Maria Gaetana Agnesi

Maria Gaetana Agnesi (May 16, 1718 – January 9, 1799) was an Italian linguist, mathematician, and philosopher. Agnesi is credited with writing the first book discussing both differential and integral calculus. She was an honorary member of the faculty at the University of Bologna. Her father, Pietro, was a wealthy mathematics professor.
Maria could speak both French and Italian at five years of age. By her thirteenth birthday she had acquired Greek, Hebrew, Spanish, German, Latin, and probably a few more languages. She even educated her younger brothers. When she was 9 years old, she composed and delivered an hourlong speech in Latin to an academic gathering. The subject was women's right to be educated. When she was fifteen, her father began to regularly gather in his house 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 had published in 1738. These displays, being probably not altogether congenial to Maria (who was of a retiring disposition) ceased by her twentieth year, and it is even said that she had a strong desire to enter a convent at that time. Although her wish was not granted, she lived from that time on in an almost conventual semiretirement, avoiding all interactions with 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'Hôpital, 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 Englishspeakers and, for some reason, Spanish speakers from Mexico, Cuba, and Spain, know the curve as the "Witch of Agnesi"(La bruja de Agnesi.)) The curve is defined as:
 <math> y = {1\over {x^2 + 1}} <math>
or in general:
 <math> y = {a^3\over {x^2 + a^2}} <math>
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. She was the second woman to be appointed professor at a university. 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 and devoted herself to the poor, homeless and sick. 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.
References
 Larson, Ron; Hostetler, Robert P.; and Edwards, Bruce H. (2003). Calculus of a Single Variable: Early Transcendental Functions (3rd edition). Houghton Mifflin Company. ISBN 061822307X.
 Mathematics History archive entry for Maria Gaetana Agnesi at the University of Andrews, Scotland (http://wwwgap.dcs.stand.ac.uk/~history/Mathematicians/Agnesi.html)
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