has been often and variously repeated. But it might be sufficient to remark in relation to this, that Euclid, Archimedes, Galileo, Napier, Newton, and Euler were not only in the first class as mathematicians, but also in the first rank as excellent men. It has justly been remarked, that "it requires but little insight into man's heart to perceive that profession and professional advancement, that power and wealth, have a far more frequent and more effective influence on his judgment than any mental habits he may be supposed to have cultivated." We may then, without hesitation, recommend the study of mathematics as best calculated to strengthen and discipline the mental powers, and as in no way calculated to injure the moral faculties, but as affording even valuable illustrations of the truths of religion.

Algebra is the introduction to all those more important branches of mathematics that depend on analysis. If this is not mastered to the satisfaction of the student, if it is not in some degree rendered interesting and attractive, few will think of pursuing mathematics further. Hence the importance of having a text-book properly prepared. So many text-books are yearly issued, that most teachers think it not worth while to be at the expense of procuring and examining them. In recommending the work of Mr. Clark to the public, we say without hesitation that we think it has stronger claims on the attention of teachers and all others interested in the subject than any work of a similar character with which we are acquainted. The work will bear examination; and no one who is disinterested, we think, can carefully study it with reference to the selection and arrangement of its materials, the simplicity and precision with which the principles and rules are expressed, the unity of the work, the natural manner in which the topics succeed each other, each preparing the way for that which is to follow, and not be convinced that this work is not only better calculated for an elementary text-book, but also for an introduction to the higher branches of mathematics, than any work now in use.

ART. III.-Kant, and Kantism.

KANT.

THE reforms attempted by Bacon and Descartes, in the methods of philosophizing, produced in their own countries phenomena most interesting. The inductive system, as developed by the former, was fully carried out in the Principia of Newton and the Treatise on the Understanding by Locke. The latter work, on account of the sifting discernment of the writer, met with a highly flattering reception, which did not, as is often the case, suddenly die away, but which has continued even unto our own times. The influence of this philosophy was, however, in many cases most hurtful, because of the premise upon which all its investigations were founded; which affirmed that there were but two sources of ideas, sensation and reflection. Proposing as it did to take nothing for granted which had not passed the ordeal of rigid investigation, it assumed an error in the very first step, which, entering into the remaining portions, distorted the whole. With such a fundamental error, its influence was necessarily injurious, as all may perceive by following the path marked out by its development.

In the hands of Hume it produced infidelity; with Berkeley, through reaction, perfect idealism; in the system of Condillac of France, gross sensualism. Systems most pernicious sprang out of it; systems, too, which could not be overthrown while the Treatise on the Understanding was received. On the continent at this time philosophy was assuming a not less distorted, though less hurtful state. The imaginings of Descartes were followed by the system of Leibnitz, with the ideas so prominently advanced of the sufficient reason, and pre-established harmony. Like the system of Locke, it was well received and taught in the universities. Wolf, its succeeding champion, added much, changed its form, and called it by his own name. Throughout all Germany was the philosophy of Wolf received when the books of Mr. Hume appeared, and in Germany as in England produced trembling and dismay. He made his most formidable attack on the idea of cause, asserting that from sensation or reflection no ideas of cause can be obtained, and therefore all ideas of this kind are mere chimera. Of course in this attack all religion was in danger, as well as the system of Wolf, which rested upon the principle of sufficient reason. In England and Scotland the Church fell back immediately upon faith as her basis, while in Germany religion was uprooted and destroyed.

In such crises master minds usually arise; nor could the great interests of man, the independency and freedom of his will, the immortality of his thinking part, be resigned without a desperate conflict. Of the great champion who arose we proceed to speak.

Immanuel Kant was born in 1724, at Konigsberg in Prussia. His father, George Kant, was a saddler by trade, originally from Scotland. To Immanuel first instructions in reading and writing were given at the charity school of his own parish, but on account of the ability and inclination to learn which he manifested, he was soon removed to the college of Fredericianum. Here mathematics and natural philosophy became his favorite studies. Having quitted the institution at the close of his course, he acted in the capacity of tutor in various situations for nine years.

In 1755 the degree of Master of Arts was conferred upon him, when he immediately commenced lecturing with great success to crowded audiences. During the space of fifteen years which now passed peacefully over him, he published many works both upon physical and metaphysical subjects. In 1770 the metaphysical department at Konigsberg having become vacant, the professorial chair was offered to him.

Here metaphysics occupied all his time, and in this new relation we find the great powers of his mind suddenly developing to an unexpected greatness. His celebrated work, the "Critique of Pure Reason," ("Critik der Reinen Vernunft,") appeared in 1781, attended by circumstances of distinguishing peculiarity. For six years did it remain in the hands of the bookseller, uncalled for and unknown, and it was when he had concluded to destroy the copies for waste paper that a sudden demand required and exhausted three editions. After this appeared several important works containing the system which he upheld, applied to practical and theoretical ethics.

In 1786 he was appointed rector of the university, in 1788 senior of the philosophical faculty, in 1798 he took his leave of the public as an author, and early in 1804 death removed him to a happier clime.

Before speaking of his philosophy, we will consider his character as we find it delineated in the notices which have been furnished by various writers. In philosophy, say they, he was celebrated for his depth of intellect, and powers of generalization. In the world he was a bright example of benevolence and love. "His mind, polished like the diamond, was the philosopher's stone of his age." There was no subject which he could not investigate, and the accuracy and minuteness of his investigations were without a parallel.

He has created for himself an undying reputation, and posterity will look upon him as having brought us nearer than ever to that Socratic wisdom, of acknowledging our ignorance and the limits of our possible acquirements.

It was his intention to strip philosophy of everything that did not belong to her as a science, and we may infer from this that he aspired with unwonted vigor after the truth. But he did not alone devote himself to abstruse and dry reasoning. His eyes and ears were ever open to the actions and opinions of the moving world, and he studied his fellow-men that he might please and instruct. The students of the university in which he taught, acquired a quickness and depth in metaphysical reasoning which is but rarely known.

He made everything tributary to himself, and history, philosophy, mathematics, and experience, alternately and in unison, ministered to his pleasure, and became his instruments in imparting knowledge. As we have remarked, he fixed his eye upon immortal truth, and he acquainted himself with her offspring, beauty and goodness, that he might aspire to her own lofty throne. No cabal, no sect, no advantage, no ambition of a name, had the smallest charm for him when compared with the extension and development of truth. Man was to him a creature far above the beasts that perish, one who aspires to higher and holier scenes. Gentle benevolence and goodness were ever seen lighting up his countenance, and his noble forehead, while it revealed the depth and power of his understanding, ever wore the aspect of imperturbable serenity and joy. It was necessary but to know him, to love him; for joined to his giant intellect there was a tenderness of heart, and strictness in morality, which made him a bright example to the youth of his age. No one could say that he was selfish, for the happiness of others was ever his great desire. He viewed the world through the medium of his own happy temper, and found everything agreeable and alluring. No breeze of passion ever ruffled the mirror surface of his calm mind, and in him the acuteness of reasoning was joined with the polish of a gentleman.

He was a most decided enemy to falsehood of every kind. The world ever saw him as he was, unvarnished by any false art, and making no attempts to conceal his own merits. In his youth he paid his attention to the physical sciences, and arrived at a good degree of proficiency in demonstrative reasoning. It was not, however, until he entered into metaphysics that the great powers of his intellect became fully developed. Here we see him, not rushing to new and untried conclusions, which peradventure could not

stand the test of experience, but moving slowly and surely, clipping off here and there those things that do not belong to true reasoning, casting aside mysticism and prejudice, until he arrived at the fountains of all knowledge. Then he noted their number, limits, and peculiarities, and starting from these a priori truths, he followed down the many streams that flowed from them, until they all united and formed the beautiful river of science. This system speaks for iself, and is but a representation of the excellent arrangement of his own mind.

But there is yet another peculiar characteristic of this great man, and it may be found in his love for his native place. We are told that he spent eighty years in Konigsberg, contented and happy. Many offers were made to him to remove to other and more flourishing universities, with promises of many honors, but they had no effect. His love for his home was far greater than his love for riches and fame. Having received from his mother a spirit of reverence and devotion, he aspired after true religion, and made the great principle of right his guide in morals, as was truth in science.

How much he was esteemed may be inferred from the fact that in the universities of Jena, Halle, Gottingen, Erlangen, &c., lectures were delivered on his system; and books were written by his advocates to illustrate and defend his doctrines. "Professors were even sent at the request and expense of princes and crowned heads, to learn more minutely, by a personal conference, what had not been sufficiently elucidated in his books. His lecture rooms were crowded, and many from afar came as disciples to sit at the feet of the German Gamaliel."

Such was the character of this philosopher. His intellect was deep and discriminating, his affections were bound up in universal benevolence, his religion was that of the heart. Few have known and appreciated his merits, because they have looked for faults instead of virtues, and read his works rather to criticise than imitate. His failings were few, and resulted from viewing all nature as happy as himself. His virtues were many, and will not be forgotten, when the philosophy which he taught shall be swallowed up in universal knowledge; and error, and falsehood shall be known no

more.

KANTISM.

We have already remarked that Locke ascribed the origin of all our ideas to sensation and reflection, which was the fruitful source of numerous glaring errors. This Kant perceived, and finding that the phenomena of mind could not be established upon the in