Johannes Buteo

Background

Johannes Buteo was born in 1492, in Charpey, Dauphiné, France. Buteo’s father, François, seigneur d’Espenel, is said to have had twenty children.

Education

Because he did not wish to be a burden to his parents, Buteo entered the Abbaye de St.-Antoine about 1508. He had so much feeling for languages and mathematics, that he soon could comprehend Euclid in the original Greek. In 1522 he was sent to Paris, where he studied under Oronce Fine.

Career

By 1528 Buteo longed for his monastic life and returned to the Abbaye de St.-Antoine; he was abbot during two of his years there. In 1562, during the first of the Wars of Religion, he had to leave the monastery and take refuge with one of his brothers in Romans-sur-lsère. He died there of grief and boredom.

Buteo published his works only after he was sixty years old. The Opera geométrica contains fifteen articles on different subjects, the last six showing his interest in law through the treatment of such mathematical aspects of jurisprudence as a division of land and inheritances. The first nine articles treat mechanical, arithmetical, and geometrical problems. The most original is Ad problema cubi duplicandi, in which he refutes Michael Stifel’s claim of an exact solution to this problem and gives an approximate one.

This is also the main theme of De quadratura circuit, in which Buteo refutes the pretensions of those who claimed to have found the solution of the quadrature, most notably those of his master, Oronce Fine. By contrast, he discusses appreciatively the approximations found by Bryson, Archimedes, and Ptolemy.

In the second part of this work, Buteo criticizes errors of many of his contemporaries, particularly in terminological questions. An interesting point is his proof that the author of the proofs of Euclid’s Elements was not Theon, as was the current opinion, but Euclid himself. Here, too, are the beginnings of the famous dispute involving Peletier, Clavius, and many others on the angle of contact. In the Apologia (1562) Buteo pursued his refutation of Peletier’s theories.

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.

Achievements

• Buteo achieved his fame solely through 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 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.
  
  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.

Works

More photos

• book

  • Delphinatici Opera Geometrica Quorum Tituli Sequuntur 1554
  • De quadratura circuli libri duo, vbi multorum quadraturae confutantur 1559

Religion

In his religious affiliation, Buteo was a Roman Catholic. By 1528 he longed for his monastic life and went to the Abbaye de St.-Antoine, where he was abbot during two of his years there.

Personality

Johannes Buteo's original French name was Jean Borrel (bourreau means “executioner,” but is also a popular name for the buzzard, and in this last sense is translated as Buteo). There were such variants as Boteo, Butéon, and Bateon.

Buteo’s has been a solitary figure in his love of mathematics and mechanics, and he wanted to be so. As far as it is known, he had no pupils; and his criticism, often excessively sharp, must have estranged other mathematicians.

Connections

Father:

François Buteo

teacher:

Oronce Finé

Oronce Finé (Latin: Orontius Finnaeus or Finaeus; Italian: Oronzio Fineo; 20 December 1494 – 8 August 1555) was a French mathematician and cartographer.

References

• Dictionary of scientific biography
  1981