# El cálculo infinitesimal y su historia en la obra de Julio Rey Pastor entre 1921 y 1940

01 Jan 2008-Vol. 1, Iss: 1, pp 367-376

Abstract: A textbook by Rey Pastor on infinitesimal calculus, from the first to the third edition, and several related papers by the same author about the history of the calculus are considered. These works were published at Buenos Aires in the period 1921- 1940. The simultaneous interest of the Spanish-Argentine author on both the mathematical and the historical work is emphasized, and the first mention of Rey Pastor to P. Mengoli is analyzed.

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01 Jan 1956

Abstract: Origins. Egypt. Mesopotamia. Ionia and the Pythagoreans. The Heroic Age. The Age of Plato and Aristotle. Euclid of Alexandria. Archimedes of Syracuse. Apollonius of Perga. Greek Trigonometry and Mensuration. Revival and Decline of Greek Mathematics. China and India. The Arabic Hegemony. Europe in the Middle Ages. The Renaissance. Prelude to Modern Mathematics. The Time of Fermat and Descartes. A Transitional Period. Newton and Leibniz. The Bernoulli Era. The Age of Euler. Mathematicians of the French Revolution. The Time of Gauss and Cauchy. Geometry. Analysis. Algebra. Poincar? and Hilbert. Aspects of the Twentieth Century. References. General Bibliography. Appendix. Index.

974 citations

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Abstract: An important step in 17th-century research on quadratures involved the use of algebraic procedures. Pietro Mengoli (1625–1686), probably the most original student of Bonaventura Cavalieri (1598–1647), was one of several scholars who developed such procedures. Algebra and geometry are closely related in his works, particularly in Geometriae Speciosae Elementa [Bologna, 1659]. Mengoli considered curves determined by equations that are now represented by y = K ⋅ x m ⋅ ( t − x ) n . This paper analyzes the interrelation between algebra and geometry in this work, showing the complementary nature of the two disciplines and how their combination allowed Mengoli to calculate quadratures in a new way.

15 citations

01 Jan 2001

Abstract: A few years after its arrival to Buenos Aires in the 1920's, Rey Pastor renewed the publishing of their investigations on mathematical analysis, and he did it in a different subject that in the previous decade he was working. The reasons why he forsook the conformal representation and he replaced it by the summability of divergent series, field in which he was active during the period 1928-36, are unknown. In this paper we enlighten about Rey Pastor's interest in divergent series by finding several precedents of his taste for this field. Moreover, we locate his papers about this subject on the general development of the theory in a stage of systematization and dialectic synthesis when it was adjusting oneself to a normal science. Finally, we review the four author's papers which seem its essential between those he wrote on summability of divergent series.

3 citations