Chapter6    Evaluation by Other Geometers


     The esteem in which Jesuit geometers have been held over the centuries is evident from what has been written about them in their own time as well as today. The evidence is presented under the following six   headings. 

a.    In learned journals   of that period                                                     

b.    In the histories of that period

c.    By their membership in learned societies of that period

d.    By their engaging in controversies with other geometers

e.    In recent histories, books and commemorations


a.    In learned journals   of that period                                                      

       How highly respected they were in their own day is evident from the frequency with which Jesuit geometers' own works as well as commentaries on their works appear in learned journals such as the  Philosophical Transactions of the Royal Society (TRS) and  the Journal des Scavans. Their names appear frequently in the early histories of mathematics and are listed in the learned societies such as Academie Royale des Sciences.    How seriously their opinions were taken is seen in their many public controversies with other geometers.   Today's appreciation is seen in the encyclopedias and in the numerous books written about them, in particular the Dictionary of Scientific Biography (DSB).

       The TRS   performed a very important function, that of scientific reporting.   It made widely available information formerly communicated to only a few individuals by private correspondence.   The Transactions were an immediate success, both at home and aboard.   The first editor, Henry Oldenburg, had created a new field of literature, which was rapidly extended because the Transactions   was the first journal to  print original communications.

       Conor Reilly 1 has collected the references to Jesuit works in the TRS for the early 17th Century, and these include some rather remarkable items.   For instance, an apology to the readers was needed for any intercommunication with Jesuits.


Whose goal . . . is to propagate their faith, and to greaten and enrich themselves by their craft; though I deny not but some of them are also ingenious and curious in the  matters of a philosophical nature; these that are so, are, I doubt not, obliged to communicate them to heretics, except they were sure they would be well requited for it. 2


To emphasize this point  John Beale once wrote a letter flattering Robert Boyle for his   positive influence on these impossible, obdurate men, the Jesuits.


I am confident that by your philosophy you have converted these very Jesuits to make some recompense for the destruction they have so long made of mankind, that by their universal commerce, incessant industry, and bottomless   purses we may receive useful intelligence and experimental formation from all parts of the world. 3


       Some Jesuit publications were translated and presented to the Royal Society by famous people such as Robert Hooke, Robert Boyle and Samuel Johnson.  Thomas Birch'sHistory of the Royal Society4 gives interesting connections between Jesuits and the Royal Society and it is to the credit of the first secretary, Henry Oldenburg, that, despite his undeniable personal prejudices, he did not refrain from including accounts of the "undertakings and labors" of considerable numbers of Jesuits.    Actually it would have required a special effort to neglect them, because at that time Jesuits were astonishing Europe with their geographical and intellectual discoveries.  New lands were still being discovered, people were eager for information about them, and  Jesuits were in the forefront of both the exploration and the articulate reporting of their findings. It was obvious that their world-wide organization of highly educated men would be in a very favorable position for sending back valuable information to Europe.  Oldenburg was well aware of the possibilities and made many efforts to enlist Jesuits among his overseas correspondents.   So he was pleased when Ignace Pardies wrote, showing interest in the TRS.  He replied, expressing his satisfaction at the prospect of having the French Jesuit as a continental correspondent.


       Especially as those of your celebrated Society (the Jesuits) have the advantage of making, by means of your international correspondence, numerous excellent and useful observations on Nature and the Arts. 5


       In 1701, when the first reorganization of the Journal des Savants   was taking place, the Jesuits were completing arrangements to publish their own Jesuit periodical Memoires pour l'histoire des sciences et des beaux-arts, or, as it came to be known to contemporaries, the Journal de TrŽvoux.   The Jesuits who planned the new periodical were members of the faculty of the College of Louis-le-Grand in Paris, the most famous of the Jesuit schools in France.  It  was later to be the school attended by "the father of modern mathematics,"   Evariste Galois.

     Like the Journal des Savants,  after which it had been modeled, the Jesuit Journal de TrŽvoux  was a literary journal published chiefly for the lettered class in France. The new journal would be dedicated to the advancement of interest in the arts and the sciences; its aim would be to satisfy the intellectual interests of the learned.  The largest part of each monthly issue was to consist of summaries and excerpts of all the important books recently published, but if significant original articles were made available to the editors, these too would be published.


b.  In the histories of that period

     The Jesuit mathematicians were known for their independence and bold innovations, a fact not lost on Bossut, the famous mathematical historian,  who lists 303 names in his table of the most eminent mathematicians of all time - from 900 B.C. to 1800 A.D.  As has   already been mentioned, sixteen on the list of 303   are Jesuits.  What is remarkable about this is the fact that the Jesuits existed for only 2   of those 27 centuries.     A similar collection of names is found in the works of Montucla, who wrote the first comprehensive history of mathematics. 6  M. Maximilian Marie's Histoire   lists 6  of the top 59 mathematicians for a period at the beginning of the 17th century.      Lalande's famous Astronomy (1792)  lists many Jesuit geometers and  astronomers, as does historian Michael Chasle (d 1880).7 At the time of the suppression of the Jesuits, 30 of the 130 astronomy observatories in the world  were Jesuit observatories. 8   Many of these were taken over by the state and still survive to this day, such as those observatories at Vienna, Heidelberg (then Mannheim), Prague, Vilna, Milan, and Rome.  


c. By their membership in learned societies of that period

     The Transactions show how seriously the Jesuit geometers were taken, not only because their works were reviewed and commented on, but  the Royal Society undertook experiments to decide in the cases of contrary findings.   Christiaan Huygens criticized Boyle's explanation of an experiment proposed by Frances Line in De corporum inseparabilitate .  The Royal Society carried out the experiment and ruled in favor of Boyle.   A good deal of space was used to describe a dispute between HonorŽ Fabri and John B. Borelli on whether a stone thrown horizontally will hit the ground in   a shorter time than if it simply dropped.  

     Hooke's fascination with the "aerial globe" of Francesco Lana-Terzi resulted in the construction of a model of the flying ship by the Royal Society.   The assertions of Francis Line opposing Isaac Newton about light and color led to an investigation favoring Newton.   In his New experiments Boyle shows familiarity with the works of the Jesuits Acosta, Kircher, Riccioli, Clavius and  Zucchi and considered them worthy of mention along with Descartes, Pascal, Huygens, Kepler and Galileo. 

     In Mazovia, a group of Polish Jesuits formed four observatories: in Wilno, in Warsaw, in Poznan, and in Lwow.       In France, Jesuit geometers belonged to numerous mathematical organizations, and   Joseph Lalande, the great French astronomer said of the Jesuits:


Among the most absurd calumnies which the rage of the Protestants and Jansenists exhale against the Jesuits, I found La Chalotais, who carried his ignorance and blindness to such a point as to say that the Jesuits had never produced any mathematicians.     I happened to be just then writing my book on Astronomy and I had concluded my article on 'Jesuit Astronomers' whose number astonishes   me.     I took the occasion to see La Chalotais   on July 20, 1773 and reproached him with his injustice, and he admitted it.9


This happened the same year that the Jesuit Society was suppressed.  

d.    By their engaging in controversies with other geometers

       Francis Line entered the Society the year that Robert Southwell was hanged, drawn and quartered.    It was a time when  those who harbored Jesuits in England were pressed to death.    How seriously Line's opinions were taken is clear from the reactions of Isaac Newton and Robert Boyle when he attacked their positions, neither of whom were partial to Catholics, especially Jesuits.   Boyle had already written a tract Reasons why a Protestant should not turn Papist: or, Protestant prejudices against  the Roman Catholic Religion. 10 

       The academic confrontations between these Jesuit and non-Jesuit scholars had the happy effect of forcing Newton and Boyle to clarify imprecise language.   When Line persisted in his objections, Newton considered taking up law as a less litigious enterprise.    

       In 1660 Robert Boyle published his book New physico-mechanical experiments   touching the spring of air 11after experimenting with Hooke's vacuum pump.  Not only does he give credit to Hooke for building this pump, but he also expresses gratitude to "the industrious Jesuit"  Gaspar Schott in whose book Mechanica hydraulica-pneumatica, he had read the description of the original airpump built by von Guericke.    Boyle's book proposes the existence   of a vacuum and it was this that brought him into conflict with Francis Line.      

After Torricelli's experiment with the inverted tube of mercury, the question of a vacuum seemed to be settled in the mind of Robert Boyle.   Francis Line , however, still clung to the Aristotelian premise that nature abhors a vacuum and so he took issue with Boyle's explanation of the experiment.   This led to a prolonged  debate between the two, and in the following year, 1661, Line published his  book De corporum inseparabilitate   against Robert Boyle's doctrine on the properties of   air.  Line allowed that air has both spring and weight, but suggested that these two properties were insufficient to account for the phenomena Boyle had described in his New experiments.   He suggested that air has a third property, the "funiculus" or extremely thin substance, which would not require postulating a vacuum.

       This precipitated Boyle's remark in the TRS:


For this is to be decided not by discourse, but new trial of the Experiment.   What it is that imposes upon Mr. Line I cannot imagine: but I suspect he has not tried the Experiment since he acquainted himself with my theory, but depends upon his old notions taken up before he had any hint given to observe the figure of the colored Image.   I shall desire him therefore, before he returns any answer, to try it once more for his satisfaction, and that according to this manner. 12


       Then Boyle published his work using the sweeping title:  Defense of the doctrine touching the spring and weight of air . . . against the objections  of   Franciscus Linus, wherewith the objector's funicular hypothesis is also examined.    Boyle's   "spring of air" theory is no more acceptable today than is Line's "funiculus"; it was attractive then   only because it was the less absurd of the two explanations.   Boyle apologized for the controversy but was convinced to publish by his friends; also since this doctrine was held by the Jesuits, Boyle felt he had to answer it.


I was more willing to pay them that respect, as not to dissent from persons, divers of whom for their eminence in mathematicks and other learnings I much esteem, without showing that I do it not but upon considerations that I think weighty.13


His latter book had the effect of converting Line and forcing himself, Boyle, to sharpen his language.   In the course of the debate, Boyle showed his esteem, not only for Line but for his colleagues "who with much civility wrote against them, never being the least bit antagonistic."   He quoted St. Augustine's words against an adversary.


In mala causa non possunt aliter, at malam causam quis eos coegit habere? 14 

 (You can't change a hopeless case, but who asked you to defend this   hopeless case in the first place?)


       In spite of the anti-Jesuit prejudices of his friends (and his own initially), Boyle had a sincere esteem for Jesuits.   After vanquishing Francis Line he appreciated the fact that Line forced him to state (more clearly) what has become Boyle's law.   Boyle's biographer writes, "I do not remember that he had the least antagonism toward Francis Line (who with much civility wrote against him)." 15

       Later an elderly Francis Line was to get embroiled in a dispute with Isaac Newton over the well-known experiment in geometrical optics in which white light is dispersed into colors after passing through a prism.     Newton's explanation centered on the fact that the colors resulted from differing "refrangibility," since the "light of the sun consists of rays differently refrangible."   

The TRS printed critiques of Newton's theory by Robert Hooke and by the Jesuit Ignatius Pardies . . . some animadversions upon Mr Isaac Newton . . . his Theory of Light 16   but Newton did not take it well.      It is referred to in the TRS as the Newton-Hooke- Pardies debate, but it really started with the teachings of Francesco Maria Grimaldi. 17   In the course of the correspondence between Pardies and Newton published in the TRS, Pardies   takes his arguments from  Grimaldi,  as does Hooke (who is also one of Newton's sources). 18     Pardies had argued that such a drastic departure from the accepted theory should not be entirely founded on the one experiment of the prism since the radical implication of Newton's paper would overthrow the accepted foundations of geometrical optics.     But  Pardies gradually comes to Newton's position,  making a rather generous admission of error, which precipitated this reply from Newton:


In the observations of Reverend Fr. Pardies, one can hardly determine whether there is more of humility  and candor in allowing my arguments their due weight, or penetration and genius in stating objections.19


        Pardies then clarified some points that had not been clear in his initial treatment.    Within a year of his reply to Newton, on April 22, 1673, Pardies, at the age of 37, died of a fever caught while ministering to prisoners at Bicetre, near Paris.    His death did not go unnoticed among his correspondents in England.  At the end of a review of La  Statique   which appeared in the TRS for May 1673, Oldenburg wrote that the book was only part of a work that Pardies had planned.


But since the publications of this part of it we understand that he hath been prevented and cut off by an untimely death; being regretted by those that knew his frankness and strong inclinations to promote philosophical knowledge.   How far indeed he hath advanced these other parts of his design, and whether those of his Society, in case he hath made good progress therein, will take care to see it published, we know not but yet hope he hath gone a good way therein, and, if so,

that his companions will not suppress his labors for the benefit of the young students in this kind of knowledge. 19


       Francis Line pursued Pardies' line of objections after Pardies met his untimely death.  This caused a long dispute with Newton and lasted even until after Line died because his pupils continued the correspondence with the TRS and Newton.    One of the Line letters includes the following defense of Pardies:


Wherefore Mr. Newton had no reason to tax on page 4091 P. Pardies of Hallucination, for making on page 4088, those two Refractions very unequal:  For, that learned Optike very well saw, that in a clear day so great an inequality of length and breadth could not be made, unless those two Refractions were also made very unequal.  These places, I say, might be added to the former, and further here explicated if need were; but there being no need, I cease to detain you any longer herein. 20


e.    In recent books and commemorations           Historians of mathematics are  acquainted with the works of Henri Bosmans, S.J. (1852-1928), who has written about ninety papers concerning mathematicians of the 16th and 17th centuries. Belgian Jesuit mathematicians constituted   his special,  although not exclusive, interest.  His papers are not readily available in the United States, but historian Adolphe Rome, S.J., issued a critical bibliography in ISIS. 21 Many of the Jesuit geometers mentioned here have been reported on and documented by Bosmans  in his monographs and to the persistent offer opportunity for further study.

       In Dubrovnik is found not only a street named Boscovich , but his old school was named after him,   and his statue stands on the grounds of Zagreb Atomic Institute.    A museum on the island of Lokrum and streets in Milan and Rome are named after Boscovich.      On the bicentenary of his birth a bust of him was unveiled in Zagreb. 


     Anniversaries have been frequent;   in Belgrade 100 articles appeared on the 150th anniversary of his death, and on the bicentenary of his book, Theoria ,  celebrations were held in London and Zagreb.   On the bicentenary of his death in 1987 five Symposia were held:   in Dubrovnik, in Rome, in Paris, in London and in Milan.

     Extraordinary praise has been heaped on this extraordinary Jesuit, a man two centuries ahead of his time, "the   commanding genius to whom Rome paid the honor of calling him her master, whom all Italy esteems as a precious treasure, and to whose memory Greece would raise a monument even at the expense of destroying a statue of one of her illustrious heroes.   Boscovich is the greatest genius Yugoslavia has ever produced. "

Cassirer considered the Theoria "the leading work in natural philosophy of the eighteenth century." I join Nietzsche in holding it to be "the greatest triumph over the senses that has yet been achieved on earth."   But perhaps most important of all is the lucid simplicity of Boscovich's ideas.22


       The Encyclopedia Britannica in 1801 devoted fourteen pages to Boscovich's theory;  and the influence of his Theoria was profound in the 19th century.     "He was the geometer of atomism, the Euclid of Democritus."23

       The Boscovich archives at Berkeley contains over 180 manuscripts and 2000 pieces of correspondence.    The number of Boscovich congresses and the number of articles written about him in scientific journals shows an enduring Boscovichian   revival.    "There is a crying need for research on this important eighteenth century polymath,"   said Professor Roger Hahn of Berkeley.  If this is not enough, a crater on the moon is named Boscovich.   


       In fact, on the Goddard Space Center selenograph no less than 34 craters are found which are named after Jesuits. They are Bettini, Billy, Blancanus, Boscovich, Cabaeus, Clavius, Cysatus, DeVico, FŽnyi, Furnerius, Grimaldi, Grienberger, Hagen, Hell, Kircher, Kugler, Malapert, Mayer, McNally, Moretus, Petavius, Ricci, Riccioli, RodŽs, Romana, Scheiner, Schoemberger, Secchi, Simpelius, Sirsalis, Tannerus, Tacquet, Zucchi, Zupus.   Moreover, until recently five other names have been on past moon maps.   They are Arzet, Bartolius, Deriennes, Rivas and Tibor.  

       These names conflicted with other later versions of moon maps and so have been deleted.   Today names of scientists throughout the world   are nominated for lunar surface features and the decision is made by the International Astronomical Union founded in 1922.   But up to this time the basic map for lunar nomenclature was the one mentioned in Chapter 2, drawn by Grimaldi and published by Riccioli, the first complete selenograph, and it is found at the entrance to the moon exhibit at the Smithsonian.


       Commemorative stamps occasionally remind us of the works of Jesuit geometers.   One instance is a beautiful 1983 Belize stamp illustrating the flying ship of "the father of aviation" Francesco Lana-Terzi , discussed in chapter 3.  It is his own sketch of the  proposed airship, four evacuated metal balloons supporting a sailboat with oars.

       Occasionally there are exhibitions of Jesuitica which surprise even Jesuits.   One such was the exhibition of Jesuit-authored rare science/mathematics books borrowed from the history of science collection housed in one of the best science libraries in the world, The Linda Hall Library in Kansas City, Missouri.  Held in 1986, it was a four month display ending on the feast of St. Ignatius, 31 July. The exhibit documented the tremendous scope of Jesuit science in the century of the scientific revolution, and displayed 44 works (not all concerning geometry) of the men mentioned in this book.  The introduction states the theme of the exhibition.


The Society of Jesus in the 17th century contained within its ranks an astonishing number of enthusiastic students of the natural world.   Indeed, for the first sixty years of the century, the Jesuits were the only scientific society in existence anywhere.   At a time when experimental science was decidedly unfashionable, Jesuits were charting sunspots, calibrating pendulums, timing the fall of weights off towers, and devising a variety of ingenious inventions.   Indeed, in the fields of geometry, optics, magnetism, cartography, mechanics, and earth sciences, most of the principal authorities throughout the century were members of the Society of Jesus. The Jesuits were a remarkably bold and imaginative scientific body. 24


       Of course, it must be remembered that these individual endeavors to discover, utilize and promulgate geometry were backed by one organization, the Jesuit Society.   It was done before the epoch of "grants in aid" and "foundation funding." Commenting on Jesuit activities, Robert Boyle once remarked:


Among the Jesuits  you know that Clavius and divers others, have as prosperously addicted themselves to mathematics as  divinity.   And as to physics, not only Scheiner, Aquilonius, Kircher, Schottus, Zucchius and others, have very laudably cultivated the optical and some other parts of philosophy, but Ricciolus himself, the learned compiler of that voluminous and judicious work of the Almagestum Novum .25


       This is as it should be, not only for Jesuit geometers, but also for Jesuit scientists, theologians, philosophers, linguists, historians, and artists according to the tenth and last section of the constitutions of the Society of Jesus.    Ignatius Loyola indicated that   the Society and its apostolate   were to be preserved in the service of others, not only by the spiritual means of zeal and solid virtue   but also with diligence  and solid learning.26


Chapter 6 Footnotes


1.     Conor Reilly: "A Catalog of Jesuitica in the Philosophical Transactions of the Royal              Society of London" in Archivum Historicum Societatis Jesu . 1958, p. 339-362.

2.     Ibid., p. 340.

3.     Ibid., p. 341  Many readers of the TRS seemed convinced that the Jesuits had vices of                  heroic degree.  Mr. Beale would not be swayed from that tradition.

4.     Thomas Birch:   History of the Royal Society.   London: 1756 vol. 2, p. 151.  

5.     Conor Reilly: Francis Line, S.J., an exiled English Jesuit . Rome: I H S I, 1969, p. 109.

6.     Maximilian Marie: Histoire des sciences mathematiques et physiques .  12 vols.                       Paris: 1883-1888.

7.     Michael Chasle: Aper�u Historique des methodes en gŽomŽtrie. Paris: Gauthier 1875,

        vol. 2,   p. 212.

8.     Daniel O'Connell:   "Jesuit men of science" in   Studies in Irish literature and science.                 Dublin: vol.44, 1955, p. 5.

9.     Thomas Campbell: The Jesuits 1534-1921. New York: Encyclopedia, 1921,  p. 355.

10.   Louis More: Life and works of the honourable Robert Boyle . London:  Oxford, 1944,

        p. 167.    The author, who is rather hostile to Line, defends the claim that Boyle wrote          this tract, even though it was presented anonymously.

11. Ibid., p. 243n.  Boyle supposes that particles of air were like tiny coiled watch springs,     each having a complicated circular motion to explain phenomena like rarefaction and                                      condensation.   This was to offset the "funiculus" theory of Line.

12.   TRS, vol. 10 p. 500.

13.   Conor Reilly:   Francis Line  op.cit., p. 72.

14.   Ibid., p. 83.

15.   Ibid., p. 79.

16.   TRS, April 9,1672.

17.   Reilly:   op.cit., p. 107.

18    Reilly:   op.cit., p. 111.

19.   TRS, vol. 7,   1672 p. 5012.

20.   TRS, vol. 10, p. 501.

21.   ISIS,   vol. 12,  1929 p. 100-112.

22.   Lancelot Whyte:   Roger Joseph Boscovich , New York: Fordham, 1961,  p. 124.

23.   Ibid., p. 105,107.

24.   William B. Ashworth: Jesuit science in the age of Galileo. Kansas City: Lowell Press

        p. 5.

25.   Thomas Birch:The works of the honourable Robert Boyle. 5 vols. London:1744,

        vol. 4   p. 62.

26.   Ignatius Loyola: The Constitutions of the Society of Jesus . (Translated by George E.               Ganss, S.J.) St Louis: The Institute of Jesuit Sources, 1970, Part X, 3, #814, p. 333.








Introduction to Jesuit Geometers
Ch 1. Jesuit textbooks and publications
Ch 2. Jesuit inventions in practical geometry
Ch 3. Jesuit innovations in the various fields of geometry
Ch 4. Jesuit influence through teaching and correspondence
Ch 5. Jesuit teaching innovations, methods and attitudes
Ch 6. Evaluation of these Jesuit geometers by professionals. < br> Appendix to Jesuit Geometers

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