From: rusin@adams.math.niu.edu (Dave Rusin) Subject: Re: Help on Roman Numericals Date: 22 Apr 1999 04:18:13 GMT Newsgroups: sci.math.num-analysis Keywords: Jacques Tacquet rrb wrote: >What date does this roman numerical number represents? MDCCXL >Is it 1740? Yes. >Anybody heard of a Jesuit Math Professor named Jacques Tacquet? I hadn't, but found some interesting things strolling through Math Reviews. 98b:03003 03-03 (00A35 01A99) Bellissima, Fabio; Pagli, Paolo Consequentia mirabilis. (Italian) Una regola logica tra matematica e filosofia. [A logical rule between mathematics and philosophy] Biblioteca di Storia della Scienza [Library of the History of Science], 38. Leo S. Olschki Editore, Florence, 1996. 232 pp. ISBN 88-222-4381-1 "Consequentia mirabilis" is the name given in the seventeenth century to the logical rule which states that "if a proposition follows from its own negation, then that proposition is true". Modern formal logic would formalize it as $(\not A\to A)\to A$, which is in fact a tautology. [deletia] The theme was taken up in the seventeenth century by the Flemish Jesuit Tacquet, who tried in vain to convince the Dutch mathematician Huygens of the possibility of drawing true conclusions from false premises. Huygens insisted that showing a theorem to follow from its own negation is not conclusive; instead one should show that the negation leads to contradiction, hence cannot be true: ($\not A\to(A &\not A))\to A$, which is the explicit form of a reasoning ex absurdo. According to Huygens, demonstrations should be intuitively evident rather than merely formally valid. The authors also cite a paradox of Jakob Bernoulli, which states that although sometimes truth follows from falsity, this is always absurd. They consider this a neutral echo of the Tacquet-Huygens debate. [deletia] 92h:01021 01A45 (03-03) Nuchelmans, Gabriel A 17th-century debate on the {\it consequentia mirabilis}. Hist. Philos. Logic 13 (1992), no. 1, 43--58. Summary: "In modern times the so-called consequentia mirabilis (If (if not-P, then P), then P) was first enthusiastically applied and commented upon by Cardano (1570) and Clavius (1574). Of later passages where it occurs, Saccheri's use (1697) has drawn a good deal of attention. It is less known that about the middle of the 17th century this remarkable mode of arguing became the subject of an interesting debate, in which the Belgian mathematician Andreas Tacquet and Christiaan Huygens were the main representatives of opposite views concerning its probative force. In this article the several phases and moves of that debate are delineated." ________________________________________________________________________ 94a:01012 01A45 (01A20) Palladino, Franco On the theory of proportions in the seventeenth century. Two noteworthy contributions: {\it Cuts of rational numbers} by the Galilean G. A. Borelli and {\it Classes of measures} by the Jesuit A. Tacquet. (Italian. English summary) Nuncius Ann. Storia Sci. 6 (1991), no. 2, 33--81. From the summary: "The classical definitions of ratio and proportion, defined respectively by the third and the fifth definitions of Book V of Euclid's Elements, were subjected to a rigorous examination in the seventeenth century: Among the critics and revisers of those definitions, in this paper we deal with Giovanni Alfonso Borelli and Andre Tacquet (whose definition of `equal reasons' has inspired generations of mathematicians). Borelli and Tacquet devised refined procedures to figure out the `equality of reasons' by approximation." _________________________________________________________________ 89c:01024 01A45 (01A50 01A55) Yushkevich, A. P. The development of the concept of the limit up to K. Weierstrass. (Russian) Istor.-Mat. Issled. No. 30 (1986), 11--81. [deletia] Infinitesimal methods were used in the seventeenth century to short-circuit tedious proofs by exhaustion; they made an essential contribution to the scientific revolution in astronomy, mechanics and optics. Differential problems and problems of integration were tackled successfully, thus preparing the way for the Newton-Leibniz synthesis. Old criteria of rigour were practically abandoned and new ones were not established; nevertheless, people did worry about rigour, at least in the sense of trying to find sufficiently convincing arguments. Both infinitesimals (of various orders) and limiting processes were used. In discussing this period, the author pays particular attention to the work of Valerio, St. Vincent, Tacquet, Wallis, Mengoli and James Gregory, and he mentions the influence of Wallis on Newton and of Mengoli on Gregory. [deletia] _________________________________________________________________ 88m:01102 01A73 (01A50) Vanpaemel, G. Echoes of a scientific revolution. The mechanistic natural science at the Arts Faculty in Leuven (1650--1797). (Dutch. English summary) Verh. Konink. Acad. Wetensch. België 48 (1986), no. 173, 202 pp. [deletia] It does not seem that much modern mathematics entered into the curriculum. We do not see the names Bernoulli, Euler, D'Alembert, nor even the names of important mathematicians active in the Belgium of those days, such as Sluse, St. Vincent or Tacquet. As said before, the faculty was a closed, very self-sustained, group. _________________________________________________________________ 85e:01016 01A50 Brigaglia, Aldo; Nastasi, Pietro(I-PLRM) Unpublished correspondence between the Palermian mathematician Girolamo Settimo and Gabriello Manfredi. (Italian) Boll. Storia Sci. Mat. 3 (1983), no. 1, 19--35. [deletia] In a period when Sicily was still backward in many respects, Settimo was notable for his determination to keep in touch with mathematical developments in the rest of Europe. The more substantial of his two treatises (discussed at some length in his correspondence with Manfredi) concerns "cylindrical groins' (unghiette cilindriche), figures which Settimo defines as follows: "If any cylinder is cut by a plane which intersects both its axis and its base, the part of the cylinder remaining on the base is called a cylindrical groin." Such figures had already been studied by Gregoire de Saint Vincent (1584--1667), Andre Tacquet (1612--1660) and Blaise Pascal [deletia]