Maria Gaetana Agnesi (May 16, 1718 - January 9, 1799) was an Italian linguist, mathematician, and philosopher. Agnesi is credited with writing the first book which discussed both differential and integral calculus. She was an honorary member of the faculty at the University of Bologna.
By her thirteenth year she had acquired Greek, Hebrew, French, Spanish, German and other languages. Two years later her father began to assemble in his house at stated intervals a circle of the most learned men in Bologna, before whom she read and maintained a series of theses on the most abstruse philosophical questions. Records of these meetings are given in de Brosse's Lettres sur l'Italie and in the Propositiones Philosophicae, which her father caused to be published in 1738. These displays, being probably not altogether congenial to Maria, who was of a retiring disposition, ceased in her twentieth year, and it is even said that she had at that age a strong desire to enter a convent. Though the wish was not gratified, she lived from that time in a retirement almost conventual, avoiding all society and devoting herself entirely to the study of mathematics.
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'H˘pital, which, though highly praised by those who saw it in manuscript, was never published. She discussed the curve known as the "witch of Agnesi" or "versiera" as she named it in 1748. (Italian for the rope that turns a sail, taken from the Latin "versoria" which was the term used by Luigi Grandi before her. John Colson, who translated Agnesi's text to English, perhaps confused "la versiera" with "l'avversiera", and so mistranslated it as "she - devil" or "the witch", with the result that English-speakers, and only English-speakers, know the curve as the "Witch of Agnesi.") It is 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 long-cherished 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.