Grégoire de Saint-Vincent
Grégoire de Saint-Vincent (French pronunciation: [ɡʁeɡwaʁ də sɛ̃ vɛ̃sɑ̃]) - in Latin : Gregorius a Sancto Vincentio, in Dutch : Gregorius van St-Vincent - (8 September 1584 Bruges – 5 June 1667 Ghent) was a Flemish Jesuit and mathematician.
Grégoire gave the "clearest early account of the summation of geometric series.
"[1]: 136 He also resolved Zeno's paradox by showing that the time intervals involved formed a geometric progression and thus had a finite sum.
That year he became obsessed with squaring the circle and requested permission from Mutio Vitelleschi to publish his method.
He returned to the Netherlands in 1627, and the following year was sent to Prague to serve in the house of Emperor Ferdinand II.
When the Saxons raided Prague in 1631, Grégoire left and some of his manuscripts were lost in the mayhem.
Then it "attracted a great deal of attention...because of the systematic approach to volumetric integration developed under the name ductus plani in planum.
"[1]: 135 "The construction of solids by means of two plane surfaces standing in the same ground line" is the method ductus in planum and is developed in Book VII of Opus Geometricum[1]: 139 In the matter of quadrature of the hyperbola, "Grégoire does everything save give explicit recognition to the relation between the area of the hyperbolic segment and the logarithm.
"[1]: 138 The manuscript also claimed to solve the ancient problem of squaring the circle, for which it was criticized by others, including Vincent Léotaud in his 1654 work Examen circuli quadraturae.
A. de Sarasa noted that this area property of the hyperbola represented a logarithm, a means of reducing multiplication to addition.
In 1651 Christiaan Huygens published his Theoremata de Quadratura Hyperboles, Ellipsis, et Circuli which referred to the work of Saint-Vincent.
Saint-Vincent was lauded as Magnan and "Learned" in 1688: “It was the great Work of the Learned Vincent or Magnan, to prove that distances reckoned in the Asymptote of an Hyperbola, in a Geometrical Progression, and the Spaces that the Perpendiculars, thereon erected, made in the Hyperbola, were equal one to the other.”[8] A historian of the calculus noted the assimilation of natural logarithm as an area function at that time:
