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André Tacquet, S.J.
(1612 - 1660)
and his treatment of infinitesimals

Andre Tacquet, S.J. was born and died in Antwerp.He studied mathematics under the famous Jesuit mathematician Gregory St. Vincent and later taught mathematics at Louvain and Antwerp. Tacquet was a brilliant mathematician of international repute. His books were frequently reprinted, and several Italian and English editions appeared and were widely used. His Opera mathematica was described by Henry Oldenburg (editor of the Transaction of the Royal Society) as "one of the best books ever written in mathematics." Oldenburg commented:
". . . being an account of one of the most considerable volumes of mathematics extant, we hope we may be the better excused for its prolixity."
Tacquet's work helped pave that way for the discovery of the calculus. His use of the method of exhaustion pointed the way to the limit process later formulated by Wallis.
Carl Boyer has a fine treatment of the thorny problems that had to be faced before the articulation of calculus was possible: one such problem was infinity and infinitesimals. The former problem has theological implications, since nervous churchmen felt it was an intrusion into God's infinity. Cantor found this out in a later century and went to the Jesuit (non-mathematician) John Cardinal Franzelin for help in selling his ideas on infinite numbers. As a result, the strange term (a compromise) "transfinite" was introduced; it satisfied the nervous churchmen as well as the anxious mathematicians. Dirk Struik speaks of a similar problem at the time of Gregory St. Vincent and André Tacquet, when the groundwork was being laid for the infinitesimal calculus. Aristotle and Aquinas held that there is no actual infinite and a continuous line cannot be made up of indivisible parts. A point could generate a line by motion but a point was not part of a line.
. . . Georg Cantor has remarked that the transfinitum cannot be more energetically desired and cannot be more perfectly determined and defended than was done by St Augustine . . . Such speculations had their influence on the inventors of the infinitesimal calculus in the seventeenth century and on the philosophers of the transfinite in the nineteenth; Cavalieri, Tacquet, Bolzano and Cantor knew the scholastic authors and pondered over the meaning of their ideas. (See D.J. Struik: A concise history of mathematics. New York: 1948, vol 2, p. 88).


Although Tacquet was born a century before Newton published his calculus, he helped articulate some of the preliminary concepts necessary for Newton and Leibniz to recognize the inverse nature of the quadrature and the tangent. He described how a moving point could generate a curve and he treated area and volume in his major work Cylindricorum et annularium (Antwerp, 1651). This work influenced the thinking of Pascal and his contemporaries.


Archivum Historicum Societatis Iesu ( AHSI ) Rome: Institutum Historicum
Bangert, William A History of the Society of Jesus. St. Louis: St. Louis Institute, 1972uis, 1810
Boyer, Carl A history of mathematics. New York: Wiley, 1968
Gillispie, Charles. C. ed., Dictionary of Scientific biography. 16 vols. New York: Charles Scribner and Sons, 1970
{ Reference to Tacquet in the Dictionary of Scientific Biography is found in v 1 p 164, v 1 p474, v 4 p 451, v 10 p 336, v 13 p 235, v 13 p 561.
Oldenburg, Henry ed. Philosophical Transactions of the Royal Society. vols. 1-30. London: 1665-1715 { Articles by him or concerning his work are found in the Philosophical Transactions of the Royal Society of London in v 3 p 869-876.}
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
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:
Opera Omnia Cylindricorum et Annularium (Antwerp, 1651)
Elementa Geometriae (Antwerp, 1654) BR> Arithmeticae Theoria et Praxis (Louvain 1656)}

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

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Jesuit history, tradition and spirituality

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