SKETCH OF MARIA AGNES I. 407 



slie did not insist upon it, and returned to lier 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 writ- 

 ings 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, 1T48, 

 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, 1T48, 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 monas- 

 tery of St. Victor, the Instituzioni analitiche ad uso delta gioventu 

 italiana di dona Maria Gaetana Agnesi Milanese delV Accademia 

 delle scienze di Bologna, in two quarto volumes, was received with 

 enthusiasm, and soon took the place of the Marquis de I'Hopital's In- 

 finitesimal Analysis and Father Reyneau's Practical Analysis. The 

 first volume included algebra and its apjDlications 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 im- 

 portance 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 



