Francisco de Melo and the Euclidean Tradition in Portugal


FCT Exploratory Research Project

This project, funded by the Fundação para a Ciência e Tecnologia of the Portuguese Ministry of Education and Science (FCT EXPL/IVC-HFC/1290/2012), started in June 2013 and has been prolongated until December 2014. On this site, you will find information on the mathematician Francisco de Melo (1490-1536), on Portuguese manuscripts related to the Euclidean tradition in Portuguese archives and libraries.

Summary of the Project

Melo's commentaries on Euclid and Pseudo-Archimedes


The manuscript COD. 2262 of the National Library of Portugal (BNP) is one of the most valuable items of Portuguese heritage. Written in Latin, it contains a small treatise about the structure of the eye and the principles of vision, followed by commentaries on Euclid’s Optics and Catoptrics, a small study of statics formerly attributed to Archimedes (De ponderibus siue de incidentibus in humidis) and finally, an unfinished commentary on a text of the Arab astronomer known by the Latin name of Gebre.Its author was Francisco de Melo (c. 1490-1536), a Portuguese humanist to whom King Manuel I granted a scholarship to study Arts, Mathematics and Theology in the University of Paris, where he also taught, and eventually became the Director of the University of Lisbon (1529-1533). He was the most important Portuguese mathematician of his time, revered inside and outside Portugal, both by his peers and by common people. This is confirmed by many sources, such as; among others, Gaspar Lax, in the preface to his own Arithmetica Speculativa duodecim libros demonstrata (1515); Gil Vicente, in the prologue to the Trovas de Filipe Guilhém and to the Auto da Feira; André de Resende, in his Oratio pro rostris (1534).

The need to study this manuscript according to a Portuguese and European perspective has been emphasized by many national and international scholars, such as Luís de Albuquerque or Marshall Clagett; the latter even edited the part of the manuscript related to Pseudo-Archimedes, in a work internationally recognized as among the best in its field of scholarship [note: Archimedes in the Middle Ages: The Fate of the Medieval Archimedes, Philadelphia, American Philosophical Society, 1978, vol. 3, pp. 146 ss.]. The alleged reasons are very strong indeed: it is the only known mathematical work of Francisco de Melo, it is the only of its kind written by a Portuguese scholar with worldwide reputation and it constitutes one of the oldest surviving testimony of the attempts to interpret texts related to Euclid and Archimedes during the Renaissance.

Despite these facts, the contents of the manuscript remain unpublished. Two reasons justify this state of affairs. The transcription of the text is especially difficult to carry out because of the handwriting and the bad conditions of the codex itself; the translation and study are complex tasks because the text is written in a very technical Latin, and the interpretation of its contents requires specific skills in the domain of mathematics, classical studies and history of sciences. The state-of-the-art and the to-do-list related to this manuscript remains the same since Teófilo Braga wrote, some 120 years ago: “it is a shame that these commentaries remain unpublished; edited with a critical-historical study, they would relate Portugal to the intellectual movement of the Renaissance in a dignifying manner” [note:História da Universidade de Coimbra nas suas relações com a Instrução Pública Portuguesa, Lisboa, Tipografia da Academia Real das Ciências, 1892-1902, 4 vols., vol. I (1289 a 1555), p. 324].

An unexpected discovery made this task pressing and unavoidable. The BNP was informed, in the end of 2011, that the manuscript originally offered by Francisco de Melo to King Manuel I as a gift in return for the scholarship granted to him, and whose relation to the copy located in the BNP remains obscure, had been found in the small City Archive of Stralsund (Germany), after being lost for almost 250 years.

This project proposes to edit, translate and study the commentaries of Francisco de Melo to Euclid and Pseudo-Archimedes, based on the two copies known at the moment, now that the existing circumstances are so much favourable to interpret such fundamental source of Portuguese culture with so high an international significance.

The Euclidean Tradition in Portugal


This being an exploratory project, the team members wish to follow a second line of investigation, which will complement the main research. Given the fact that Francisco de Melo states that he had taught some lessons on Euclid’s Elements, it will be determined whether there is a specific Portuguese tradition related to the interpretation of Euclidean treatises on optics and geometry. To achieve this task, a list of Euclid-related manuscripts and printed sources available in libraries and archives of Lisbon will be made, without any chronological boundaries. An anthology, with an introductory study, will be prepared, in order to produce new perspectives for future projects of investigation. The study of a particular mathematical tradition with roots in Antiquity as a part of Portuguese culture is a novelty in our country. The work of Francisco de Melo alone justifies such an endeavour.


Updated: 4 February 2015