The most valuable result of her labours was the Instituzioni analitiche ad uso della gioventu italiana, a work of great merit, which was published Milan in 1748. The first volume treats of the analysis of finite quantities and the second of the analysis of infinitesimals. A French translation of the second volume by P. T. d'Antelmy, with additions by Charles Bossut (1730  1814), appeared at Paris in 1775; and an English translation of the whole work by John Colson (1680  1760), the Lucasian professor of mathematics at Cambridge, was published in 1801 at the expense of Baron Maseres. Madame Agnesi also wrote a commentary on the Traite analytique des sections coniques of the marquis de l'Hôpital, which, though highly praised by those who saw it in manuscript, was never published. She invented and discussed the curve known as the "witch of Agnesi[?]" or "versiera" (Italian "she  devil" or "the witch"), as she named it in 1748 and defined as:
or in general:
The curve was already studied before by Fermat and by Grandi[?] in 1703.
In 1750, on the illness of her father, she was appointed by Pope Benedict XIV. to the chair of mathematics and natural Philosophy at Bologna. After the death of her father in 1752 she carried out a longcherished purpose by giving herself to the study of theology, and especially of the Fathers. After holding for some years the office of directress of the Hospice Trivulzio for Blue Nuns at Milan, she herself joined the sisterhood, and in this austere order ended her days.
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