Alberti, Leone Battista
Baif, Lazare de
Baliani, Giovanni Battista
Benedetti, Giovanni Battista
Borelli, Giovanni Alfonso
Cicero, M. Tullius
Foscarini, Paolo Antonio
Guevara, Giovanni di
Jordanus de Nemore
Marci of Kronland, Johannes Marcus
Monantheuil, Henri de
Monte, Guidobaldo del
Schreck, Johann Terrenz
Stelliola, Niccolò Antonio
Wolff, Christian von
Buteo, Johannes (actually Borrel, Jean)
born around 1492, died between 1564 and 1572, French mathematician
His father François, a Seigneur d’Expenel, hailed from German nobility and supposedly fathered twenty children. Because Buteo did not want to be a burden to his parents, around the year 1508 he entered the Abbey of St. Antoine, where he studied primarily languages and mathematics, soon learning to read and understand the original Greek texts by Euclid. In 1522 he went to Paris, where he studied with Oronce Finé (1494 – 1555). In 1528 he returned to St. Antoine to resume his life as a monk. During this time he was also abbot of the monastery for two years. During the first religious war in 1562 he was forced to leave the monastery and flee to Romans-sur-Isère, where he is supposed to have died of sorrow and boredom shortly thereafter.
Buteo’s fame is based solely on his books, all of which he published after the age of sixty. His Opera geometrica appeared in Lyon in 1554 and contain fifteen articles on different mathematical subjects. The first nine articles deal with mechanical, arithmetical and geometrical problems; of these the article “Ad problema cubi duplicandi” is the most original. In this article Buteo shows that Michael Stifel (1494 - 1555) was incorrect in asserting that he had found an exact solution for the duplication of the cube, and presents his own approximate solution for this classical problem. In the final six articles he deals with the mathematical treatment of juridical problems, such as partitioning land and dividing up inheritances.
In his book De quadraturi circuli, published in Lyon in 1559, Buteo proves that the supposedly exact solutions for the squaring of the circle given by a variety of mathematicians, for instance, his teacher Oronce Finé, are incorrect, and explains the approximate solutions for squaring the circle given by Bryson of Heracleia, Archimedes and Ptolemy. The second part of this work concerns terminological issues and criticizes many of his contemporaries for their terminological errors. This second section is of particular interest for the history of mathematics for Buteo’s proof that the author of the proofs in Euclid’s Elements was not Theon of Alexandria (second half of the 4th century A.D.), as was generally presumed at that time, but rather Euclid himself. Here is where the famous dispute about the problem of the angle of tangency to a circle (Euclid Book III Prop. 16) began, in which many important mathematicians of the day participated, such as Clavius (1537 - 1612) and Peletier (1517 - 1582). In his Apologie, published in Lyon in 1562, Buteo elucidated his objections to Peletier in greater detail.
The most influential work Buteo published is his Logistica, sub-divided into five books (Lyon 1559). In the first two books Buteo deals with arithmetic, and in a third book with algebra. The fourth and fifth books concern many problems which can be solved primarily by combining arithmetic and algebra. For instance, Buteo deals quite successfully with the solution of systems of linear equations and also provides good approximate solutions for the calculation of square roots and cubic roots.
Buteo himself is a very isolated figure in the history of mathematics, as he published his books quite late in life and apparently cultivated little contact to other contemporary mathematicians, whom his sharp critique may well have antagonized.