Gerard of Brussels

Background

Gerard was born in twelfth century in Brussels, Belgium.

Education

Gerard presumably studied at the University of Paris.

Career

Gerard's career remains obscure except for his having written treatise entitled Liber de motu, which remains in six manuscripts. Four of these date from the thirteenth century. Written sometime between 1187 and 1260, the Liber de motu quotes the translation of Archimedes’ De quadratura circuli (“On the Measurement of the Circle”) by Gerard of Cremona. The translation was completed before the translator died in 1187. On the other hand, the Liber de motu is mentioned in the Biblionomia of Richard of Fournival, who lived in 1260.

Gerard seems to have known the Liber philotegni de trangulis of Jordanus de Nemore, whose exact dating is as difficult to determine as that of Gerard but who can be placed, with some confidence, in the early decades of the thirteenth century. The similarity in their names suggests that Gerard may be identified with the unknown mathematician Gernardus who wrote an arithmetical tract Algorithmus demonstratus.

The Liner de motu contains thirteen propositions, in three books. In these propositions the varying curvilinear velocities of the points and parts of geometrical figures in rotation are reduced to uniform rectilinear velocities of translation. The four propositions of the first book relate to lines in rotation, the five of the second to areas in rotation, and the four of the third to solids in rotation, Gerard’s proofs are particularly noteworthy for their ingenious use of an Archimedean-type reductio demonstration, in which the comparison of figures is accomplished by the comparison of their line elements. In this latter technique Gerard assumed that if the ratio of the elements of two figures taken in pairs is the same, then the ratio of the totalities of the elements of the figures is the same. Such a technique resembles the procedure followed in Archimedes’ Method, which Gerard could not have read.

Gerard’s influence on Thomas Bradwardine, the founder of the Merton school of kinematics, is evident, for Bradwardine knew and quoted Gerad’s tract. Furthermore, Nicole Oresme’s De configurationibus qualitatum, written in the 1350’s, shows some possible dependency on the De motu.

Achievements

• Gerard of Brussels was an eminent mathematician. He is known primarily for his Latin book Liber de motu, which was a pioneering study in kinematics. His chief contribution was in moving away from Greek mathematics and closer to the notion of "a ratio of two unlike quantities such as distance and time", which is how modern physics defines velocity.

Works

More photos

• book

  • The Liber de Motu

References

• Dictionary of Scientific Biography