232 THE POPULAR SCIENCE MONTHLY 



(hundred), and its evolution is traced through later manuscripts. As 

 interesting, but not as conclusive, is an illustration from a fifteenth- 

 century manuscript containing the possible progenitor of ihe dollar sign. 



A beautifully written and illuminated copy of the Boethius arith- 

 metic, written on vellum about 1294, is one of the most valuable pieces; 

 the pigskin binding is of about the same date as the text. Just as 

 valuable, because of the rarity of the material, is the copy of al-Kho- 

 warazmi's Algebra, a Latin manuscript of 1456. The title is " Book 

 of Mohammed on Algebra and Almuchabala, or Restoration and Oppo- 

 sition." The word " algebra," like the words alchemy and almanac, is 

 of Arabic origin, having the meaning " to restore." So a surgeon, 

 restorer of broken bones, is called in Don Quixote an " algebrista." 

 The word " almuchabala " contains the idea of balance. Both of these 

 terms were applied to early algebras appearing in Europe. 



That no expense has been spared in the preparation of the " Eara 

 Arithmetica " is shown by the 255 photographic reproductions, largely 

 full-page, which constitute one of the most valuable features for bib- 

 liophiles and librarians. The tremendous labor involved in searching 

 out twelve hundred printed works, as opposed to De Morgan's one 

 hundred, can be understood only by one who has tried to make a com- 

 plete bibliography of any subject. The citations and references which 

 have been given are sufficient to indicate the fundamental importance 

 of the " Eara Arithmetica " in the history of the development of 

 arithmetic. The actual additions in the notes, to our present knowl- 

 edge, are entirely too numerous to mention. They show that the library 

 offers a rich field for research in the history of mathematics. Biblio- 

 graphically the " Eara Arithmetica " will always be an authority in so 

 far as arithmetical books of the period treated are concerned and Amer- 

 icans may justly be proud that this work, which in the nature of the 

 subject might have been considered more properly the field of a Euro- 

 pean scholar, has been so ably and finally done by a Columbia professor. 



The first of the great collections of mathematical works at all to be 

 compared with Mr. Plimpton's was made by Guillaume Libri, the author 

 of the " History of the Mathematical Sciences in Italy." The first 

 volume of his great work was just off the press at the time of the great 

 fire in Paris in 1835. Libri, who had been at the printer's, took a few 

 copies home under his arm ; the rest were destroyed. One of the copies 

 preserved, to which Libri made corrections for the second edition of 

 1838, is on exhibition in the museum of Teachers College, having been 

 bought in Italy by Professor Smith. 



Libri began his mathematical career as a boy prodigy, for at the 

 early age of fifteen he was in correspondence with famous mathema- 

 ticians, and at the age of twenty he was appointed professor of mathe- 

 matics in the University of Pisa. Being exiled from Italy for political 



