MARIA GAETANA AGNESI THERE IS NO INNOVATION WITHOUT MEMORY

Maria Gaetana Agnesi was born in Milan on May 16, 1718 so this year marks the 300th anniversary of his birth. She is "considered to be the first woman in the Western world to have achieved a reputation in mathematics." The most valuable result of her labours was the Instituzioni analitiche ad uso della gioventù italiana, (Analytical Institutions for the Use of Italian Youth) which was published in Milan in 1748 and "was regarded as the best introduction extant to the works of Euler." The goal of this work was, according to Agnesi herself, to give a systematic illustration of the different results and theorems of infinitesimal calculus. The Instituzioni did not assume any previous knowledge of algebra and was the first attempt to provide and extensive and accessible introduction for the beginners. In this article, we present two significant problems, which one can find in her book and that could even be put back into our high schools now. The two problems Maria Gaetana found in the Renaissance Mathematical tradition: the first is the famous problem about King Hiero’s crown, that we find in Vitruvius and Galileo Galilei, and, after Maria Gaetana, in Paolo Romeo da Siderno. The four solution are very different each other. The second problem is an application of logarithms to a problem of everyday life that we can find in more elementary form in Luca Pacioli’s De Viribus Quantitatis.