We shall now introduce two female characters of note. The first is Maria Gaetana Agnesi, a lady of extraordinary genius, and most extensive acquirements, who was born at Milan, on the 16th of May, 1718. Her father, Pietro Agnesi, of Milan, was royal feudatory of Monteveglia, and its dependencies ; and being a man of some rank and consequence, he was disposed, from paternal affection, to provide suitably for the education of his infant daughter, who gave the most strik ing indications of talent. From her tenderest years, she discovered a wonderful aptness, and a vehement desire, for acquiring languages. Under the direction of proper masters, she studied at the very same time the Latin and Greek, the French and German ; and while the rapidity of her progress excited astonishment, such were the prodigious powers of her memory, that she could easily pursue those diversified objects without feeling the smallest degree of confusion. \V hen yet scarcely nine years old, this surprising child delivered a Latin oration, to prove that the cultivation of letters is not inconsistent with the female character, - before an assembly of learned persons, invited to her father's house.

Maria Gaetana Agnesi.

At the age of eleven, the young Agnesi could not only read Greek, and translate it instantly into Latin, but could even speak that refined language with the same apparent ease and fluency as if it had been her native tongue. Nor did these acquisitions absorb her whole attention; a nobler field was opened to the exercise of her mental faculties. She now began to read Euclid's Elements, and proceeded in algebra as far as quadratic equations. Thus prepared, she advanced with ardour to the study of natural philosophy; but not content with the sober proofs there unfolded, she soared to the height of metaphysics, and engaged in the most abtruse and intricate disquisitions of that contentious science. After this young lady had attained the age of 14, her father, anxious to forward her ardour for improvement, and willing to gratify her ambition for literary distinction, invited occasionally to his house a number of persons, the most respectable in Milan for their rank and learning. In the midst of this grave auditory, Donna Agnesi made her appearance; and, without resigning the native delicacy of her sex, she maintained a succession of new theses on various difficult parts of philosophy, and handled the arguments with such dexterity and commanding eloquence, as singly to vanquish every opponent that entered the field of controversy. These disputations were all of them carried on in the Latin language, which she spoke with the utmost ease, purity, and copious elegance. Every thing conspired to heighten the impression produced on the admiring spectators. In the full bloom of youth, her person agreeable, her manner graceful, an air of gentleness and modesty gave irresistible charms to her whole demeanour. Such, for several years, was the great theatre of her glory. But having nearly completed the circle of philosophy, and exhausted the chief topics of discussion, she resolved at length to close that career with a solemnity suitable to the occasion.

In the year 1738, Agnesi made her last brilliant display, before an august assembly, composed of the most learned and illustrious of the Milanese nobility, the senators, and foreign ministers, with the most distinguished professors in all the branches of science and literature. The substance of these philosophical conferences was afterwards published in a quarto volume, entitled, "Propositiones Philosophies, quas, crebris Disputationibus domi habitis, coram clarissimis viris, explicabat extempore, et ab objectis vindicabat Maria Cajetana de Agnesi Mediolanensis."Agnesi now bent her whole attention to the culture of mathematics; and, without guide or assistance, she composed a very useful commentary on L'Hospital's Conic Sections, which is said to exist still in manuscript. In the sublimer departments of that science, her studies were directed by the matured experience of Rampinelli, professor of mathematics in the university of Pisa; but she soon gave proofs of her amazing proficiency, in digesting a complete body of the modern calculus. This excellent work, entitled, "Analy-tical Institutions, for the Use of the Italian Youth," appeared in 1748, in two volumes quarto, and was highly esteemed by the best judges, and justly regarded as exhibiting the fullest and clearest view of the state of the science at that period. She was, in consequence, elected by acclamation a member of the Institute of Sciences of Bologna; and the pope farther conferred on her the title of Professor of Mathematics in the university of that city.

But Agnesi was already sated with literary fame. That sun, which in its ascent had shone forth with such dazzling: radiance, was, through the rest of its course, shrouded in clouds and darkness. The fever of genius had preyed on her mind, and the high fit of excitement was quickly succeeded by a hopeless depression of spirits. She repelled the seductions of human learning, and abandoned for ever her favourite mathematical pursuits. Renouncing the vanities of this world, she withdrew from society, embraced a life of religious seclusion, and sunk by degrees into the languor of religious melancholy. She studied nothing but Hebrew, and the rhapsodies of the Greek fathers of the church. For upwards of twenty years she denied all access to strangers. The famous Lalande complains, in his "Travels through Italy," that he was not allowed the honour of visiting that prodigy; and Father Bos-covick himself, whose religious principles must have been unexceptionable, experienced, notwithstanding his repeated importunities, a similar refusal. Indulging that gloomy temper, she retired into a convent, and assumed the habit of a Blue Nun. She sought to forget the world, and was herself forgotten. She died about the year 1770. The Inshhiziom Analytiche of Agnesi were translated into English, many years ago, by Mr. Colson, Lucasian professor of mathematics at Cambridge. The translation was discovered among the papers of that ingenious mathematician, by the learned Baron Maseres, who put the manuscript into the hands of Mr. Hellins, as editor, and generously defrayed the expenses attending the publication.