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Paul Guldin, S.J.
(1577 to 1643)

applications of Guldin's Rule

Guldin's Rule

Paul Guldin was born Habakuk Guldin in Saint Gall, Switzerland to a Jewish family and in 1643 died in Gratz. He later converted to Catholicism and changed his name to Paul. Paul entered the Jesuit Society as a Coadjutor Brother, and after a few years he was asked to become a Jesuit Scholastic and then was later ordained a Jesuit priest. Paul Guldin's second volume of De centro gravitatis contains what is known as Guldin's rule:
"If any plane figure revolves about an external axis in its plane, the volume of the solid so generated is equal to the product of the area of the figure and the distance traveled by the center of gravity of the figure."
Guldin did not know that the fundamental theorem which bears his name and which he used extensively, is found in a somewhat vague form in the Collection of the well-known Greek mathematician Pappus (ca. A.D. 300). Nevertheless Guldin has been unjustly accused of plagiarism by earlier writers. This defamation has been thoroughly refuted, however, by recent historians expert in that period, such as Paul Ver Ecke, who shows that the translation of Pappus available to Guldin, and faithfully quoted by him, lacked the theorem in question. Furthermore, he demonstrates that the accusation against Guldin is weakened by the fact that various geometers who lived at about the same time as Guldin did not credit Pappus with this theorem but Guldin. Among these writers is the noted astronomer Kepler, who presented applications of Guldin's theorem. The injustice of the slight to Guldin is emphasized in an article in Science Magazine (Science vol. 64, #1652 8/27/26 p. 205.)
The world owes a great debt of gratitude to those who, like Cardan and Guldin, contributed powerfully towards the enlightenment of the human race, especially at a time when so few people took an active interest in scientific matters. It seems therefore to be very fitting that wide currency should be extended to results which tend to remove from their names unjust defamatory associations due to carelessness on the part of earlier writers.
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. Although Paul Guldin also was the chief critic of Kepler in his use of infinitesimals because of a lack of rigor and mathematical foundation, he 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 the Catholic heirarchy the less inclined he was to become a Catholic. In 1627 a correspondence on religious subjects developed between Guldin and Johannes Kepler when the latter wrote Guldin concerning his objections to the Catholic religion. Guldin tried to refute them with theological arguments, but apparently to no avail. Kepler had greater difficulties with Catholic heirarchy than with the Catholic religion.

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. 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).


Archivum Historicum Societatis Iesu ( AHSI ) Rome: Institutum Historicum
Johannes Kepler: The Dream of Kepler: Silesia: 1634, p. 165.
Gillispie, Charles. C. ed., Dictionary of Scientific biography. 16 vols. New York: Charles Scribner and Sons, 1970
{ Reference to him in the Dictionary of Scientific Biography is found in v 1 p164, v 3 p152, v 4 p110, v 5 p 527, 588-9, v 7 p 583, v 9 p97, v 10 p301, v 13 p561, 615.}
Johannes Kepler: The Dream of Kepler: Silesia: 1634, p. 165.
Oldenburg, Henry ed. Philosophical Transactions of the Royal Society. vols. 1-30. London: 1665-1715
Reilly, Conor "A catalogue of Jesuitica in the Philosophical Transactions of the Royal Society of London" in A.H.S.I. vol. 27,1958, p. 339-362
Sarton, GeorgeThe study of the history of mathematics. Cambridge, Mass: Harvard, 1936
Sommervogel, Carolus Bibliothèque de la compagnie de Jésus. 12 volumes. Bruxelles: Société Belge de Libraire, 1890-1960
{7 entries are found in Sommervogel; some examples are the following:
Problema Arithmeticum (Vienna, 1622)
de Centro Gravititatis Trium (Vienna, 1635}
Paul Ver Ecke, "Le Theorem dit de Guldin considéré au point de vu historique," Mathesis. 1932 vol. 46, 395-397.

Adventures of Some Early Jesuit Scientists

José de Acosta, S.J. - 1600: Pioneer of the Geophysical Sciences
François De Aguilon, S.J. - 1617: and his Six books on Optics
Roger Joseph Boscovich, S.J. - 1787: and his atomic theory
Christopher Clavius, S.J. - 1612: and his Gregorian Calendar
Honoré Fabri, S.J. - 1688: and his post-calculus geometry
Francesco M. Grimaldi, S.J. - 1663: and his diffraction of light
Paul Guldin, S.J. - 1643: applications of Guldin's Rule
Maximilian Hell, S.J. - 1792: and his Mesmerizing encounters
Athanasius Kircher, S.J. - 1680: The Master of a Hundred Arts
Francesco Lana-Terzi, S.J. - 1687: The Father of Aeronautics
Francis Line, S.J. - 1654: the hunted and elusive clock maker
Juan Molina, S.J. - 1829: The First Scientist of Chile
Jerôme Nadal, S.J. -1580: perspective art and composition of place
Ignace Pardies, S.J. - 1673: and his influence on Newton
Andrea Pozzo, S.J. - 1709: and his perspective geometry
Vincent Riccati, S.J. - 1775: and his hyperbolic functions
Matteo Ricci, S.J. - 1610: who brought scientific innovations to China
John Baptist Riccioli, S.J. - 167I: and his long-lived selenograph
Girolamo Saccheri, S.J. - 1733: and his solution to Euclid's blemish
Theorems of Saccheri, S.J. - 1733: and his non Euclidean Geometry
Christopher Scheiner, S.J. - 1650: sunspots and his equatorial mount
Gaspar Schott, S.J. - 1666: and the experiment at Magdeburg
Angelo Secchi, S.J. - 1878: the Father of Astrophysics
Joseph Stepling, S.J. - 1650: symbolic logic and his research academy
André Tacquet, S.J. - 1660: and his treatment of infinitesimals
Pierre Teilhard de Chardin, S. J. - 1955: and The Phenomenon of man
Ferdinand Verbiest, S.J. - 1688: an influential Jesuit scientist in China
Juan Bautista Villalpando, S.J. - 1608: and his version of Solomon's Temple
Gregory Saint Vincent, S.J. - 1667: and his polar coordinates
Nicolas Zucchi, S.J. - 1670: the renowned telescope maker

Influence of Some Early Jesuit Scientists

The 35 lunar craters named to honor Jesuit Scientists: their location and description
Post-Pombal Portugal opinion of Pre-Pombal Jesuit Scientists: a recent conference
Seismology, The Jesuit Science. a Jesuit history of geophysics

Another menu of Jesuit Interest

Jesuit history, tradition and spirituality

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