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the purpose of improving and extending their good influences, he often wrote communications in the papers of the day. As a father and as a friend, he was admirable, and won the affections of all who knew him. As a political opponent, no one was more inflexible, but at the same time, no one was more kind to his adversaries.
These traits in the character of Judge Livingston, we have obtained from those, who were long and intimately acquainted with him; and we were again and again assured, that we could not over-estimate his merits. In further illustration of them we shall conclude with the following extracts from a very able obituary notice, which was published at New York, immediately after his decease.*
'His judicial character is, of course, the most interesting to the public, and as a Judge, his character was very peculiar and strongly marked. He was eminently a man of genius, of strong, vivid, and rapid perceptions, and the frankness of his character always prompted the immediate impression of his convictions. Such a disposition and habit must of course, and not unfrequently, induce mistakes. But here intervened a redeeming principle resulting from one of the most peculiar characteristics of his happily composed nature. For a man of strong and ardent genius, and profound learning, and these too rendered conspicuous by great reputation and high office, Judge Livingston was in one respect, almost a miracle. He seemed to be without vanity. He did not listen, or affect to listen, to arguments in opposition to his declared opinions merely from official decorum, but his mind was literally and truly open to conviction. Others may have committed fewer errors, but who has left fewer unrepaired ?
*Livingston was appointed Judge of the Supreme Court of New York, in January, 1802, and of the Supreme Court of the United States, as the successor of Mr Justice Patterson, in December, 1806.
He was buried under Wall Street Church, in the city of New York; and in the church itself is the following inscription, written by a friend at the request of his family.
Peracuto ingenio præditus,
Eloquentiâ tum suavi, tum splendidâ ornatus,
Multis bonis carissimus, multis flebilis,
Liberi ejus mærentes hoc monumentum
"The kindness and suavity of his character were strongly displayed in the discharge of his official duties. At every moment of his life, he was an amiable and a finished gentleman. He never manifested anything of the petulance or insolence of station. He ever seemed to be of opinion, that there was a dignity in the administration of justice, which reached even to its inferior ministers; and without ever forgetting the propriety of his station, he treated the gentlemen of the bar as his friends and brethren, over whom he was called, as it were, to preside for some temporary purpose.
'To say that he was just and impartial, would be low and inadequate praise. He was prompt, laborious, and indefatigable. His own ease and pleasure always gave way at the call of duty. He never delayed or slighted anything. He often labored most without the stimulus of fame. He was, perhaps, rather too averse to the parade of display and publication. Causes were not unfrequently heard at his own house, and many of his most elaborate opinions, the result of laborious and profound investigation, were communicated only to the counsel interested.'
'In all the relations of domestic life-and it is there that a man's true character is best known, and its influence-he was far above the reach of commonplace commendation. None but those who saw him in retirement and knew him intimately, can appreciate his character in this respect. He was ever most affectionate, attentive, and considerate, exacting little for himself, and always consulting the interests and feeling of his family. The main object of his life, at least that which seemed to interest him most, was to transfuse his own knowledge and character into the minds of his children. Every hour that could be spared from his public duties, and more than could well be spared from the time necessary for his relaxation and the care of his health, was devoted to their education.'
ART. X.-Elements of Geometry, by A. M. LEGENDRE, Member of the Institute and the Legion of Honor, of the Royal Society of London, &c. Translated from the French for the use of the Students of the University at Cambridge, New England, by JOHN FARRAR, Professor of Mathematics and Natural Philosophy. Second Edition, corrected and enlarged. Printed by Hilliard and Metcalf, at the Univ. Press, Cambridge, N. E. 1825. 8vo. pp. 224.
THOSE who are fond of reconciling apparent contradictions in national character, may find amusement in attempting to
account for the singular fact, that the French, who are so remarkable for their constitutional vivacity, and, we had almost said, levity of character, should nevertheless have been unrivalled for nearly a century, in almost every department of scientific research. That they should have taken precedence of other nations in elegant literature, if such were the fact, would not be very surprising; for we should imagine we could discover a decided adaptation to such pursuits, in the prominent features of their character. But when we see them engaging with wonderful ardor and perseverance in those studies, which almost entirely exclude imagination and feeling, and demand for their successful prosecution, the severest efforts of reasoning and abstraction, we witness a phenomenon, of which we find ourselves unable to give a satisfactory explanation.
Of what discordant elements must the character of that people be formed, who, within the short space of thirty years, have gone through a revolution so momentous, that it broke up all the strong foundations of society, and yet, within the same time, have advanced physical science and pure mathematics to such a height as they never attained before. We have seen them rise, with a fearful unanimity, to hurl reason from the throne and trample truth in the dust, and then, before our terror and amazement have had time to subside, we have seen reason and truth reinstated among the same people, and worshipped with a devotion as fervent and enthusiastic, as ever was paid to them before. The very same individuals, who now give up their days and nights to abstruse speculation, were once strenuous actors in the stormy scenes of the Revolution. There was one, especially, whose life exhibited a scarcely credible contrast. During that disastrous period, so expressively denominated the Reign of Terror, his mind, then all for action, caught to the full the mad phrenzy of those around him; and he engaged, heart and hand, in the infernal business of the time. But the moment that the moral hurricane was over, this same wonderful man, sitting down as it were amidst the very ruins he had helped to create, and apparently forgetting all that had passed, gave up his whole mind to the investigation of the celestial motions. In these serene and sublime contemplations, he was chiefly occupied for the last twenty years of his life; and next to Newton, Philosophy now hails him as her brightest name.
But to pronounce a panegyric upon French philosophy, is
not the purpose for which we have selected the book, whose title is placed at the head of this article. This work of Legendre forms one of a series translated by Professor Farrar, for the use of the students at Harvard University. The entire course, both of pure and applied mathematics, being now completed, we avail ourselves of this opportunity to call the attention of our readers to it. In bestowing upon it the tribute of our commendation, we do but echo the general voice of the scientific community, in our country. If the course be examined with the scrutiny which it may safely challenge, and meet only with that acceptance from the public, to which its real merit entitles it, we are sure it cannot fail to be adopted in all the distinguished seminaries of learning throughout the United States. Several of them, as we are informed, have already introduced it. We regard it as high testimony in favor of its excellence, that it was selected for the manual in the University of Virginia, by the judgment of such profound and sagacious men, as Jefferson and his associates. Nor should we prize less highly the ample sanction it has received at West Point, where, if we are correctly informed, the entire course has been introduced, and where, let it be remembered, Mathematics and the kindred sciences are pursued to a greater extent, than at any other institution in the country. To these authorities, we may add that of Columbia College, in New York, where we are safe in saying there is ample ability in this department, to scan the merits of the course severely. But we will not consume further time in adducing extrinsic evidence in support of the merits of these works. We prefer to let them speak for themselves.
The entire course translated and compiled by Mr Farrar, including all the subjects which fall within his department, as Professor of Mathematics and Natural Philosophy, is contained, as the books are usually bound, in eight volumes, comprising about 3000 octavo pages. The following is a list of the several works, which are comprehended in it, in the order in which they are intended to be studied.
'An Elementary Treatise on Arithmetic, taken principally from the Arithmetic of S. F. Lacroix.'
'An Introduction to the Elements of Algebra, designed for the use of those who are acquainted only with the first principles of Arithmetic. Selected from the Algebra of Euler.' 'Elements of Algebra, by S. F. Lacroix.'
Elements of Geometry, by A. M. Legendre.' VOL. XXVII.--NO. 60.
* An Elementary Treatise on Plane and Spherical Trigonometry, and on the Application of Algebra to Geometry; from the Mathematics of Lacroix and Bézout.'
'First Principles of the Differential and Integral Calculus, or the Doctrine of Fluxions, intended as an Introduction to the Physico-Mathematical Sciences; taken chiefly from the Mathematics of Bézout.'
'An Elementary Treatise on Mechanics, comprehending the Doctrine of Equilibrium and Motion, as applied to Solids and Fluids.' This work is a compilation. The authors principally used, are Biot, Bézout, Poisson, Francœur, Gregory, Whewell, and Leslie.
'Elements of Electricity, Magnetism, and Electro-Magnetism, embracing the late Discoveries and Improvements, digested into the form of a Treatise.' This volume with the exception of the notes, is selected from Biot's Précis Elémentaire de Physique, and translated with such alterations as were necessary to adapt it to the English reader.
'An Experimental Treatise on Optics, comprehending the leading Principles of the Science, and an Explanation of the more important and curious Optical Instruments and Optical Phenomena.' The body of this volume like that of the preceding, is selected and translated from Biot's Précis Elémentaire de Physique Expérimental.
'An Elementary Treatise on Astronomy, adapted to the present Improved State of the Science.' This treatise is selected and translated from Biot's Traité Elémentaire d'Astronomie Physique.
Such is the ample list of works, by the preparation of which Mr Farrar has proved himself a benefactor to the cause of science, and acquired a durable reputation for most patient industry and profound judgment. Nor is this all. It is but justice to add that this Herculean task has been achieved, in addition to the constant and able discharge of the duties of one of the most important professorships in our University.
Our readers will scarcely believe us when we add, that besides all this, the same persevering hand has prepared and published, for the use of schools, an epitomized exposition of the principles of Mechanics and Natural Philosophy, under the title of Fischer's Elements of Natural Philosophy. It is a translation from the French of Biot, who himself translated it, with many additions, from the German of Fischer. It has