Biography of Benito Bails (1730-1797)

Spanish mathematician, born in Barcelona in 1730, and died in Madrid in 1797. He/She studied first at the University of Toulouse, and later continued in Paris, where he/she received the protection of the Spanish Ambassador. To stop this in his post and return to Madrid, he/she took with him to his protégé, which presented in the intellectual circles. Their remarkable culture, encompassing philosophy, law, humanities and theology, the sciences and the correct knowledge of languages such as latin, Italian, English, German and French, made him creditor to a position at the Academy of the language, history and the sciences and arts of Barcelona. The count of O´Reilly, inspector-general of infantry, commissioned the drafting of a Treaty of mathematics for the use of schools for cadets who settled in all regiments of infantry, which took place with the collaboration of Gerónimo Capmany. Tricks, on the other hand, was appointed "director of Mathematics" of the Royal Academy of San Fernando, which drafted a few elements of mathematics in ten volumes. This work is the mathematical work of most important encyclopedic character published in Spanish during the 18th century. The first three volumes contain arithmetic, geometry and trigonometry (I), algebra (II), conics, infinitesimal calculus and differential equations (III). The volumes IV to VI include dynamics, hydrodynamics and optics. The VII and VIII are some elements of physical astronomy, in which the historical part is of great importance. Finally, volumes IX and X are exposed to civil and hydraulic architecture and the table of logarithms. All of them go preceded by prologues in which is given news of the works consulted or copied, and becomes a bibliographical criticism which is substantial part in the whole of the work.

The importance of this Treaty in the panorama of mathematics in Spain forces to make some considerations on their preparation and influence in the scientific environment. The general plan of the work is based on the idea of exhibiting in didactic theory, with their latest developments, mathematics, physics and astronomy part. The author explains in the general prologue the motives and the limitations of his work: "more aware of what we would like that were very strange for our men the doctrines that we were going to publish, and how much that matter out to the public with all possible as soon as our work, we stopped shortly in materials, which touched us to try to givelook very different from what it was in the classics that we are dedicated to extract or copy; We only care in lay your hands on the most celebrated, and bind all carefully pieces which we drew different [...] for the formation of a treaty but we thought then that four volumes of pure mathematics, could give overtones of well-founded complaints of some men who watched with no little opposition our destiny, which, he/she his patriotism to the short number of objects which reaches, or has around itself, they contribute with disgust, or were violent opposition to universal utility companies. And made that charge, all considered good, mixed agreements are those who matter most, we sacrifice the speculative practice..." (Elements of math, I, pp. XIII - XIV).

Educational and informative intentions about any others predominate in the work. So although it literally translates substantial parts of the works of Étienne Bézout , Gabriel Cramer, you enter explanatory paragraphs in some issues which are given by known in the development of the material contained in the cited works; "arithmetic which brings seemed us clearly very cabal [...]" copy it to the letter, which Mr. Bézout published it"(elements, I, p. XVIII). In the drafting of the geometry, use annotated editions of the most important elements of Euclid . Purpose of this part, collects the following comment about Newton: "that Newton arrepintiese of having engolfado in the analytical methods before possessing the Euclid, this can prove when more than the great man felt, Wolfio (Christian Wolff), says it not having read with corresponding maturity, because according to concerns his historian, they seemed so easy to their 'elements', which despised to study them" (elements(, I, p. XXXIII). To Algebra, again using the book of Étienne Bézout "until the resolution of the above equation" (items II, p. IV) and, in addition, the authors more important as Newton and Leonhard Euler. In volume III, where gathered the latest discoveries in the analysis, it adopts the Gottfried Wilhelm Leibniz notation for the differential calculus and enter the calculus of variations, which says "is invention of M. de la Grange (Joseph Lagrange)" (elements, III, p. XXXIV). In the preface to the dynamics, says: "Although complete for our purposes, according to dexamos evoked, our dynamic is very oft include everything in this industry need to know; in many points we had to stick to the fundamental principles, being carefully to news in this foreword to writings where fans will find with the detail that they want some doctrines than our touched, to say, no more pass"(elements, IV, p. XIX). Optics, he/she spends a good deal to the description of optical instruments and preparation of glass, with the intention of serving the naturalists and astronomers. In the first of the volumes dedicated to astronomy, speak of the "system of the world" with revealing precautions of ignorance and backwardness makers of science in Spain. Begins by stating that there are several systems, but that "once I am forced to stick, will only propose the most celebrated of all, renovated in the 15th century by Nicolás Copérnico, Canon of Thora, city of Poland, whose system has day has many enlightened Nations of Europe, by the true system of nature." But I, suspicious that is given me in face with that I was forbidden to be so bold or so gullible, I section with simply propose it, and if I then add the arguments that have been allowed to concern some philosophers in his favor, is with the sight no more do patent founded quan is the authority of men in tackling what it calls excesses of human reason"(elements(, VII, p. 90). Later adds: "pass, therefore, to meet the main arguments, so it is challenged him in the past." I say in other times, because not known in our days none opposite, in Germany, in France or in England"(elements, VII, p. 107). This part of the work has the interest, like the rest, introduce clear problems that were considered at that time, as the three bodies. The two following volumes, which exposes the civil architecture, were the last ones published. Formerly edited the volume X, which is not limited to tables of logarithms and trigonometry, but also using modern notation and treats them as a function ax = and (elements, X, p. 225).

Towards the end of his life, tricks was banished to Granada (2 March 1792). The reason is not well clarified. In a letter to the King (AHN, State leg. 3127), calls "serve pardon of exile... and if not... pleads with the least that the Court or judges having V.M. well name be made charges that has been challenged." The Bishop of Jaen approached the Duke of Alcudia (AHN, State, leg. 3127) indicating that tricks didn't matter with the Inquisition, and asking to grant you clemency. Finally, in November 1792, the Duke of Alcudia agreed to the request.



Elements of mathematics, 10 vols., Madrid: Joachim Ibarra, 1772-1776, 1783. Principles of mathematics, 3 vols., Madrid: Ibarra VDA, 1776. Arithmetic for dealers, Madrid, 1790. Institutions of geometry for the use of young artists, Madrid, 1795.


CAJORI, f.: A History of Mathematical Notations, 3rd ed., 2 vols., La Salle (Illinois): The Open Court Publishing Co., 1952.VERNET GINES, j.: history of the Spanish science, Madrid: Instituto of Spain, Chair "Alfonso X, el Sabio", 1975.