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 the 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 “ Rara 
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 “Rara 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 brary 
offers a rich field for research in the history of mathematics. Biblio- 
graphically the “ Rara 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 
