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232 (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 arithmetic, 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-Khowarazmi's Algebra, a Latin manuscript of 1456. The title is "Book of Mohammed on Algebra and Almuchabala, or Restoration and Opposition." 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 bibliophiles 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 complete 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 knowledge, are entirely too numerous to mention. They show that the library offers a rich field for research in the history of mathematics. Bibliographically the "Rara Arithmetica" will always be an authority in so far as arithmetical books of the period treated are concerned and Americans may justly be proud that this work, which in the nature of the subject might have been considered more properly the field of a European 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 mathematicians, and at the age of twenty he was appointed professor of mathematics in the University of Pisa. Being exiled from Italy for political