Alphonse Antonio de Sarasa and Logarithms

The discovery of hyperbolic logarithms has been variously attributed to Gregory of St-Vincent and to Alphonse Antonio de Sarasa. In this paper we describe the relationship between St-Vincent and de Sarasa, the challenge from Mersenne which provoked de Sarasa's publication, de Sarasa's understanding of logarithms, and the propositions of de Sarasa where the connection between hyperbolic areas and logarithms was first claimed. Since de Sarasa's hyperbolae were not defined analytically, he did not insist on a particular base for his logarithms, nor did he choose a value for log 1 which would have implied log AB=log A+log B, so we conclude that he did not focus on what Euler later called natural logarithms. An explanation of the different accounts of the origin of natural logarithms offered by twentieth century writers is tentatively proposed. Copyright 2001 Academic Press.Die Entdeckung hyperbolischer Logarithmen ist verschiedentlich Gregorius a S.Vincentio und Alphonse Antonio de Sarasa zugeschrieben worden. In diesem Artikel beschreiben wir die Beziehung zwischen St.Vincentius und de Sarasa, die Herausforderung von Mersenne, die de Sarasas Veröffentlichung provozierte, de Sarasas Verständnis von Logarithmen und die Sätze de Sarasas in denen der Zusammenhang zwischen Hyperbelflächen und Logarithmen zum ersten Mal behauptet worden ist. Da de Sarasas Hyperbeln nicht analytisch definiert waren, forderte er keine Basis fuer seine Logarithmen. Er wählte auch keinen Wert fuer log 1, der log AB=log A=log B impliziert hätte. So können wir schliessen, dass er sich nicht auf das konzentrierte, was Euler später natürliche Logarithmen nannte. Eine Erklärung der unterschiedlichen Darstellungen über den Ursprung der natürlichen Logarithmen, die Autoren des 20. Jahrhunderts geben, wird ansatzweise versucht. Copyright 2001 Academic Press.MSC 1991 subject classification: 01 A 45.     

Probability and exams: The work of Antonio Bordoni

The Italian mathematician Antonio Bordoni is mainly known for his adherence to the Lagrangian approach to the foundations of calculus and for his role in creating an important school of mathematics. In this paper, I consider his less known work on the application of probability to design exams and analyze their outcomes. Within this framework, he obtained in 1837, as Mondésir and Poisson, the result that would lead Catalan to formulate his “new principle” of probability (Jongmans and Seneta, 1994). Moreover, in 1843, Bordoni also gave an early complete proof of the finite rule of succession.     

导数空间另一类D’Alembert原理及任意阶非完整系统的新型Maggi方程

作为笔者在文献[1,2,3]中提出的“导数空间”和导数空间中“相当动能”的概念及“将非完整系统变为形式上的完整系统处理”思想的具体应用,本文导出了又一类新型的万有D′Alembert原理及适用于任意阶非完整系统的新型的Maggi方程,并给出了应用此方程的算例。