she did not insist upon it, and returned to her interrupted studies. She only asked "three favors" from her father, and these were such as many women would hardly have been satisfied with: that she might dress simply, go to church when she pleased, and give up all unreligious amusements. She then devoted herself to algebra and geometry, "the only provinces of the literary world in which peace reigned," and soon her fame, passing beyond the circle of her friends, was spread through the whole learned world. Giovanni Battisto Bertucci intrusted her with his manuscript De Telluris ac siderum vita (September 19, 1738). She detected some inaccuracies in it, which the author corrected at once. Giacomo and Giordano Riccati read her works with great interest. Eustaccio Zanotti entertained her with his observations on eclipses. Paolo Frisi (brother to the one who composed her biography) sent her his manuscript, De Figura et Magnitudine telluris. Carlo Belloni intrusted his writings to her. The president of the Institute of Bologna, Beccani, submitted to her judgment the Acta of his academy; and finally—a well-merited distinction—Zanotti announced to her, June 20, 1748, that that learned society had just called her to be one of its members.
This election to the academy still further, if possible, stimulated Agnesi's zeal for science; and, notwithstanding the death of the last of her brothers, October 23, 1748, she published at the close of that year the great treatise on analysis which definitely established her reputation as a mathematician. Begun under the advice of Father Bampinelli, professor of anatomy and physics in the monastery of St. Victor, the Instituzioni analitiche ad uso delta gioventu italiana di dona Maria Gaetana Agnesi Milanese dell' Accademia delle scienze di Bologna, in two quarto volumes, was received with enthusiasm, and soon took the place of the Marquis de l'Hôpital's Infinitesimal Analysis and Father Reyneau's Practical Analysis. The first volume included algebra and its applications to geometry, and the second treated of the differential and integral calculus. They were dedicated to the Empress Maria Theresa, who in recognition of the homage gave the author a box made of rock crystal and adorned with a brilliant. Pope Benedict XIV sent Agnesi a coronet of precious stones ar.d a gold medal, which Cardinal Antonio Rufo brought to her, together with a very flattering pontifical letter, in which among other passages we read: "We undertook in the flower of our early youth the study of analysis, but afterward gave it up. We therefore only know enough of analysis to appreciate its importance and to realize how glorious it is for our Italy that it has professors of it. So far as we have been able to judge from looking over the table of contents of your work, and particularly from reading a few chapters of the analysis of finite quantities, we are in a
