Jesuit Geometers

Excepts from the book by Joseph F. MacDonnell, S.J.

Jesuit Geometers

A Study of Fifty-six Prominent Jesuit Geometers During the First Two Centuries of Jesuit History
by Joseph MacDonnell, S.J.
Professor of Mathematics
Fairfield University

Published jointly in 1989 by
The Institute of Jesuit Sources and The Vatican Observatory

Distributed (except in Italy and Vatican City State) by:
The Institute of Jesuit Sources
St. Louis University
3700 West Pine Blvd.
St. Louis, Missouri 63108
Tel. 314-652-5737

Distributed in Italy and Vatican City State by:
Libreria Editrice Vaticana
V-00120 Citta' del Vaticano
Vatican City State

Library of Congress Catalog Card number: 89-80568
ISBN 0-912422-94-7

The contents of the whole book JESUIT GEOMETERS is now on the web and can be viewed at the following location:

The OBELISK of Jesuit Kircher
resting on Bernini's ELEPHANT
For the first two centuries of Jesuit history 631 Jesuit geometers are listed in Sommervogel's twelve volume work Bibliotheque de la Compagnie de Jesus 1 where their publications are evaluated and described. The title Jesuit Geometers, however, might seem incongruous since the word Jesuit conjures up images of martyrs and missionaries like Brebeuf, Xavier and deNobile, theologians like Suarez, the Church Militant exemplified in Bellarmine, or preachers like Bourdaloue.
On the other hand Euclid, Appolonius, Menelaus, Descartes, Fermat, Euler, Desargues and Lobachevski were geometers but not Jesuits. So what does the Society of Jesus have to do with geometry? In the educational work of the Society geometry played a very important role right from the very beginning.

Apart from their classroom teaching, many Jesuits by their curiosity, ingenuity, correspondence, and publications contributed greatly to the growth of geometry. Their practical geometrical inventions, their discoveries of new forms of geometry, and their innovations in the teaching of geometry contributed greatly to its development. Furthermore their knowledge of geometry proved an invaluable aid in establishing missions in all parts of the world so that non-Jesuit, non-Catholic, non-Christian geometers benefited from their labors and skill. While there is no such thing as Jesuit geometry, it is certain that the geometries so familiar today would have a different form and encompass far less if these men had never existed.

The first sketch of a photometer was by Peter Pau lRubens
and is found in the book on OPTICS by the Jesuit d'Aguilon.
During their first two centuries the Jesuits were involved in an explosion of intellectual activity, engaged in over 700 schools. Then suddenly these were all lost in 1773. During the 1769 conclave the Franciscan Friar Lorenzo Ganganelli became Pope Clement XIV. Four years later, yielding to pressure from the Bourbon courts, fearing the loss of his Papal States, and anticipating that other European countries would follow the example of Henry VIII, he issued his brief Dominus ac Redemptor suppressing the Society. This religious order of twenty-three thousand men dedicated to the service of the church was disbanded. All seminarians were sent home, all houses given away, and the Jesuit general Lorenzo Ricci was arrested and put in solitary confinement in the prison of Castel Sant' Angelo, where he died a few years later. The property of the Society's many schools was either sold or made over into a state controlled system. The Society's libraries were broken up and the books either burned, sold or snatched up by those who collaborated in the suppression. Ever since then the Society's books have been appearing in private collections of book harvesters or in the great libraries throughout the world. The unusual method of promulgation of the brief of suppression (wherein each bishop had to proclaim it to all Jesuits within his jurisdiction) caused perplexing canonical difficulties. So when Catherine, Empress of Russia, rejected the brief outright and forbade its promulgation, 200 Jesuits continued to function in Russia.

Jesuit Riccioli's lunar map is found at the entrance to the Smithsonian's lunar exhibet.
The Society was restored 41 years later in 1814 by Pope Pius VII, who celebrated the feast of St Ignatius by reading the bull Sollicitudo Omnium Ecclesiarum , revoking the suppression, in the presence of 150 members of the suppressed society.
Although many of the men had died by then, the memory of their educational enterprise had not, and the new Society was flooded with requests to take over colleges: in France alone, for instance, 86 schools were offered to the Jesuits; of course they could accept only a few.
The Jesuits have had more than their share of enemies but even the bitterest would not deny their mathematical accomplishments. These have, however, been minimized by past historians. The claim, for instance, was made that Jesuits were Aristotelians and therefore were not open to modern geometrical trends or that their religious convictions hindered free inquiry. The assumption was that only agnostics are truly free from bias and able to pursue truth with an open mind. An earlier edition of the Encyclopedia Britannica (the eleventh) branded the work of Jesuit geometers as "respectable mediocrity". Later editions leave out this derogatory passage, which is not shared by modern historians. Another problem occurs when some writers unskilled in church matters, make the assumption that all priests are Jesuits. Thus an article in Scientific American blames the suicide of Galois' father on the "Jesuit priest of Bourg-la-Reine". Although this occurred at a time when there were no Jesuits within hundreds of miles.
D'Aguilon's theory of binocular vision was illustated by Peter Paul Rubens.
And, finally, some Jesuit mathematicians and scientists have not been identified as Jesuits. The world famous Jesuit astronomer Angelo Secchi, S.J. of the past century has been referred to as P. (for Pater) Secchi. The P. Secchi has been transformed into Pietro Secchi by an inventive writer.
The purpose of this work is to examine these Jesuit geometers and their accomplishments during the 17th and 18th centuries while geometry was in a crucial stage of its development. Their effective influence on the growth of geometry should be evident from their original thinking, inventions, innovations, publications, teaching, correspondence and their determination to disseminate geometrical concepts accurately. Their evaluation by their peers and by later professionals makes it even more evident.
These two centuries between 1570 and 1770 were also critical in the growth of mathematics during the time the calculus was evolving. Discoveries were being made and concepts developed which enabled giants like Newton and Euler to articulate the foundations of modern analysis. In particular it was a critical time for geometry because not only were the seeds being planted for the later geometries but also proofs of the precalculus as well as the calculus principles had to be geometrical. Until the time of Fermat and Descartes nongeometrical proofs simply were not acceptable: Newton, for example, proved his theorems geometrically. The motto of the American Mathematical Society, founded a hundred years ago in 1888, was inspired by Clio, the muse of history, and Urania, the muse of mathematics and astronomy. It reminds its readers that admittance to Plato's academy requires geometry. A rough translation of the Greek inscription is: "Let no one unversed in geometry enter my door."
Furthermore, geometry in these centuries came to include not only the synthetic geometry of Euclid but all kinds of applications: dyalling, gnomonics, geometrical optics, map-making, stereometry, plane and spherical trigonometry. The need for rigor and logic was being recognized, also, and it was in geometry that this need was felt most acutely. Histories of geometry may emphasize the works of these aforementioned giants, but the story of geometry cannot be fully appreciated without examining the contributions of the lesser geometers in order to trace how the ideas originated, in order to gain a fuller understanding of the concepts. In his History of Mathematics Carl Boyer quotes Newton writing to Hooke: "If I have seen farther than Descartes, it is because I have stood on the shoulders of giants."
On the other hand, the same two centuries were critical for Jesuits since the young society grew from ten members in 1540 to twenty-three thousand members at the time of the suppression in 1773. The number of Jesuit schools in Europe kept increasing so that it became the largest school system in Europe. Around the middle of the eighteenth century, the Jesuits operated 740 educational institutions throughout the world 14 of which were universities. Besides this, Jesuits taught in 11 state universities. In particular it was a critical time for Jesuit geometers since they were engaged in the great creative innovations in geometry. George Sarton spoke of the Jesuit mathematicians of the time in his article An Appeal for the Republication in Book Form of Fr. Bosmans' Studies. "One cannot talk about mathematics in the 16th and 17th centuries without seeing a Jesuit at every corner".
The story of the Jesuit contribution to geometry at this time has not been told, even though much work has been done by Jesuit historians such as Henri Bosmans. Conor Reilly noted that "Jesuits have done little to reveal the contributions of their predecessors to the foundations of modern science." Jesuits, furthermore, are challenged by the historian D. J. Struik: "When are you Jesuits going to write a coherent history of Jesuit mathematics basedon the groundwork of Henri Bosmans?"
Jesuit Perspective Geometer, Andrea Pozzo's Triumphant Ceiling in St. Ignatius Church in Rome
This work is certainly not an adequate response to Struik's invitation but may serve as a step in that direction. It is not meant to be a history of Jesuit mathematics but rather a story about Jesuit mathematicians; it does not describe the details of their geometry but instead stresses the contributions Jesuits made during the development of geometry. All of the 56 men mentioned wrote books on geometry. They were, therefore, geometers, even though many of them worked in other fields as well. Indeed, some were better known as astronomers, physicists or "philosophers of nature." These men were not of the stature of Newton and Euler but were some of the lesser geometers mentioned above whose story should be told. To speak only of Jesuit geometers here does not mean that other geometers were doing nothing; on the contrary a common effort and exchange of ideas occurred that moved geometry forward and made it possible for the greater mathematicians to discover and articulate the major breakthroughs leading to the calculus. The story of similar non-Jesuit geometers can be told elsewhere.
The exchange of ideas was not only through letters and publications but also through the normal teacher/student process. After a teacher presented his analysis, an alert student would take the notes and try to improve on the matter and then later as a teacher pass the improved version on to the next group of students. Jesuits and non-Jesuits quoted each other without always giving credit. Euclid, for instance, was not accused of this, yet he was writing down what was the accumulated geometrical wisdom of that time. Galileo made very free use of Jesuit geometers' teaching notes without making any acknowledgment. While serious priority arguments did occur, historians have, perhaps, made accusations of plagiarism too lightly without considering the spirit of the times.
Jesuit Geometer Kircher's famous Tower of Babel
A case in point is that of the Jesuit Paul Guldin, author of Guldin's rule for finding volumes of revolution by using the center of gravity. A few decades ago some authors and publishers had removed his name from calculus textbooks and substituted Pappus' name because an unfounded accusation of plagiarism was believed. It has been well established by modern historians, specialists in that era, such as Paul Ver Eecke, that Guldin was falsely accused. The Dictionary of Scientific Biography (DSB) brings up another problem regarding false accusations about Jesuit scientists and the fact that after the suppression of the Jesuits in 1773 they had no forum to defend themselves. Konradin D'Occhieppo speaks of "the public defamation of the Jesuits then in vogue." The case regards Maximilian Hell, the Jesuit geometer-astronomer accused of falsifying his data. He was not cleared of this calumny for over a century.
One word of caution about these centuries. It would be a mistake to assume that ease in transportation and communication were in any sense analogous to that of today, and to forget that books and publications were not immediately available. Discussion and seminars were sometimes impossible. In fact travel was often impossible because wars were continuous and the English anti-Jesuit laws were in force with a vengeance. Jesuit communities and schools, like others, did not escape these perils and the turmoil of the times. It was a time when a whole community, caught between warring factions, would be suddenly set upon and massacred. In 1594 for instance the Jesuits were forced out of the College de la Trinité following an attempt on the life of Henry IV by one of their students. One member of the community was hanged, another stretched on the rack and the student was torn apart by horses. In 1582, the fourth day of October was followed by the fifteenth day of October and 10 days were dropped when Clavius' calendar was adopted. This precipitated riots, as well as rocks hurled at the windows of Jesuit houses by irate citizens whose lives suddenly became complicated. In the past some historians seem to have forgotten the turmoil of the times when making judgments about irregularities occurring in Jesuit contributions to geometry and science.
World maps of Geometer Schall von Bell of the Jesuit China mission
The real contribution of Jesuit geometers can best be understood from the numerous Jesuit specialists in geometry, and so in Appendix 2 is found a list of 105 Jesuit geometers who are listed in Sommervogel's Bibliothèque de la Compagnie de Jésus. There are 470 more, not listed. Also there is a shorter list in Appendix 1 of the 56 more prominent Jesuit geometers, describing their lives and their contributions. These latter 56 Jesuit Geometers appear in bold print in the text. The main body of this work concerns the contributions these men made in the growth of geometrical studies. Books by Eves, Boyer, Struik, the encyclopedias and the Dictionary of Scientific Biography all have impressive descriptions of them and their work. Less available, but more to the point are the many writings of Henri Bosmans,12 a Jesuit mathematician and mathematics historian of a later century. The library of the house of writers in Rome, Institutum Historicum Societatis Jesu (IHSJ), has a rich collection of these and similar articles about Jesuit geometers.
In this work I draw on all these sources especially the non-Jesuit sources such as the Dictionary of Scientific Biography (DSB) and The Philosophical Transactions of the Royal Society (TRS). While attempting to steer a course between the callous neglect of the Jesuit effort, and inordinate triumphalism, I try to make the case that geometers of today owe much to the Jesuit geometers of the 17th and 18th centuries. The evidence for this Jesuit influence is divided into six parts:
  1. their textbooks and publications
  2. their inventions in practical geometry
  3. their innovations in the various fields of geometry
  4. the indirect influence they have had through teaching and correspondence
  5. their teaching innovations, methods and attitudes
  6. the evaluation of these geometers by professionals, then and now
    This same argument comes by way of reluctant testimony from Francis Bacon, scarcely a Jesuit enthusiast, in his workThe Advancement of Learning .. He was commenting on the Jesuits' influence on science.
This excellent part of ancient discipline, has in some measure been revived of late by the colleges of Jesuits abroad. . . . And of late years the Jesuits, partly of themselves and partly provoked by example, have greatly enlivened and strengthened the state of learning. (Francis Bacon)

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