# Alphonse Antonio de Sarasa

Solutio problematis a R. P. Marino Mersenno minimo propositi, 1649

Alphonse Antonio de Sarasa was a Jesuit mathematician who contributed to the understanding of logarithms, particularly as areas under a hyperbola.[1]

Alphonse de Sarasa was born in 1618, in Nieuwpoort in Flanders. In 1632 he was admitted as a novice in Ghent. It was there that he worked alongside Gregoire de Saint-Vincent whose ideas he developed, exploited, and promulgated. According to Sommervogel,[2] Alphonse de Sarasa also held academic positions in Antwerp and Brussels.

In 1649 Alphonse de Sarasa published Solutio problematis a R.P. Marino Mersenne Minimo propositi.[3] This book was in response to Marin Mersenne’s pamphlet "Reflexiones Physico-mathematicae" which reviewed Saint-Vincent’s Opus Geometricum and posed this challenge:

Given three arbitrary magnitudes, rational or irrational, and given the logarithms of the two, to find the logarithm of the third geometrically.

R.P. Burn[4] explains that the term logarithm was used differently in the seventeenth century. Logarithms were any arithmetic progression which corresponded to a geometric progression. Burn says, in reviewing de Sarasa’s popularization of de Saint-Vincent, and concurring with Moritz Cantor, that "the relationship between logarithms and the hyperbola was found by Saint-Vincent in all but name".

Burn quotes de Sarasa on this point: "…the foundation of the teaching embracing logarithms are contained" in Saint-Vincent’s Opus Geometricum, part 4 of Book 6, de Hyperbola.

Alphonse Antonio de Sarasa died in Brussels in 1667.

## Works

Sarasa, Alfonso Antonio (1649). Solutio problematis a R. P. Marino Mersenno minimo propositi, datis tribus quibuscumq[ue] magnitudinibus, rationalibus vel irrationalibus, datisque duarum ex illis logarithmis, tertiae logarithmum geometricè invenire. Jan van Meurs, Jacob van Meurs.