# Popular Science Monthly/Volume 53/July 1898/Sketch of Maria Agnesi

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MARIA AGNESI.
* SKETCH OF MARIA AGNESI.
By M. JACQUES BOYER.
TO assert that women have had an important influence on the progress of science would certainly be exaggeration; but to say that they have always been wholly foreign to it would be still more inexact. The female sex have, in fact, been for many centuries contributing to the extension of the field of scientific knowledge; and now that they are beginning to take a more prominent part in affairs of this category it seems a favorable time to review some of their achievements, and to notice some of the women whose scientific accomplishments have been most remarkable.
We begin with a Milanese mathematician of the eighteenth century—Maria Agnesi, a woman who was unique among the few who have occupied themselves with the exact sciences. Her precocious intelligence and a prodigious memory, which permitted her to express herself correctly in seven languages, and her rare aptitude for one of the most arduous branches of mathematics—the infinitesimal analysis of which Leibnitz and Newton had only just indicated the formulas—the saintliness of her life, divided between study, prayer, and charitable works—all contribute to make her one of the most agreeable characters which the scientific history of the last century offers us.
This illustrious learned lady was born in Milan, May 16, 1718. Her father, Dom Pietro Agnesi Mariami, was a royal feudatory of Monteveglia, and her mother was named Anna Brivia. Baptized on the 23d of May in the basilica of Santo Nazzaro il Maggiore, she was given the name of Margaretta Gaetana Maria. She showed marked aptitude for languages from a very early age. She spoke French well when five years old, as we learn from the following sonnet by a friend of her father's: "At that age which retains only the first forms of the language of her country, and which is still easily fatigued by the task, a pretty little girl uses the French idiom with such grace and ease that a nymph on the banks of the Seine could not speak in a sweeter and more pleasant manner. It seems as if Time was afraid his flight could not keep up with the ​mind of this young person, and had appeared to slacken his march; and I, between the sight of so young an age and the charm of such an elocution, do not know which to believe—what I see or what I hear."
It was not only in French that Agnesi made wonderful progress. She followed also the lessons in Latin which the Abbate D. Nicolo Jemelli gave to one of her brothers, and when nine years old she translated from Italian into Latin an essay which she recited before several auditors. She thus maintained—nearly two hundred years before Marya Chéliga and Maria Pognon—the right of women to study letters, the fine arts, and science if they feel called to it. This essay is dedicated to Dom Augustino Tolotta, a friend of her family and a very well educated man, to whom she modestly attributed all the merit of it. She mentions in it, among other celebrated women, Cornelia Piscopia (the oracle of seven languages), to whom the University of Padua awarded the laureate of philosophy, and Madame Dacier, translator of Homer.
Agnesi's coming out was then a brilliant one, and the rest of her life did not contradict the hopes it awakened in the minds of her friends. When eleven years of age she knew enough Greek to recite the Office of the Virgin in that language, a pious practice which she kept up till her death. Long before reaching her twentieth year, besides speaking Greek, Latin, French, and Italian, she was acquainted with German and Spanish. These many idioms, according to Mazzuchelli, caused no confusion in her mind, and she translated freely from one language into another. She also left in manuscript a Greek translation of Il Combattimento spirituale of P. Lorenzo Scupoli, the two books of Supplements to Quintus Curtius of Freikshemius, translated into French, Italian, German, and Greek; three small volumes of a Greek and Latin Lexicon containing more than thirteen thousand words; and a Greek translation of a work on mythology.
Miss Agnesi's health was seriously disturbed by so close application, and in December, 1730, the doctors advised her father to find some way of diverting her mind from her studies. But she, in the ardor of her application, doing everything with passion, followed ​the prescriptions too faithfully and too far, and balls and horseback riding, instead of curing her, brought on convulsions. Her disorders continued to increase immediately after the death of her mother, March 13, 1732, but she was subsequently gradually restored to quiet. This death gave rise to some changes in the family life, and Maria's father, who had five daughters and two sons by his first wife, was married a second time, February 23, 1734, to a Milanese lady, Mariana Pezzi. Two children resulted from this union, which was unfortunately brief, the second Madame Agnesi dying August 19, 1737, at the age of twenty-three years.
As a means of consolation in the grief that had fallen upon her father's household, Agnesi extended the field of her knowledge, and at last found her true' career in the cultivation of philosophy and mathematics. She was not destined, it is true, to make a very prominent mark, but simply to occupy a highly honorable place among the great algebraists of the eighteenth century. Father Manera, of Cremona, and Father Michaelo Casati, professor in the Royal University at Turin, who was afterward (in 1754) nominated Bishop of Moudoir, taught her logic, metaphysics, Euclid's elements, and physics. She soon acquired great proficiency in all these sciences, and sustained theses in the presence of qualified persons. In these assemblies, after having discussed and refuted the arguments of her antagonists, she was accustomed to express her own opinions in very pure Latin. Her sister, Maria Teresa, an accomplished musician, introduced the artistic element into these meetings, which at last became so celebrated that princes and illustrious travelers passing through Milan often attended them. Many persons retained pleasant recollections of them, as is attested by the following passage from De Brosses' Letters from Italy, which is cited in M. Robière's excellent book on Women in Science, and which we quote as the story of a witness: "I would like to tell you, Mr. President, of a kind of literary phenomenon I have recently witnessed, and which has seemed to me something more stupendous than even the Duomo of Milan, and at the same time I was not taken unawares. I have just been to Signora Agnesi's, where I told you yesterday I was going. I was introduced into a large apartment, where I found thirty persons of all the European nations arranged in a circle, and Mademoiselle Agnesi seated alone with her younger sister on a sofa. She is eighteen or twenty years old, neither pretty nor plain, with a very simple and pleasant expression. First, plenty of iced water was brought in, which seemed to me a good augury. I was anticipating, when I went in, only an ordinary conversation with the lady; but instead of that. Count Belloni, with whom I was, now planned a kind of public act. He began by making the young lady a fine ​address in Latin, so that every one could understand it. She regarded him attentively, and they then began to converse in the same language on the origin of fountains and the cause of the flow and ebb, like that of the sea, which some springs exhibit. She spoke like a superior intelligence on the subject; I have heard nothing upon it that gave me more satisfaction. After this conversation. Count Belloni invited me to talk with her in the same way on any subject I pleased, in philosophy or mathematics. I was astonished to find that I was expected to speak impromptu and in a language to which I was little used; but, be it as it might, I paid her a handsome compliment, and then we discoursed concerning the way in which mind could be affected by corporeal objects and communicate concerning them with the organs of the brain; and afterward concerning the emanation of light and the primitive colors. Toppin conversed with her on the transparency of bodies and on the properties of certain geometric curves, of which I understood nothing. Evidently Agnesi's parties are hardly of this world!"
When Agnesi was nineteen years old, she had already sustained one hundred and ninety-one philosophical theses. Of course, they are somewhat superficial theses, in which, after having cited the principal views of various authors, Agnesi discussed and affirmed her own opinion. This proves, nevertheless, that she had received a somewhat more solid instruction than was till recently given to the young women of our time. The inquiring quality of her mind and her taste for science are likewise revealed in her correspondence. On April 26, 1733, she received from Father Manara a letter from Rome which resolved some of her doubts concerning ballistics. In another letter she sent Count Charles Belloni the solution of a problem in analytical geometry; and a response from him (July 5, 1735) cleared up some difficulties which she had met in reading the Conic Sections of the Marquis de l'Hôpital, published in 1707, of which she had undertaken to make a commentary.
Not these labors alone engaged her thoughts. Toward her twentieth year, in the very midst of her success, she contemplated retiring from the world to enter a religious society, now suppressed, called the Celeste, or Turquine, from the color of their dress, or Carcanine, from the name of their founder, Giovanni Pietro Carcano. But, in view of the distress that this resolution cost her father, ​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 ​position to declare sincerely that you are incontestably one of the foremost professors of that subject, that your work will be very useful, that it will contribute to the literary reputation of Italy and of our Academy of Sciences at Bologna." In another quarter, two members of the Royal Academy of Sciences of Paris, de Mairan and de Montigny, were commissioned to examine the Instituzioni analitiche, and they observed in their report that order, lucidity, and precision reigned in all parts of the work. They regarded it, in short, as "the most complete and best composed treatise" extant on that difficult subject. De Montigny, too, in the letter accompanying the transmission of the report to Agnesi, informed her that he had desired to see her while traveling in Italy, in 1740, but circumstances had disarranged his plans, and he had been obliged to return by way of Geneva without passing through Milan. He added: "I much regretted thus missing you, but my regrets are much increased now, after having read your book; and I can never console myself for not having had the pleasure of seeing you and talking with you, for Italy has not offered me any object more worthy of my admiration. I admire especially the art with which you have brought together under uniform methods so many facts scattered through the works of the geometricians, most of which have been acquired in very various ways." The work of our learned lady had therefore a very flattering success. Other evidences of its merit are afforded by its having been translated into English by Colson in 1801, and by the translation of the second volume by d'Anthelmy into French, with notes by Bossu, under the name of Traités élémentaires du calcul différentiel et du calcul intégral (1775). Its remarkable character is further indicated by an observation by M. Rebière that the first works on so difficult and new a science as the infinitesimal calculus are of extreme importance.
Besides his gift to Agnesi, Pope Benedict XIV nominated her in 1750 professor of mathematics in the University of Bologna. But notwithstanding the invitation of the Roman pontiff, who reminded her that Bologna had already heard persons of her sex in its public chairs, and that he pressed her to "continue so commendable a tradition," she did not teach. Her delicate health and the education of her brothers, with which she had charged herself after the death of her father (March 19, 1752), confirmed her determination to give up her scientific work. After that, Agnesi no longer existed as a mathematician. Maria Gaetano devoted herself exclusively to the care of the orphans and bade good-by to the world in a profession of faith in which she proclaimed, in substance, that "man ought always ​to work for some end—the Christian for the glory of God; my studies have had this glory in view, for they were conformed to the desire of my father. Now, finding better means of serving God, so near me, I must use them."
She began by taking two infirm persons into her rooms; and afterward she withdrew into a remote part of her house, and gave a home there to a considerable number of women, which the sale of the Empress Maria Theresa's valuable gift to a rich Englishman enabled her to increase. In 1759 she hired a house near the church of San Benedetto, at the gate called "Vigentina," in which she lived with one of her brothers after the division of the family estate was made in 1764. When this house was sold in 1771, she moved into another between the churches of Santa Maria de la Visitatione and Sant Appolinare, where, assisted by the liberality of Prince Antonio Ptolomeo Trioulzi, she took care of four hundred and fifty poor persons of both sexes. She still found means, with all these multifarious occupations, to accept invitations to dinner, for she was a foe to even the slightest eccentricity. She won the admiration of her fellow guests by the sweetness of her manners and the easy grace of her conversation. This did not cause her to neglect the reading of the Holy Scriptures, for she composed theological and ascetical writings. But after 1791, having suffered an attack of gout and her sight being weakened, she became a frequent visitor to one of the country houses of her father's estate. She died of dropsy of the breast, after a long illness, January 9, 1799, and was buried in the parochial basilica of Santo Stephano, where she is described in her epitaph as a woman remarkable for her piety, knowledge, and benevolence.
* ↑ In the Éloge historiquie de Maria Gaetano Agnesi, demoiselle célèbre par ses grands talens dans les mathématiques, par se pieté et sa bienfaisance, ouvrage traduit de I'ltalien de Frisi (Paris, 1807, 8vo, p. 5), she is said to have been born March 16, 1718, but that is a typographical error. We should read May. This work, composed from the archives of the Agnesi family, is otherwise very exact, and a large number of the facts that follow have been derived from it. It is needless to add that the general dictionaries, including even the Biographic Universelle de Michaud (new edition, 1843, vol. i, p. 233), have rejected Frisi's error.
* ↑ The sonnet was dedicated, "Alia nobile fanciulla D. Maria Gaetano Agnesi, che nell' eta cinque parla mirabilmente Francese" (To the noble child Donna Maria Gaetano Agnesi, who, when five years old, spoke French admirably), and was written in Italian. We give it in an English unversified translation.
* ↑ Mazzuchelli. Gli Scrittori d'ltalia, vol. i (1795), Part I, p. 198.
* ↑ The Ambrosian Library of Milan possesses, besides, numerous scientific manuscripts of Agnesi which bear witness to her prodigious industry. The principal among them are: Metâfisica e fisica, fisica e matematica, Studi di Cosmografia, Gnomonica geometrica, Fisica e matematica, Studi e correspondenze sopra varii punte del Trattato analitico.
* ↑ They have been published under the title Propositiones philosophicæ quas crebris disputationibus domi habitis coram clarissimis viris explicabet ex tempore et ab objectis vindicabat Maria Cajetana de Agnesis Mediolanensis (Philosophical propositions which Maria Gaetana Agnesi, of Milan, explained ex tempore and vindicated from objections in frequent disputations held at home in the presence of the most distinguished men), Mediolani (1738), and they are dedicated to Charles Belloni, of Paris.
* ↑ Her father had married his third wife, the noble Milanese lady, Dona Antonia Barati, and had by his three wives twenty-four children.
* ↑ The inscription on her tomb reads: Maria Gaetano Agnesi: Pietate, Doctrina, Beneficentia Insignis. H. S. E. Dec. An. MDCCXCIX, V. I. D. IAN. Aetat. LXXXI.