Using Euclid in a Practical Context: Claude Richard’s Course on Sectors at the Imperial College (Madrid, ca. 1656)

Father Claude Richard (Ornans 1589 – Madrid 1664) was professor of mathematics at the Jesuit Imperial College in Madrid (1627-1767) from 1630 until his death. He published Euclides elementorum geometricorum libros tredecim Isidorum et Hypsidem et Recentiores de Corporibus Regularibus, et Procli propositiones geometricas (Antwerp, 1645), and Apollonii Pergaei Conicorum libri IV cum commentariis Claudii Richardi (Antwerp, 1655). Furthermore, the Spanish Royal Academy of History keeps a legacy of eleven manuscript files –titled Mathesis varia– by Richard, together with eighty factitious volumes containing Jesuits’ manuscripts on mathematics and physics. Among these, two draft copies of the course on the construction and use of sectors taught by Richard around 1656 have been identified, one written by Richard himself, the other by one of his students. Richard claimed that the whole practical geometry consisted of the brief and easy use of sectors, an instrument first invented by the Flemish Michel Coignet, he said. However, his “Treatise on the division of the twelve diverse straight lines of sectors, with their practical use in practical geometry, and also the proofs of these divisions and the use” was not only concerned with the brief and easy instrumental practice of geometry. It also insisted on demonstrating the solid Euclidean foundations of this practice, which would justify the numerical consideration of continuous magnitudes as quantities –accepting a margin of error sensorially imperceptible and irrelevant for the purposes of application.