CALCULUS Understanding Its Concepts and Methods

Gregory of St. Vincent (1584--1667) --- Historical Sketch

Gregory of Saint Vincent is also known as Gregorius Saint-Vincent and as Gregory St. Vincent, SJ. He was born in 1584 in Bruges or Ghent, Belgium and he became a Jesuit. He taught in Brussels, Antwerp, Louvaine, and Ghent, where he lived out his life, dying in 1667.

Gregory was reputed to be a brilliant mathematician. Leibniz reportedly included him with Descartes and Fermat as one of the founders of analytic geometry. He is reported to be the first to settle Zeno's Achilles paradox, doing it the way we would do it now---summing an infinite geometric series (see the problem below). This paradox had baffled philosophers for centuries, and still baffles today. He found areas and volumes computing limiting forms of sums of small areas and volumes---essentially by integral calculus---very much as Archimedes did. He essentially integrated the function , and got what we today call the logarithmic function. His written mathematical works are contained in a book of some 1250 pages.

Here is Zeno's Paradox in a nutshell**:** I am in a room and want
to leave. I must first cover half the distance from where I am to the door.
Having done that, I must then cover half the remaining distance to the door.
Having done that, I must cover half the remaining distance to the door. And so
forth, forever, so I cannot get to the door. Can you resolve this paradox by
summing an infinite geometric series?

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.