234 THE POPULAR SCIENCE MONTHLY 



The small collection of Augustus De Morgan is worthy of note, as it 

 furnished the stimulus for the publication of the first work dealing 

 wholly with the bibliograhy of arithmetic, De Morgan's " Arithmetical 

 Books/' published in London in 1847. Of the fifteenth and sixteenth 

 centuries De Morgan described some seventy arithmetics, while the 

 " Eara Arithmetica " describes well over four hundred. A quotation 

 from the prefatory letter by the great English mathematician in which 

 the book is inscribed to the Eev. George Peacock, a writer on the history 

 of arithmetic, is worth giving : " The most worthless book of a bygone 

 day is a record worthy of preservation. Like a telescopic star, its 

 obscurity may render it unavailable for most purposes; but it serves, 

 in hands which know how to use it, to determine the place of more 

 important bodies." De Morgan's felicity of expression in his numerous 

 publications — he was an extensive contributor to encyclopedias — sug- 

 gests his kinship to the present popular novelist, William Frend De 

 Morgan, his son. 



While the " Arithmetical Books " by De Morgan dealt wholly with 

 arithmetical works, many others have treated the bibliography of mathe- 

 matics. One of the earliest to give fairly extensive bibliographical 

 references to mathematical literature is the " Kitab al-Fihrist," or 

 " Book of Eecords," an Arabic treatise written in a.d. 987. The mathe- 

 matical section of this large book was translated into German by H. 

 Suter and appeared in Leipzig in 1892. The author, who went by the 

 melodious name of Abou'l-Faradsch Mohammed ibn Ishak, or more com- 

 monly by the name Ibn Abi Ja'kub al-Nadim, included all the writers 

 known to him, of whatever nationality. The Kitab al-Fihrist is of the 

 greatest importance in the history of mathematics, as it is, indeed, in 

 the history of the development of Christianity, for the writer describes 

 various early sects of the christians. An appreciably large part of our 

 knowledge of Greek mathematics comes from such Arabic sources, for 

 the Arabs kept the spark of Greek learning alive while Europe was in 

 the darkest of the dark ages. 



Our interest, however, is in the bibliographers who treated the early 

 printed works. Gerard Joannis Vossius in 1650 published in Amster- 

 dam his work, " On the Four Arts," which is an unreliable mixture of 

 bibliographical and historical material. Naturally many histories of 

 mathematics treated also the bibliography of the subject. The first 

 German work to attempt a somewhat complete list of early printed 

 books in mathematics was the " Einleitung zur mathematischen Biicher- 

 kentnis," which J. E. Scheibel completed in 1769 and of which at least 

 two editions appeared. Other German publications, purely bibliograph- 

 ical, are F. G. A. Murhard's " Literatur der mathematischen Wissen- 

 schaften " of 1797 and J. Eogg's " Handbuch der mathematischen 

 Literatur," which catalogued and described books from the invention of 



