt Nicomachus Gerasenus, et Boethius. Hujusmodi 

 investigationem nominabat Eratosthenes cribrum (KoaKtvov). 

 Sicut enim cribro pollinario, partes farinas subtiliores a crassiori- 

 bus secernuntur; ita ope hujus methodi, numeri simplices a 

 compositis, tanquam per cribrum segregantur et rejiciuntur. 

 Cribri hujus meminit etiam Jamblichus Chalcidensis, in Isagoge 

 ad Arithmeticam Nicomachi pag. 89 et 42 ex edit. Tennulii." 



It is curious that the word which seems to have been used to 

 denote both the table itself and the general method of forming it, 

 should be so exactly appropriate to the perforated sheets, which 

 j)lay so imjDortant a part in the construction of a factor table by 

 Burckhardt's method (see § 20). 



§ 15. In 1814 Burckhardt published at Paris his " Tables 

 des diviseurs pour tous les nombres du deuxieme million, ou plus 

 exactement, depuis 1020000 a 2028000, avec les nombres pre- 

 miers qui s'y trou vent.... Par J.-Ch. Burckhardt... Paris... 1814." 



It contains the least factor of every number not divisible by 



^ His words are: "His.de causis, hujtismodi tabularum conditores, in iis ador- 

 nandis via incednnt non directa, et numeros primos adgrediuntur, non aperto 

 Marte, nee a fronte, sed a tergo. Loqnar planius: methodo, a vnlgari discrepaute, 

 matlieseos cultoribus non iguota, qii£eri-int compositorum diyisores. Quibus inventis 

 numeri primi antea delitesceutes in apertum prodeunt, quasi nudati et divisoribus 

 destituti." {Isagoge ad tabidam, p. Ti.) 



