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By I. Satake

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This was basically a 122-page bibliography of Portuguese mathematics works written in the 19th century, compiled according to the norms of the 1889 Congrès International de Bibliographie des Sciences Mathématiques, but also included two very small introductory essays on both Portuguese and International mathematics of the 19th century. Encouraged by a review from Gustav Eneström (1852–1923) in Bibliotheca Mathematica, Guimarães worked in the following nine years in expanding this work, not only producing a comprehensive bibliography of all Portuguese mathematical works, but also including a 96-page essay on the History of Portuguese mathematics [12].

This work was published in book form in 1909 with the slightly modified title Les Mathématiques en Portugal, reflecting the change in scope of the book. It included a 51-page Appendice with a bibliographical update for the period 1906–1908. In 1911 a second Appendix appeared [13], with a list of works not included in [12], as well as a bibliographical update for the period 1909–1911. 1. Les Mathématiques en Portugal (1909) Guimarães has 10 of his 96 pages of this book on the so-called the decline period (1536–1750).

12] This quotation highlights the strength and weakness of da Cunha’s writing: he is aware of important works done on history outside the mathematics field, he gets some interesting ideas, but he seems unable (or not wanting) to do further research on his own, based on the new ideas he gets from these sources. His statements have a vagueness and a lack of precision that prevents the reader from having any clear view of the situations described or analyzed. For instance, from the above quote one could never understand what is the specificity (and relevance) of the Ratio Studiorum.

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