Chapter 4 Influence on Other
Geometers
The influenceJesuits had
on other geometers is treated under two headings:
a.
In teaching other geometers
b.
In correspondence with other geometers
a In teaching other geometers
Apart from the direct contributions
to geometry, the Jesuits indirectly influenced its development by their relations
with non-Jesuit geometers. They did this as teachers, as relatives, as friends,
as correspondents, and as adversaries.
Gilbert Highet speaks about the Jesuit educational experience in the
years before the suppression of the Society.
The best thing about its method
was the thoroughness with which they planned.
. . .The Jesuit regulations made sure that the pupils realized what they
were doing, and why. It is noticeable
that very many of their pupils have turned out to be men of very strong will-power
and long vision. A good modern example is the Irishman who spent seven years
on writing a book about the events of a single day, and then spent seventeen
more on writing about the dreams of a single night.
You may not admire Ulysses
and Finnegans Wake,
but they are monuments of aesthetic planning and perseverance,
and it was the Jesuits who taught Joyce how to make such plans.
The success of Jesuit education
is proven by its graduates. It produced, first, a long list of wise and learned
Jesuit preachers, writers, philosophers, and scientists.
Yet if it had bred nothing but Jesuits it would be less important.
Its value is that it proved the worth of its own principles by developing
a large number of widely different men of vast talent: Corneille the tragedian,
Descartes the philosopher and mathematician, Boussuet and Bourdaloue the orators,
Moliere the comedian, d'Urfe the romantic novelist, Montesquieu the political
philosopher, Voltaire the philosopher and critic, who although he is regarded
by the Jesuits as a bad pupil is still not an unworthy representative of
their ability to train gifted minds.
The Company of Jesus had many enemies, but none of them ever said that
it did not know how to teach. 1
One of the well-known Jesuit
teachers of geometers was P�re Laurent Beraud,S.J. (1702-1777) who was born
in Lyons, and taught mathematics in Avignon, Aix and Lyons, where he died.
His obituary was printed in the Journal des
Scavans.
He taught two of the earliest historians of mathematics, Charles
Bossut and Jean Etienne Montucla, as well as the distinguished astronomer
Joseph Lalande. The latter
received some of his formation in the special small college astronomy observatory
constructed by P�re Beraud. It was because of Beraud's encouragement that
Bossut, whose mathematical preparation at the time was meager, dared to write
to Bernard de Fontelle (another Jesuit alumnus), the
secretary of the AcadŽmie Royale des Sciences, who introduced
him to the famous mathematicians Clairaut and d'Alembert. This led to Bossut's
interest in mathematics and to the history of mathematics.
Later Bossut's
treatment of the Society was certainly less than friendly, and
he ended his days a devoted Jansenist.
Despite this fact, he lists 16 Jesuits as the most important
geometers of all time in a list
of 303 names.
Some of the non-Jesuit geometer/scientists
who were Jesuit-trained in one or other of the seven hundred Jesuit schools
were Bossut, Jean Cassini, Descartes, Fontenelle, Ghetaldi, Guyton, Lagny,
Lalande, Marci, Mersenne, Montucla, van Roomen, Torricelli,
Valerio, Vivani, Volta, Zanotti. The contributions of these
men to geometry as well as their relationship to the Society
are all listed in the DSB. Below is a brief summary of their contributions
and the names of the Jesuit schools they attended.
This list, of course, does not include all geometers who were
Jesuit educated.
Jean Dominique Cassini(d 1712)
was trained at the Jesuit college in Genoa. He introduced a class of curves,
the Cassini ovals (of which the lemniscate is a special case). The
ovals were first described in print by another mathematician,
his son Jacques Cassini.
RenŽ Descartes (d1650) was one
of the most celebrated Jesuit graduates and
always had great praise for the Society. Of LaFl�che he said,
"This is where was planted the first seeds of all my later accomplishments
and for which I am eternally grateful to the Society of Jesus." He has been
incorrectly listed by some historians as a Jesuit.
He wasn't, of course, but he had a nephew Philip Descartes,
S.J.,who was a Jesuit mathematician.
RenŽ Descartes was allowed to sleep late at LaFl�che because of ill health
and later said that he found these morning hours the most productive of the
day.
Bernard de Fontelle (d 1757),
who attended the Jesuit school at Rouen, was secretary of the AcadŽmie Royale
des Sciences. He later attacked the Jesuits because of what he considered
their cavalier attitude toward miracles. Marino Ghetaldi (d 1626) was taught
by ChristopherClavius
and was a frequent correspondent
of Christopher Grienberger
. Louis Guyton (d 1816) had the Jesuits at Lyons, for which he was not terribly
grateful. He wrote a poem satirizing the Jesuits and was rewarded by being
chosen "honoraire" at the AcadŽmie des Sciences. After the suppression of
the Jesuits, he proposed to the government a plan for dividing up and distributing
the property of Jesuit schools.
Philippe de La Hire (d 1718) was taught
by HonorŽ Fabri and
later became part of a circle formed by HonorŽ Fabri
which included Cassini, Deschales, both Huygenses, Leibniz, Descartes and
Mersenne. La Hire was a pioneer in projective geometry and was considered
by Carl Boyer in A History
of Mathematics (New York,
1968) "the only mathematician of stature in France" after the demise of Desargues,
Pascal and Fermat.2
Thomas Lagny (d 1660)
attended the Jesuit college at Lyon. He was known for his
theorems on convergence of series and with computational methods. Using one
such series he computed ¹ to 120 places. He also attempted to compose
trigonometric tables using binary numbers.
Joseph LaLande
(d 1807) also attended the college
at Lyon and wanted to join the
Jesuits but was unable to do so because of parental objections. He was one
of the most prominent mathematician-astronomers of the century. It was his
work that paved the way for the solution of the three body problem. He organized
observations for two of those
rare spectacular astronomical events, the transits of Venus across the sun
in 1761 and 1769.
Johannes Marci of Kronland
(d 1667)3
lived in Bohemia (now Czechoslovakia) and attended the Jesuit college
in Jindrichuv Hradec. He was taught by Gregory St. Vincent
at Prague and when in Rome met Guldin
and Kircher. His
work was mostly in geometrical optics but he was involved in physics and
proposed using a pendulum clock for measuring pulse. During a political disturbance
he initially represented the anti-Jesuit party at Prague University, but eventually
the Jesuit school and the University of Prague joined together.
On his deathbed he was
admitted into the Jesuit Society.
Marin Mersenne (d 1648)
4 was trained by the Jesuits at La Fl�che, and later became one of
the most remarkable of all the Jesuit alumni. He became a Minim friar.
In prejournal times he had the vision of developing a community
of science. He lived in Place Royale (what is now Place des Vosges) in Paris,
carrying on an intellectual apostolate.
Not only Jesuit geometers would meet in his cell to discuss mathematics
but also Gassendi, Descartes, Hobbes, Fermat, Pascal (in fact, if one were
to look through the l2-volume work of his correspondence, one would find virtually
all the geometers of his time).
Jean Montucla (d 1799)
5 was taught at the
Jesuit college in Lyons and later wrote the first comprehensive and accurate
description of the development of the various branches of mathematics in
all countries. His friend Joseph LaLande completed Vol. III and IV after
Montucla died.
Adriaan van Roomen
(d 1615) attended the Jesuit school in Cologne. He knew
Clavius and is remembered
for his work on isoperimetric problems.
His work Ideae mathematicae pars prima
was dedicated to Clavius.
In it he tried to find a general rule for calculating the sides of a polygon;
he succeeded in finding to 32 decimal places the sides of
polygons up to 15 x
2 60 sides (by doubling sides)
then with the help of one side of the
regular 251,658,240 sided polygon he
calculated ¹
to 16 places.
6
Evangelista Torricelli
(d 1647)7
attended the Jesuit school at Faenza. He wrote two letters
to a former Jesuit teacher, Michael
Ricci, S.J., in June
1644 to describe
his successful experiment with a 76-cm column of mercury,
which proved that vacuum exists.
8 The toys called
"Cartesian devils" were invented by Torricelli, not by Descartes.
His only book was Opera geometrica
(1644), and he communicated to Mersenne
his greatest discoveries, depending on Mersenne to relay them
to other scientists. Even though
he is remembered for his discoveries in physics, he spent all his life doing
geometry. He had worked out
twenty different ways to find the area of a parabola. He studied the generalized
hyperbola x
my n = c
n and thus
anticipated the result of
Jean de la Faille
in 1632. In modern terms his process is an integral in Cartesian coordinates
which is replaced by an integral in cylindrical coordinates. Cavalieri, Barrow
and other pioneers of the calculus depended on the works of Torricelli.
Luca Valerio
(d 1618) was
taught by Clavius at
the Roman College and influenced the thinking
of Galileo.9
Some of his geometry is found in Newton and Cavalieri
(center of gravity), Torricelli, de La Faille, Tacquet,
St Vincent and
Guldin.
Vincenzo Viviani (d 1703)
10 attended the Jesuit school in Nente; he attempted to reconstruct
the fifth book on conics of Apollonius. He duplicated the cube using conics
and trisected the angle by using the cylindrical spiral or a cycloid and was
also engaged in a number of other special geometrical problems.
The father of Alessandro Volta
(d 1827)11 had been
a Jesuit for 11 years, his uncle was a Dominican and he himself
was in a Jesuit seminary for a short time.
Alessandro was the first to make quantitative measurements
on the potentials of charged
bodies and for him is named the unit of potential difference. He was a strong
theoretician and some of his ideas on electricity were inspired by Boscovich
.
Eustachio Zanotti
(d 1782)
was educated by the Jesuits
in Bologna. He was a pioneer in the study of variable stars
and proposed a lucid treatment of the method of indivisibles. His interest
included perspectives and he contributed to the study of projections meant
for artists as well as mathematicians.
A rather celebrated visitor
to the Jesuit Roman College was
Galilei Galileo. His friendship with members of the Society of Jesus started
in 1587, when at the age of 23, he met Christopher Clavius,
and continued for the rest
of his life. Some incorrectly claim Galileo was a Jesuit;
but in 1589 he did go away to become a monk, entering the
monastery of Santa Maria in Vallombrosa as a novice, against his father's
will, and within the year his father took him out of the monastery. Later
in 1611 the Jesuits of the Roman College confirmed his discoveries of the
motion of the earth and honored him, even though he had been embroiled in
a dispute with Scheiner
over a separate matter, the discovery of sunspots. Later he demolished
Scheiner's idea that
sunspots were tiny planets around the sun. In his writings he attributed
his interest in falling bodies to a "certain Jesuit father, Niccolo Cabeo,
S.J." Cabeo once described a
type of wireless telegraph, with the admonition that it would be impossible
to realize in practice.
The Dominican scholar William
Wallace, O.P., in his book Galileo's Early Notebooks
(Notre Dame, 1977), has demonstrated, by using the internal evidence of
terminology, word order and symbols, that much of Galileo teachings came from
Jesuits teaching at the Roman College. He names nine of them,
thus corroborating the research of other scholars such as A. C. Crombie and
Adriano Carigo. After studying Galileo's manuscripts for fifteen years, he
found that all Galileo's notebooks show considerable evidence of copying.
Practically all of the material derives from textbooks and lecture notes
which were being used by the Jesuits at the Roman College. This evidence
is available in collections like Sommervogel.
This
was not considered plagiarism. People felt they had a right
to ideas: when they were shown
to be right, they were the property of everyone.
In fact, teachers were flattered to have their class notes
used by another instructor. Galileo is still the father of modern science,
but now there is evidence that there was a grandfather as well. The grandfather
which Wallace has been able to establish is a collection
of nine Jesuit mathematicians and teachers of natural philosophy,
such as Christopher Clavius
and his colleagues: Benito Pereiro, Francisco de Toledo, Antonio Menu,
Paul Valla, Muzio Vitelleschi, Robertus Jones, Stephanus del Bufalo
and Ludovico Ruggiero. Though his Latin prose is more simple
than Clavius'
sophisticated style, the parallels between Galileo and Clavius
are unmistakable. Galileo's debt to Jesuit contemporaries can be seen also
in the authorities he quotes, who are identical to those quoted by the Jesuits.
Wallace itemizes the lecture
notes in manuscript form that have been studied and identified as the same
lecture notes which were used by Galileo:
12
Benedictus Pererius, 1565-1566,
Physica, De caelo, De generatione
Hieronymus de Gregoriis, 1567-1568,
Physica, De caelo, De generatione
Antonius Menu, 1577-1579,
Physica, De caelo, De generatione
Paulus Valla, 1588-1589,
De generatione
Mutius Vitelleschi, !589-1590, Physica, De caelo , De generatione
Ludovicus Rugerius, 1590-1591, Physica, De caelo ,De generatione
Robertus Jones, 1592-1593, Physica, De caelo
Stephanus del Bufalo,1596-1597, Physica, De generatione
The mathematical
organization was not new with Galileo, and the place of mathematics in physical
analysis occurred to Galileo through contact once again with reportationes
of the Collegio Romano. A mathematical approach to nature was
indelibly etched in his Jesuit colleagues' physical mind-set by Christopher
Clavius.
It was Clavius
who supplied the formal apparatus for "geometrical philosophy," and his
influence on Galileo through his commentary on Sacrobosco
was apparent.
Clavius knew all the
techniques of handling motion which had been invented since the fourteenth
century. In other words, the
Roman Jesuits were the immediate source of a number of Galileo's leading
mathematical concepts. The notion of specific gravity ultimately descends
from Archimedes, but it was made proximately available to Galileo through
lecture notes, for example, those of Valla, Vitelleschi, and Rugerius.
Examples of the evidence include Galileo's phrasing
identical with that of the Jesuits' as well as of authorities cited: Ockham,
Sylvester of Ferrar, Durandus, St. Thomas and Scotus.
In his review of Wallace's book these things were mentioned
by William Shea, who points
out that the professors of the Roman College frequently made their notes
available to their students.
Wallace argues that lecture notes of four other Jesuit professors show even
more striking parallels and coincidences with the words actually used by Galileo.
. . Wallace has given us an outstandingly lucid and intelligent account of
matters of great interest. This
book is the first comprehensive and unified treatment of the influence that
the Jesuits exerted on one of the greatest minds of all times.
13
b In correspondence
among geometers
Hooke performed his first experiments on diffraction after reading
of Grimaldi's
book in the Philosophical Transactions of the Royal Society.
Furthermore both
Hooke and Newton show familiarity with his works.
14 Newton credits Fabri
as the source of his knowledge on diffraction.
Newton's initial
description shows he did not perform the experiments outlined by Grimaldi.
Later when Newton did perform the experiments, he referred to it as a kind
of refraction and by careful
measurements made clear the periodic nature of the phenomenon.
As has been suggested, many
of the geometers at this time, though not trained by Jesuits, were familiar
with their books. Leibniz was inspired and enlightened by them,
as were Huygens, Barrow, Desargues, Gregory, Lambert, Mercator,
Boyle, and Newton, by their own admission.
There were many strong friendships
between Jesuit and non-Jesuit geometers. The son-in-law of Tycho Brahe once
told Clavius
that he should write more often to Tycho and that
he should not hesitate to ask for anything, because even though
Tycho Brahe was not Catholic he was not a bigot, and in fact liked Clavius
.15
Another instance of strong friendships is the fact that it was
to the Jesuits that Galileo turned during his crisis with the Church.
In 1588 this unknown young scientist wrote to Clavius
asking about a center-of-gravity demonstration and expressed great admiration
for Clavius.
From the remarks in this letter, as well as in later letters,
his esteem for Jesuits is quite compelling.
I prefer Your Reverend Lordship's (Clavius) judgment above that of any other.
If you are silent, I shall be silent, too: if
not, I shall turn to another demonstration. . . . I know that
with friends of truth like Your Reverend Lordship one may and ought to speak
freely. Excuse my delight in
dealing with you, and continue to grant me your grace, for which I supplicate
you in every instance. Also
gain for me the grace of the other, Father Christopher (Grienberger),
your disciple, whose reputation for mathematical ability has
aroused my highest admiration.16
When Galileo, with the help
of his "cannocchiale" or "telescopio"
discovered the phases of Venus, the "three-bodied" appearance of Saturn,
and the mountains of the moon, Clavius
verified these phenomena and praised Galileo for his discoveries.
Galileo was delighted and expressed his joy with Clavius'
compliments, "as much appreciated as it was desired and little expected,"
bringing him "such testimony to the truth" of his observations.
In fact Galileo was sick in bed when he received Clavius'
letter and claimed that the letter brought him so much joy, it occasioned
his immediate recovery. Galileo
knew the impact Clavius
' opinions had on the learned world, and wrote: "All the experts, especially
the Jesuit fathers, agree with me, as everybody will soon know."
There was a voluminous and constant
flow of correspondence between Jesuit and non-Jesuit geometers of these two
centuries. In Rigaud's Correspondence
of Scientific Men of the Seventeenth Century
17 Jesuit names frequently
appear. Letters passed,
for instance, between Galileo,
Viete, both Cassinis, both Huygens, Fermat, Descartes, Leibniz, Newton and
Kepler and many Jesuit geometers
such as Clavius, Scheiner,
Guldin, de la Faille, de Chales, Grienberger
. In Mersenne's twelve-volume collection of correspondence are found many
Jesuit entries.
The works of Joannes Kepler
have been collected into 18 huge volumes and published by Max Caspar.
Among the curious items is one concerning Thomas Lydiat, the
rector of Oxford, who, with obvious scorn, called Kepler's
chronology of the life of Jesus Christ "that of the Jesuits."
Kepler, smarting from the intended insult, wrote a criticism
of Lydiat's book. "Judging by
the way Jesuits are treated in England, it must be a great crime to hold Jesuit
doctrine; but if Lydiat has no more serious charge against the Jesuits than
that they approve the Keplerian chronology, by that very charge the conduct
of his country stands condemned."
Kepler had a long friendship
with Jesuits, even though he found himself in controversy with them frequently.
18 Guldin was
quite devoted to Kepler's studies and well-being.
An edict had been issued that all non-Catholics had to move
out of Linz; so when Kepler refused to capitulate and become a Catholic, he
was exiled from Linz and had
to move to Graz and so was cut off from Prague. In 1626 he had been thinking
about becoming a Catholic, but the more he learned of Catholics the less inclined
he was to become one.
Guldin
was concerned about Kepler's financial predicament as well as his inability
to study the skies, since he
owned no telescope. The Jesuit Nicolas Zucchi
was well known as a telescope maker; at the urging of Guldin,
he
brought a telescope to Kepler.
Kepler, like a child with a new toy,
wrote to Guldin
of his gratitude for the latter's
concern and kindness. It was one of many letters he would write to Guldin
in his lifetime
and these are published in the Johannes Kepler Gesammelte Werke
.19 One of the most touching letters
was the dedication of his last book, The Dream by Johannes Kepler, the
late imperial mathematician, a posthumous work on lunar astronomy
(1634), published by his son after he died. In this work he
tells of his discoveries concerning the surface of the moon and describes
an imagined trip there as well as how it might be inhabited.
At the end of the book he publishes a long letter of gratitude which he sent
to Guldin. In part it reads:
Geographical, or, if you prefer, Selenographical Appendix.
To the very reverend Father Paul Guldin, priest of the Society of Jesus,
venerable and learned man, beloved patron. There is hardly anyone at this
time with whom I would rather discuss matters of astronomy than with you .
. . Even more of a pleasure to me, therefore, was the greeting from your reverence
which was delivered to me by members of your order who are here . . . think
you should receive from me the
first literary fruit of the joy that I have gained from trial of this gift
(the telescope).20
The Jesuits in China had much
more success in dealing with Kepler than with Galileo as they attempted to
keep abreast of astronomical developments.
The Protestant Kepler wrote often in response to Jesuit Jean
Schreck's (Terentius
) requests for information, and at the end of one letter expresses an ecumenical
prayer for the conversion of the Chinese.
Quod ratum esse velit Is cui Pater aeternus gentes in haereditatem dedit,
Christus Iesus, Deus et homo, Dominusque noster. Amen.
("May Jesus Christ, God and man, and our Lord, to Whom the
Eternal Father gave the heathen as an inheritance, will it (the conversion
of the Chinese) to be fulfilled. Amen.")
21
Although unpleasant at times,
the many controversies Jesuit geometers engaged in did not end without some
profit for geometry and science. In a long and bitter dispute with Kepler
Scheiner forced Kepler
to a more precise formulation of his terms.
Scheiner
used the pseudonym "Appelles", taken from the Greek myth.
No one could draw a line finer than the artist Appelles.
Similarly Cavalieri became more careful when his ideas were criticized by
Guldin.
Cavalieri as well as the geometer Stefano Angeli (d 1623), were Jesuati
(Gesuati), the order of St. Jerome adhering to the Augustinian rule,
which was suppressed by Clement IX in 1668.
They both are sometimes incorrectly referred to as Jesuits.
Angeli was involved with Guldin
and Tacquet in a
dispute over indivisibles.
Jean de la Faille
had wide correspondence with Christian Huygens and Langren.
Henri Bosmans published a number
of letters between Christian Huygens and AndrŽ Tacquet
in which
reference is made to correspondence with many other
geometers of the day.
22
A frequent correspondent of
Jacques de Billy was
Pierre de Fermat;this affected
the work of both geometers. Fermat has been referred to as "the prince of
amateur mathematicians" and has been called by Laplace "the true inventor
of the differential calculus."23
He was a
devout Catholic; his son Jean was an archdeacon and his daughters Catherine
and Louise were religious nuns.24
Fermatis best
remembered for "Fermat's Last Theorem": x
n + yn = z
n never holds for integers
x,y,z and n if n>2. This has been one of the most notorious unsolved problems
for the past 350 years. To make
matters worse, Fermat claimed that he had a remarkable proof, but that it
would not fit into the margins.
Some have not been very gracious at being unable to find a proof and
have consoled themselves that the proof would not be useful
anyway. The fact that 3
2 + 42 = 5
2 was used to construct right angles for the pyramids but of what
value are the higher orders?
even the special triple case of 33
+ 43 + 5
3 = 63 ? There are, moreover,
two questions:
Did Fermat really have a proof? and what was his proof?
When Pascal tried to take credit for Torricelli's experiments, Jesuit geometers
corrected him; after that Pascal had a stormy relationship with the Jesuits.
He found himself in bitter arguments more than once.
One example is his claim that
Antoine de la Louvere
did not really solve a problem concerning the roulette. Pascal lost this
battle but won more contests with the Jesuits than he lost. D'Alembert, the
angry encyclopedist, in spite of his hatred for the Jesuits, came to Roger
Boscovich for help when
he was deprived of a mathematics chair which he felt he deserved.
The chair had been left vacant on the death of Clairaut
and d'Alembert was told that his field of mathematics was not suitable.
In desperation, in a frantic letter written in haste and filled
with grammatical errors, he begs Boscovich
to help him. A translation
of a few lines of this letter follows:
I ask you reverend Father, for the love which you have for me, to take this
news to all the intellectuals of Italy who hold me in esteem.
25
Ignace Pardies
made his most important scientific contribution, not in his
writings, but in his correspondence. It is there that we find
the objections that Pardies
expressed to Newton concerning
his theory of colors and the "experimentum crucis" - objections that enabled
Newton to clarify certain difficult points.
26
Pardies was a temperate
and courteous critic of Newton.27
He was a vigorous intellect,
as is evident from his pedagogical writings and his contacts with the pioneers
of geometry. Leibniz' impression of him confirms this view.
After meeting in Rome with the
Jesuits on their way to the Chinese mission, Leibniz started a correspondence
with them and sent a suggestion for explaining the Holy Spirit as part of
a Trinity to the mathematically minded Chinese.
He suggested using the analog to the square root of
minus one as sort of intersection of number and non-number.
Leibniz was inspired by the work of Kircher
to attempt to find an alphabet of thought which would
enable all to speak of the creation of knowledge.
Leibniz also wrote to Bernoulli in 1703,
attributing his
original interest
in mathematics to the writings of Jesuit geometers.
As a child, I had studied the elementary algebra of one Lancius, and later
that of Clavius;as for that
of Descartes, it struck me as being too difficult.
I asked Buot for the work of Dettonville and of Gregory de
St. Vincent,which was kept
in the Royal Library. Without
delay, I studied these works - these gems invented by St. Vincent
and perfected by Pascal. I
culled everything that I could derive from the work of Cavalieri, Guldin,
Torricelli, Gregory de St. Vincent, and Pascal on sums of sums and
transpositions. 28
Gaspar Schott
added as an appendix to his Mechanica Hydraulio-pneumatica
(1657) a detailed account
of Guericke's experiments on vacuums, the earliest published report of this
work. As a result he became the center of correspondence, as other geometers
wrote to inform him of their inventions and discoveries. Schott
exchanged several letters with Guericke, seeking to draw him out by suggesting
new problems, and then published his later investigations.
He also corresponded with Huygens and was the first to make
Boyle's investigations on the air pump widely known in Germany. Even though
he personally held the Aristotelian abhorrence of a vacuum,
he was open to new information from experiments and rendered
great service to Germany by encouraging experimentation.
Like Mersenne, he spread news of new investigations, observations
and discoveries; he suggested
fresh problems and encouraged
controversies until there was a resolution.
It was his publication of von Guericke's research that stimulated
Robert Boyle to have an airpump constructed.
29
Chapter 4
Footnotes
1. Gilbert Highet:
The Art of teaching.
New York: Knopf,
1954, p. 221 and p. 224.
2. Carl
Boyer: A History of mathematics
. New York: Wiley, 1968, p. 404.
3. DSB vol. 9, p.
96-97.
4. DSB vol. 9, p.
316.
5. DSB vol. 9, p.
500.
6. DSB vol. 11, p.
532-533.
7. DSB vol. 13, p.
433.
8. DSB vol. 9, p.
332.
9. DSB vol. 9, p.
561.
10. DSB vol. 14, p. 48.
11. DSB vol. 14, p. 69.
12. William A. Wallace:
Galileo's early
notebooks. Notre Dame:
Notre Dame, 1977, p.13.
A very useful source for this
work is the book review by John Quinn, O.S.A, "The
scholastic mind of Galileo: the Jesuit connection" in the International
Philosophical
Quarterly, vol.
20 #3, 1980, p. 347-362.
13 William Shea: "Readings
of Galileo" in Science
vol. 227, Mar 22, 1985.
p.1462-1463.
14. DSB vol. 5, p. 544.
15. Edward Phillips: "Correspondence
of Father Christopher Clavius"
in AHSI
vol. 8
1939, p. 193-222.
Phillips lists 291 letters to Clavius from geometers as well as
church and civil potentates.
Also see:
Francisco Sanches:
"Ad C. Clauium epistola" in Opera Philosophic Coimbra
,
1955 p. 146-153.
16 Pasquale M. D' Elia,
S.J.: Galileo in China
. Cambridge: Harvard Univeristy,1960, p. 7-9
D' Elia gives the references
to these letters of Galileo taken from the Archives of the
Pontifical Gregorian University.
17 S. J. Riguard, ed.:
Correspondence of Scientific Men of the Seventeenth Century.
2 vols. London:
Oxford University Press, 1841.
Also see: A. de Morgan: Contents
of the Correspondence of the
17th and 18th century.
London: Oxford, 1862.
18. M. W. Burke-Geffney:Kepler
and the Jesuits.
Milwaukee: Bruce, 1944, p. 130.
19. Max Caspar: Johannes Kepler
Gesammelte Werke. 18 vols.
Muenchen: C. H. Becksche,
p. 195.
20. Johannes Kepler: The Dream
of Kepler:
Silesia: 1634, p. 165.
21. Pasquale M. D' Elia, S.J.:
Galileo in China. Cambridge:
Harvard University, 1960,
p. 33.
D' Elia quotes from Schreck's letter and the reply in
Kepleri Opera Omnia
,
VII, p. 667-681.
22. Henri Bosmans: "Le Jesuite
MathŽmaticien Anversois AndrŽ Tacquet" in Gulden Passer
. vol 3, 1925,
p. 63-87.
23. Carl Boyer: History of
Mathematics. New York:
Wiley, 1968, p. 367.
24. DSB vol. 2,
p. 131.
Both carried on an active correspondence which precipitated
some of de Billy's writings:
for example, his treatment of indeterminate analysis was
shared by Fermat.
25. G. Arrighi: "J L D'Alembert,
R G Boscovich ed un Patrizio Lucchese" in Bollettino
Storico Lucchese,
vol. 2 1930, n. 3, p. 27-248
". . . Je vous prie, mon RŽrŽrend
P�re, par l'amitiŽ que vous avez pour moi, de
vouloir bien apprendre cette nouvelle a
tous les Savans d'Italie, qui m'honnorent de leur estime."
26. DSB vol. 10,
p. 315.
27. James Newman: The World
of Mathematics. New York:
Simon & Schuster, ed. 1956,
vol. 1, p. 260.
28. RenŽ Tatan:
Beginning of Modern Science
: Pomerans, 1958, p. 228-229.
Also see: Joseph E. Hofmann:
Das Opus geometricum des Gregorius a S Vincentio und
seine Einwirkung auf Leibnitz
. Berlin: 1942.
29. DSB vol. 12, p. 210.
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