year, quarto.

entitled Istituzioni Analitiche, Milan, 1749, two volumes in

The first volume expounds all the operations of the analysis of finite quantities. Next is developed the art of applying these rules to the solution of geometrical problems, determinate or indeterminate, of the second and of superior degrees, rising in order from one to the other; the method for constructing their final equations, and for extracting the roots. The author then proceeds from the method of maxima and minima to the method of tangents, the discovery of points of contrary flexure and of cusps. The analysis of infinitesimals forms the subject of the second volume, in which are expounded the principles of the differential calculus, for the several orders of infinitely small quantities, and the use of these principles is shewn in their application to the investigation of tangents, of maxima and minima, of points of contrary flexure and cusps, of evolutes, and of radii of curvature.

The integral calculus is next treated of, commencing with the methods by means of which differential functions of the first order of a single variable quantity, are reduced to algebraical formulæ or to quadratures of the circle or of the hyperbola. The principles of the logarithmic calculus are given, the method of indeterminate coefficients is expounded, and the art of employing transformations in order that the radical quantities may disappear.

The use of series is shewn in order to find by approximation, the integrals of differential quantities of the same kind; i.e., composed of a single variable, when they are embarrassed by fractions and radicals. After explaining the rules, the art of applying them to the rectification of curves, the quadrature of the spaces they enclose, to the cubature of solids, are successively dwelt upon.

Passing to the exponential calculus, the different ways are explained by which it is possible to integrate differential functions, intermixed with logarithmic quantities, or with quantities elevated to variable powers: the manner of constructing the curves expressed by logarithmic and exponential equations, is given; and the use and application of this calculus is demonstrated by elegant solutions of various problems.

In the last part of this work, rules in the inverse method of tangents are explained, and those which lead to the integration and to the construction of differential equations with two variable quantities. It is shewn by what means, and in what cases, it is possible to arrive at the separation of variables. The use of this method is shewn in the solution of a number of problems, dependent on the inverse method of tangents. The author then passes to the reduction of those equations which belong to a higher order. The manner of reducing many general formulæ, each one of which represents an infinity of these equations, is next treated of; also the methods employed by several geometricians, for reducing certain particular equations of the same kind, on which operation depends

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the construction of certain beautiful geometrical problems, of which, in this book, we find the solution.

In this chef d'œuvre, of which we have given but a very imperfect idea, are collected and subjected to a rigid method all that series of truths which are indispensable to a knowledge of mathematics, all the results of the labors of the most illustrious mathematicians, of Newton, of Descartes, of Leibnitz, of Varignon, of Huyghens, of Robervalle, and of Fermat-all the discoveries published in scientific journals and deposited among the Acts of the Academies. It may be regarded as the best introduction to the works of Euler. On the 6th December, 1749, the commission of the Academy of Sciences in Paris wrote, "this book contains an entire analysis of Descartes, and of all the discoveries made up to the present day in differential and integral calculus, the reduction of these discoveries, spread over so many works of modern geometricians and explained by so many different methods by their different authors, to methods almost always uniform, give proofs of the greatest art and intelligence ; order, clearness and precision reign throughout this work. In no language have Analytical Institutes yet appeared which can so rapidly assist students of the analytical sciences. We regard them as the most complete treatise and the best written work that exists on this subject, and we believe that the academy will not disagree with us when we say that it is worthy of its approval." M. Montigny, one of the members of the academy, enclosing the above certificate to Agnesi, wrote as follows, "I have great pleasure in making known to my country so useful a work, one so long needed, and of which nothing has hitherto been published save imperfect fragments, not excepting L'Analyse Demontrée, of Father Reynaud, and the late treatises published in England. I know no work more extensive, more clearly, more methodically written than your Analytical Institutions. Individuals who know how to develop ideas in all their extension with such order and elegance as reign throughout your Institutes are sharers in the glories of their originators."

In the same year, before the same Academy, Fontenelle said, "this is the best work that has ever appeared of the kind: Mdlle. Agnesi would have been elected member of the Academy if the laws of the Institute permitted the admission of women."

The celebrated mathematician Bossut, who translated the second part of the Institutes, declared "that the principles of integral and differential calculus are explained so clearly and precisely that this work is admirably calculated to guide such students as desire to acquire the knowledge necessary for the study of mechanics and hydrodynamics." Agnesi was held in high repute by the most celebrated professors of the European universities. In a philosophical age like the eighteenth century, when even the Princes of Europe, Frederick of Prussia, Joseph II of Austria, Pietro Leopoldo of Tuscany, had enrolled themselves in the list of thinkers, or had become their patrons, it was not strange to encounter a philoso

phical Pope, sufficiently superior to the prejudices of the clerical hierarchy to inculcate the study of the Civil History of Naples, by Pietro Giannone, (a work afterwards placed in the index of prohibited books) and to accept Voltaire's dedication of his "Mahomet." "We render you," writes Pope Benedetto XIV to Voltaire on the reception of the tragedy, "due thanks for such singular goodness towards ourselves, assuring you that we entertain due esteem for your distinguished talents." September 14th, 1745. To this same Pope, Agnesi sent a copy of her Institutes, which he thus acknowledged; "the study of analysis was undertaken by us in the first flower of our youth: we know sufficient therefore to feel the importance of these studies, and the glory of our Italy in having children who devote themselves to them. Having read the heads of your chapters, and some of the articles on the analysis of finite quantities, inasmuch as we are capable of passing judgment thereon, we frankly declare that you rank among the first professors of analysis, that your work will prove most useful, that it will contribute to the literary reputation of Italy and of our Academy of Sciences at Bologna, of which, to our great satisfaction, you are elected member." June 21st, 1749. In the next year, the Pope named Agnesi honorary Professor of Mathematics at the University, and with a very un-pontifical courtesy replied to her thanks. "We love our University of Bologna and hold it in due esteem, and this has ever induced us to preserve for it all possible honors-from this desire arose the decision which we have taken, that on you shall be conferred the Professorship of Mathematics, and the consequence is, that you ought not to thank us, but that we ought to thank you." September 26th, 1750. (8)

The Analytical Institutes were translated into French by D'Antelmy, with notes by Bossut; and Colson, Professor of Mathematics at Cam

(8) The following is the text of the diploma dictated by the Professors of the University of Bologna, and by the Senate in the presence of the Pope's Legate. This diploma was transmitted to Agnesi elegantly inscribed on parchment, with the seal of the University attached by a golden cord.

esse,

"Die quinta Octobris, 1750. Congregatis Illmis. et excelsis, D. D. Reformatoribus Status Libertatis Civitatis Bononiæ in numero viginti sex in Camera Emi. et Rmi. Domini Cardinalis Legati, in ejus præsentia, ac de ipsius consensu et voluntate infrascriptum Partitum inter ipsos positum et legitime obtentum fuit videlicet.-Patres Conscripti cum censeant are litteraria idque menti Sanctissimi Domini nostri Papæ Benedicti Decimi Quarti summi Pontificis maxime respondere si Maria Cajetana Agnesi, Nobilis Virgo Mediolanensis, cuis in Universa Analysi peritiam egregium hac de re opus editum luculenter testatur cæteris Analysis Professoribus publicis Archigymnasii Rotulis adjungatur. Propterea ejusdem Archigymnasii dignitati consulentes, atque una Clementissimi Principis libertissime obsequentes voluntati, per hoc Senatus Consultum obtentum per omnia suffragia favorabilia, nomen præfatæ Mariæ Cajetanæ Agnesi in publicis Archigymnasii Rotulis ad Analysim publice legendum tamquam Lætricis honorariæ nomen immediate describi mandarunt. Contrariis haud obstantibus quibuscumque.-Ita est. Ego Angelus Michael Lotti Illmi. et excelsi Senatus Bononiæ a Secretis.

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bridge, found them so excellent that at a very advanced age he studied Italian for the sole purpose of translating them into English. He died before its publication, which was undertaken by Hellius, at the expence of Baron Maseres, London, 1801. But all this celebrity had no attractions for Agnesi. Her one earnest desire was to enter a convent, and there devote herself exclusively to works of charity and religion. The powerful opposition of her father, whom she passionately loved, prevented her carrying her wishes into effect during his lifetime, and respect for his memory, after his death; but by degrees she dropped her relations with the men of science, with whom she was in correspondence throughout Europe: and this we record with genuine regret, for, dedicating herself to the practice of private virtues, as they are conceived by Catholicism, she abandoned, to the great detriment of science, her mathematical studies as profane, and fed the cravings of her intellect with the study of the fathers of the Romish Church. In a short time she became an adept in theology; and on the occasion of some theological controversy, Cardinal Pozzombelli, Archbishop of Milan, confidentially consulted her. To Agnesi was confided the care of examining the work of the Marquis Gorini Corio, entitled Politics, Law, Religion, the method of choosing the true from the false, which work had given rise to a violent discussion, one party declaring it orthodox, the other heterodox. Agnesi decided with the latter, and the unfortunate book was consigned to the index expurgatorius. (9)

Gradually withdrawing herself from the outer world, she superintended the scientific studies of one of her brothers; and having induced her father to set apart, for her especial use, certain apartments in his house, she gave herself up to the care of poor and infirm females whom she housed therein, and daily visited the chief hospital of Milan to assist with money and assiduous care the afflicted poor of her parish.

As these expenses increased, she grew daily more economical in her own food and dress; and, in addition to the entire fortune left by her father, she sold to an Englishman a precious casket of mountain rock, adorned with brilliants, together with a diamond ring, presents from the Empress Maria Theresa, to whom she had dedicated her "Institutes." "Thus having got together a small capital, she redoubled the number of patients in her house, not excepting the ulcerous or the incurable. Unaided by any, she ministered to them in all their wants, dressing their disgusting wounds with her own hands, and as soon as one was recovered and chose to leave her abode, another instantly filled the vacant place, thus reducing

(9) Frisi possessed several folio works in M.S. of Agnesi, on religious subjects, of which he gives the list :—

Trattato contemplativo sulle virtù, sui misteri e le eccellenze di Gesû Cristo.

Un rischiaramento del Trattato di S. Lorenzo Giustiniani intitolato De sacro connubio.

Un rischiaramento del Trattato di S. Bernardo, De Passione Domini.

her splendid mansion to a private hospital, and converting her own bedroom into the general kitchen." (10)

The produce of her jewels was soon exhausted, but the number of her patients by no means diminished, so, overcoming her natural repugnance, she forced herself to ask for alms at the door of the Milanese Patricians, encountering not a few refusals, and many discourteous rebuffs. Often when she called for this purpose on the Princess of Este, then resident in Milan, the courtiers of the ante-chamber refused to admit her; those gilded plebeians, judging human worth by outward apparel, were incapable of recognising genius, magnanimity of soul, or even nobility of birth, under the poor garments worn by Agnesi. At this juncture, Trivulzi, a Milanese patrician, founded a hospital for afflicted females, and Agnesi was chosen directress. Never less than four hundred patients inhabited the hospital, who found no small solace in the assiduous and intelligent cares of Agnesi, and in her exemplary virtue found courage to support their sad and suffering existence.

Agnesi died on the 4th of August, 1799, at the age of eighty-one years, nearly fifty of which had been devoted to the mitigation of the sufferings of the most afflicted class of society. Agnesi was the most beautiful woman of her time, and the purity of her life equalled the greatness of her talents.

A. M.

LV. THE WORKHOUSE VISITING SOCIETY, AND THE DUTY OF WORKHOUSE VISITATION.

WHAT is there to be said upon Workhouses which has not ere this been said over and over again, by wise and tender hearted men and women? Why is it, that the old grievances of humanity fall so dull upon the listeners ear, that in spheres apart from the contagious activity of philanthropists, people go about their daily calling giving no more heed to reports of distress than they would to the omni-present advertisements of Rowland's Kalydor or Bass's pale ale?

Again;—what is a philanthropist, and how is it that we have coined such a long Greek word to express that nature which having ears heareth, and having eyes can see? Perhaps if all people, instead of reading, could really see that which is most deplorable in the form of man, they would make a mighty effort to cure that which they now consider with carelessness, merely because it has never been realised within their minds. For which intent it has occurred to us that stereoscopic slides of workhouse interiors might be now distributed with greater efficiency than tracts at a penny or pamphlets at a shilling, and the same wonderful art which is employed to trace and identify the criminal in the eye of the law

(10) Elogio Storico di M. G. Agnesi, p. 80. Milano, 1799.