This is a second slice from the book *From Five Fingers to Infinity*, edited by Frank Swetz and published by Open Court in 1994. *Five Fingers* was aimed at mathematics teachers and the (mythical?) general reader, as shown by the fact that I bought mine from the (now long defunct) Quality Paperback Book Club. It collected many articles about the history of mathematics organized in eight parts. The articles were a motley group: older and newer, from sources ranging from *Scripta Mathematica* to *The Mathematics Teacher*. The desire to remain accessible, however, clearly dictated that the majority of the articles should come from journals dealing in less technical materials, so there were many more articles from *The Mathematics Teacher* than from MAA journals.

A previous slice of *Five Fingers*, dealing with mathematics since 1800, was brought out by Dover with the title *The Search for Certainty.* That was also the title of part VIII of *Five Fingers*, from whence it came. There were a few bits of added material, but most of the articles were exactly the same.

The current selection has a more complex relation to the original: it collects (most of the) articles from parts IV (European Mathematics During the "Dark Ages"), VI (The Revitalization of European Mathematics), and VII (Mathematical Responses to a Mechanistic World Outlook) of the original book and spans a much broader period, about 1000 to 1800. Apart from preface, notes, bibliography and other ancillary material, the new items here are a three-page introduction entitled "Perspective: The European Mathematical Awakening" and "Historical Exhibit 9", which shows multiplication algorithms of the 15th and 16th centuries. The majority of the articles were originally published by *The Mathematics Teacher* in the 1950s or 1960s, which must have been a golden era for historical material in that journal. It is good to have them gathered here, though of course one must be cautious about checking the accuracy of 50-year-old material. In many cases, Swetz has appended a brief editorial note pointing to more recent publications dealing with the material in the article, making this version more useful than the original *Five Fingers* version.

Three articles from MAA journals are included. From the *American Mathematical Monthly* in 1919, "Leonardo of Pisa and His *Liber Quadratorum*" is a useful survey of that work that gets extra points from me for not using "Fibonacci" in the title. From the *College Mathematics Journal* in 1987 come two well-known articles: Fred Rickey's "Newton: Man, Myth, and Mathematics" and Bill Dunham's "The Bernoullis and the Harmonic Series"; the latter eventually became a chapter in *Journey through Genius.*

I'll point out one missed opportunity: Swetz includes a couple of articles on the introduction of decimal fractions in Europe, but does not include two brilliant (and hard to find) articles by David Fowler: "400 Years of Decimal Fractions" and "400.25 Years of Decimal Fractions", both from *Mathematics Teaching*, which I think is the British equivalent of our *The Mathematics Teacher*.

*The European Mathematical Awakening* is a very useful collection of historical articles that can, among other things, be used as side reading for a history of mathematics course focusing on this period. (I did that recently with *The Search for Certainty*.) Students will love the fact that it is affordable and easy to read, and some of the articles may be useful jumping-off points for further research.

Fernando Q. Gouvêa teaches History of Mathematics (and many other things) at Colby College, where he is Carter Professor of Mathematics.