A Museum for Mathematics
| The Garden of Archimedes
A Museum for Mathematics |
As well as the strictly classical tradition represented, for example, by the brothers Giovanni and Tommaso Ceva, there was, in Italy, an increasing interest in the recent discoveries reported in books, reviews, epistolary exchanges and travels made by the scholars. Leibniz himself came to Italy in 1689 for a short spell. In 1707 Jacob Hermann, who trained in Basilea where Jacob and then Johann Bernoulli taught, was asked to hold the chair of Mathematics at the University of Padua. He stayed there until 1713, establishing a close network of contacts and becoming a referral point for the Italian mathematicians who wanted to deal with the new analytic methods. He was succeeded by Nicolaus I. Bernoulli (1687-1759), while other members of the Bernoulli family, Nicolaus II and Daniel (1700-1782), spent a lot of time in Venice.
The first evidence of the use of infinitesimal calculus can be found in the works of Guido Grandi, Gabriele Manfredi, Eustachio Manfredi, Vittorio Francesco Stancari and Giuseppe Verzaglia.
The publication in Venice of the "Giornale de' letterati d'Italia" began in 1710 and became the place for contributions and discussions on the model European publications like the "Journal de Savants" in Paris, the "Acta eruditorum" in Leipzig or the "Philosophical Transactions" in London.
One dispute saw Hermann and Nicolaus Bernoulli engaged with Iacopo Riccati (1676-1754) on the inverse problem of central forces. Here, Riccati had the chance to illustrate his method of separation of the variables for the solution of differential equations. His results were then collected in a treatise compiled in 1723, which was later re-edited and included with the title On the separation of the variables in differential equations and of other subsequent degrees in the posthumous works published in 1761-1765.
Giulio Carlo de' Toschi Fagnano (1682-1766) also published numerous articles in the "Giornale de' letterati d'Italia" , and using calculus he supplied contributions on the rectification of parabolas of higher order and the lemniscate by Bernoulli. His writings are collected in Mathematic Productions which was printed in 1750 and presented to the Berlin Academy. A more comprehensive edition of his work appeared in 1911.
Domenico Corradi d'Austria was one of the first in Italy to publish a separate work entirely dedicated to the differential calculus: On differential calculus and Analytic integral notes , printed in 1743-1744.
A few years later, in 1748, Maria Gaetana Agnesi published the Analytical institutions for the use of Italian youth. Elements about algebraic equations were introduced in the first of the two volumes and in the second a complete exposition of the differential calculus is given, with analytic and geometric applications, integration rules and differential equations. The treatise was widely used by various generations of students, and the second volume was also translated into French and English.