FOOTNOTES:
[108] "Ipse mulieres Philosophas in libris Veterum sexaginta quinque reperi," Historia Mulierum Philosopharum, p. 3, Amstelodami, 1692.
[109] Plato had inscribed above the entrance of his school, Ουδεις αγεωμετρητος εισιτη. Let no one enter here who is not a geometer.
[110] Menagius in referring to this matter, op. cit., p. 37, writes as follows: "Meritrices Græcas plerasque humanioribus literis et mathematicis disciplinis operam dedisse notat Athenæus."
[111] The sentiment of the Greek epigram is well expressed in the following Latin verses:
"Quando intueor te, adoro, et sermones,
Virginis domum sideream intuens.
E coelis enim tua sunt opera,
Hypatia casta, sermonum venustas,
Impollutum astrum sapientis doctrinæ."
[112] Among modern works on Hypatia may be mentioned Hypatia, die Philosophin von Alexandria, by St. Wolt, Vienna, 1879; Hypatia von Alexandria, by W. A. Meyer, Heidelberg, 1886; Ipazia Alessandrina, by D. Guido Bigoni, Venize, 1887, and De Hypatia, by B. Ligier, Dijon, 1879.
[113] Ambrosius in his preface to the works of Abelard and Heloise refers to the latter as "Clarum sui sexus sidus et ornamentum," and declares "necnon mathesin, philosophiam et theologiam a viro suo edocta, illo solo minor fuit."
[114] Mazzuchelli says of her in his Museo, "Sembra non avervi nella Natura cosa la piu intralciata ed oscura nelle storie, ne finalemente la piu astrusa nelle matematiche e nelle mecchaniche, che a lei conta non sia e palese, e che sfugga la capacita del suo spirito." Dizionario Biografico, Vol. I, p. 122, by Ambrogio Levati, Milano, 1821.
[115] Delle Donne Illustri Italiane del XIII al XIX Secolo, p. 268, Roma.
[116] The full title of this celebrated discourse is Oratio qua ostenditur Artium liberalium studia a Fæmineo sexu neutiquam abhorere, habita a Maria de Agnesis Rhetoricæ Operam Dante, Anno ætatis suæ nono nondum exacto, die 18, Augusti, 1727. It is found at the end of a work entitled Discorsi Academici di varj autori Viventi intorno agli Stuj delle Donne in Padova, 1729. This subject, it may be remarked, frequently engaged the attention of Maria Gaetana as she advanced in years, for we find it among the questions discussed in her Propositiones Philosophicæ, pp. 2 and 3, Mediolani, 1738.
[117] M. Charles de Brosses, in his Lettres Familières écrites de l'Italie en 1739 et 1740, speaks of Agnesi in terms that recall the marvelous stories which are related of Admirable Crichton and Pico della Mirandola. "She appeared to me," he tells us, "something more stupendous—una cosa piu stupenda—than the Duomo of Milan." Having been invited to a conversazione for the purpose of meeting this wonderful woman, the learned Frenchman found her to be a "young lady of about eighteen or twenty." She was surrounded by "about thirty people ... many of them from different parts of Europe." The discussion turned on various questions of mathematics and natural philosophy.
"She spoke," writes de Brosses, "wonderfully well on these subjects, though she could not have been prepared beforehand any more than we were. She is much attached to the philosophy of Newton; and, it is marvelous to see a person of her age so conversant with such abstruse subjects. Yet, however much I was surprised at the extent and depth of her knowledge, I was still more amazed to hear her speak Latin ... with such purity, ease and accuracy, that I do not recollect any book in modern Latin written in so classical a style as that in which she pronounced these discourses.... The conversation afterwards became general, everyone speaking in the language of his own country, and she answering in the same language; for, her knowledge of languages is prodigious."
[118] At the conclusion of an elaborate review of Colton's translation of Agnesi's Instituzioni Analitiche in the Edinburgh Review for January, 1804, the writer expresses himself as follows: "We cannot take leave of a work that does so much honor to female genius, without earnestly recommending the perusal of it to those who believe that great talents are bestowed by nature exclusively on man, and who allege that women, even in their highest attainments, are to be compared only to grown children, and have, in no instance, given proofs of original and inventive powers, of a capacity for patient research, or for profound investigation. Let those who hold these opinions endeavor to follow the author of the Analytical Institutions through the long series of demonstrations, which she has contrived with so much skill and explained with such elegance and perspicuity. If they are able to do so, and to compare her work with others of the same kind, they will probably retract their former opinions, and acknowledge that, in one instance at least, intellectual powers of the highest order have been lodged in the brain of a woman.
"At si gelidus obstiterit circum præcordia sanguis; and if they are unable to attend this illustrious female in her scientific excursions, of course, they will not see the reasons for admiring her genius that others do; but they may at least learn to think modestly of their own."
[119] It is surprising how many legends have obtained respecting the life of Agnesi after the publication of her Instituzioni Analitiche. Thus, the writer of the article in the Edinburgh Review, above quoted, declares that "she retired to a convent of blue nuns,"—a statement that has frequently been repeated in many of our most noted encyclopedias.
In a Prospetto Biografico delle Donne Italiane, written by G. C. Facchini and published in Venice in 1824, it is stated that Maria Gaetana was selected by the Pope to occupy "the chair of mathematics which had been left vacant by the death of her father," while Cavazza in his work "Le Scuole dell," Antico Studio Bolognese, pp. 289-290, published in Milan in 1896, assures us that Gaetana Agnesi taught analytical geometry in the University of Bologna for full forty-eight years. The facts are that neither the father nor the daughter ever taught even a single hour either in this or in any other university. Cf. Maria Gaetana Agnesi, p. 273 et seq., by Luisa Anzoletti, Milano, 1900. This is far the best life of Milan's illustrious daughter that has yet appeared. The reader may also consult with profit the Elogio Storico di Maria Gaetana Agnesi, by Antonio Frisi, Milano, 1799, and Gli Scrittori d'Italia, of G. Mazzuchelli, Tom. I, Par. I, p. 198 et seq., Brescia, 1795.
[120] M. Rebière, in his Les Femmes dans la Science, p. 13, Paris, 1897, writes, "Ne pourrait-on aller plus loin et canonizer notre Agnesi? J'estime, moi profane, que ce serait une sainte qui en vaudrait bien d'autres."
[121] An Eighteenth Century Marquise, a Study of Émilie du Châtelet, p. 5, by F. Hamel, New York, 1911.
[122] Preface to Mme. du Châtelet's translation of the Principia of Newton, Paris, 1740.
[123] Voltaire's last tribute, "The Divine Émilie," or, as Frederick II was wont to call her, "Venus-Newton," concluded with the following verses:
"L'Univers a perdu la sublime Émilie;
Elle aimait les plaisirs, les arts, la veritè;
Les dieux, en lui donnant leur âme et génie,
N'avaient gardé pour eux que l'immortalité."
The universe has lost the sublime Émilie; she loved pleasure, the arts, truth; the gods, in giving her their soul and genius, retained for themselves only immortality.
For further information of this extraordinary woman, see Lettres de la Mme. du Châtelet, Reunies pour la première fois, par Eugène Asse, Paris, 1882.
[124] At the beginning of her correspondence with Gauss, Legendre and Lagrange Mlle. Germain concealed her sex under a pseudonym, "in order," as she declared, "to escape the ridicule attached to a woman devoted to science"—craignant le ridicule attaché au titre de femme savante. She, too, suffered from the widespread effects of Molière's Les Femmes Savantes, as had many a gifted woman before her time and as have many others of a much later date.
[125] This celebrated mathematician, as is well-known, was a collaborator with Mme. du Châtelet in her translation of Newton's Principia.
[126] For further information respecting this remarkable woman the reader is referred to Œuvres Philosophiques de Sophie Germain Suivies de Pensées et de Lettres Inédites et Précédées d'une Étude sur sa Vie et ses Œuvres, par. H. Stupy, Paris, 1896. One may also consult Todhunter's History of the Theory of Elasticity and of the Strength of Materials, Vol. I, pp. 147-160, Cambridge, 1886, in which is given a careful résumé of Mlle. Germain's mathematical memoirs on elastic surfaces.
[127] Saturday Review, January 10, 1874.
[128] Personal Recollections, From Early Life to Old Age, of Mary Somerville, p. 80, Boston, 1874.
[129] Personal Recollections, ut sup., p. 5.
[130] Sónya Kovalévsky, Her Recollections of Childhood, With a Biography, by Anna Carlotta Leffler, p. 219, New York, 1895.
[131] "The prize was doubled to five thousand francs, on account of the 'quite extraordinary service rendered to mathematical physics by this work,' which the Academy of Sciences pronounced 'a remarkable work.' The competing dissertations were signed with mottoes, not with names, and the jury of the Academy made the award in utter ignorance that the winner was a woman. Her dissertation was printed, by order of the Academy, in the Mémoires des Savants Etrangers. In the following year Mme. Kovalévsky received a prize of fifteen hundred kroner from the Stockholm Academy for two works connected with the foregoing."
[132] Men of science will realize the capacity of this gifted Russian woman as a mathematician when they learn that she gave in the University of Stockholm courses of lectures on such subjects as the following:
Theory of derived partial equations; theory of potential functions; applications of the theory of elliptic functions; theory of Abelian functions, according to Weierstrass; curves defined by differential equations, according to Poincaré; application of analysis to the theory of whole numbers. How many men are there who give more advanced mathematical courses than these?
[133] To a friend, who expressed surprise at her fluttering to and fro between mathematics and literature, she made a reply which deserves a place here, as it gives a better idea than anything else of the wonderful versatility of this gifted daughter of Russia. "I understand," she writes, "your surprise at my being able to busy myself simultaneously with literature and mathematics. Many who have never had an opportunity of knowing any more about mathematics confound it with arithmetic, and consider it an arid science. In reality, however, it is a science which requires a great amount of imagination, and one of the leading mathematicians of our century states the case quite correctly when he says that it is impossible to be a mathematician without being a poet in soul. Only, of course, in order to comprehend the accuracy of this definition, one must renounce the ancient prejudice that a poet must invent something which does not exist, that imagination and invention are identical. It seems to me that the poet has only to perceive that which others do not perceive, to look deeper than others look. And the mathematician must do the same thing. As for myself, all my life I have been unable to decide for which I had the greater inclination, mathematics or literature. As soon as my brain grows wearied of purely abstract speculations it immediately begins to incline to observations on life, to narrative, and vice versa, everything in life begins to appear insignificant and uninteresting, and only the eternal, immutable laws of science attract me. It is very possible that I should have accomplished more in either of these lines, if I had devoted myself exclusively to it; nevertheless, I cannot give up either of them completely."
From Ellen Key's Biography of the Duchess of Cajanello, quoted in Anna Leffler's biography of Sónya Kovalévsky, ut sup, pp. 317-318.