A chronology and historical analysis of the mathematical manuscripts of Gregorius a Sancto Vincentio (1584-1667)
The Flemish Jesuit mathematician Gregorius a Sancto Vincentio is chiefly known because he published a method of squaring the circle which was refuted by Christiaan Huygens. He also coined the term ''exhaustion'' for the classical Greek method of proving equality of curvilinear areas and he found the logarithmic property of the area under the hyperbola. The circle squaring episode left him with a somewhat ambiguous reputation in the history of mathematics. The present article, based on the author's unpublished dissertation (Louvain, 1979), shows that reputation hides an interesting mathematical career. Sancto Vincentio taught mathematics in Antwerp, Ghent and some other places in the southern Netherlands; several of his pupils published mathematical work, partly in defence of their master. Sancto Vincentio's book on the quadrature (1647) contains a number of beautiful results in the geometry of areas and solids. The book has an interesting publishing history. Sancto Vincentio asked permission to publish his method, and his superiors reacted with extreme caution, knowing well the dangers of official church support of scientific work on a controversial subject understood by few. After a short biographical section, the author presents a chronology and an analysis of the manuscripts of Sancto Vincentio (now kept in the Royal Library Albert I in Brussels). He devotes separate sections to special items in the collection, as e.g. a manuscript by F. de Aguilon (1566- 1617) with interesting theorems on conic sections, Sancto Vincentio's studies on the logarithmic property of the hyperbola, and his procedure called ''ductus plani in planum'' for forming solid figures and determining their volume. The article provides an insight in the activity of a school of mathematics which was out of the main stream of seventeenth century mathematics (there are no references to the new analytical methods), but which showed good knowledge of classical methods and, keeping to the old style, produced interesting results.
scientific article; zbMATH DE number 3847334