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But these studies are less connected with the business of active life than others; the Greek geometry not at all, and the Attic oratory only important as refining the taste, and being subservient to the perfection of our

soning. That it is incomparably less power-nent mathematician that has appeared in ful than the algebraic geometry, which we this country since Sir I. Newton. owe to the happy suggestion of Descartes and the subsequent discovery of Newton and Leibnitz, cannot be denied. But that its powers have been inuch underrated is manifest from the extraordinary success of Matthew Stewart in solving problems before own. Eloquence, however, can only in these deemed beyond its reach, Kepler's prob- times be worthily employed for furthering lem and the inverse problem of centripetal objects little known to, or if dimly perceived, forces; although it may well be questioned little cared for by the masters of the art in if he could by mere geometrical analysis ancient days: the rights of the people-the have pursued these investigations had New- improvement of their condition-their adton's demonstration not been known to him. vancement in knowledge and refinementIn one respect, however, the ancient analy- above all for maintaining the cause, the sasis has a singular merit, the discussion of cred cause, of peace at home and abroad. limits. Its careful exhaustive process of ex- Suffer me to dwell somewhat upon the intiamining all the cases in which any solution mate connection of this last most important is possible, and thus preventing all over- subject with the education of youth, the forsight, is invaluable, and might furnish sug- mation of their opinions, the cherishing of gestions of importance to the modern ana- right feelings upon the merits of those whose lyst. The remarkable error into which history is taught, or who are known as conNewton fell in his solution of the problem-temporaries, at least as having flourished in justly termed by him longe omnium difficilli- times near our own. Historians and politmum (of finding the comet's trajectory from ical reasoners, the instructors of the people, three observations), could never have occurred under the ancient method; for, in discussing the limits, it would have been found that the 16th Lemma has a porismatick case, and that it is the case of the comet, a matter never observed until F. Boscowich hit upon it in 1739, all of which was known before, being that the Newtonian solution must be erroneous, because it threw the comet of that year on the wrong side of the sun. Though these merits unquestionably belong to the ancient analysis, nothing can be more inaccurate than the view sometimes taken by its admirers, that it is more strict in its demonstrations than the modern; there can be no degrees of certainty, and the proofs are absolutely certain in both.

have ill discharged their duty in this most important respect. Partaking largely in the delusions of the vulgar, which they were bound to dispel, and dazzled by the spectacle of great abilities, and still more of their successful exertion, they have held up to admiration the worst enemies of mankind, the usurpers who destroyed their liberties, the conquerors who shed their blood-men who, in the pursuit of power or of fame, made no account of the greatest sufferings they could inflict on their fellow-creatures. The worst cruelty, the vilest falsehood, has not prevented the teachers of the world from bestowing the name of Great upon these scourgers, as if themselves belonged either to the class of ambitious warriors and intriguing statesmen, or to the herd of ordinary men whom successful crimes defrauded at once of their rights and their praises; and to this must be ascribed by far the greater part of the encouragement held out to unprincipled, profligate conduct in those who have the destinies of nations in their hands.

When the study of the Greek geometry is recommended to those whose rule with the Principia, must be nocturnâ versate manû, versate diurnâ, it should be borne in mind how highly the author of that immortal work prized the ancient method of investigation, as we learn both from the internal evidence of the book itself, and from the statement It is not, however, merely by abstaining of his friend and follower Halley, himself a from indiscriminate praise, or by dwelling diligent student of the Greek geometry. with disproportioned earnestness upon the Let the high authority of M. Chasles be great qualities, and passing lightly over the added, himself a great master of the most bad ones, of eminent men, and thus leaving recent improvements of the calculus; and in a false impression of their conduct, that histhis place it would be wrong to pass over torians err, and pervert the opinions and the distinguished names of Wallace and feelings of mankind. Even if they were to Ivory, both deeply imbued with the princi- give a careful estimate of each character, and ples of the modern analysis, and expert in pronounce just judgment upon the whole, their application, but diligently cultivating they would still leave by far the most imthe ancient also. They were great analysts portant part of their duty unperformed, unin all respects; and the latter the most emi-less they also framed their narrative so as

and reaction, cannot be doubted. The existence of the popular feeling in its strength, beguiles the historian, and instead of endeavoring to reclaim, he panders to it. Sounder and better sentiments might grad

to excite our interest in the worthy of past | practical discouragement might be given to times; to make us dwell with delight on the the worst enemies of our species. That in scenes of human improvement; to lessen the this, as in every thing else, there is action pleasure too naturally felt in contemplating successful courage or skill, whensoever these are directed towards the injury of mankind; to call forth our scorn of perfidious designs, however successful; our detestation of cruel and bloodthirsty propensities, however pow-ually be diffused, and the bulk of mankind erful the talents by which their indulgence weaned from their fatal error, of which the was secured. Instead of holding up to our heavy price is paid by themselves in the admiration the "pride, pomp, and circum- end. stance of glorious war," it is the historian's duty to make us regard with unceasing delight the ease, worth, and happiness of blessed peace; he must remember that

"Peace hath her victories,

It is not to be denied that the degree of reprobation due to such crimes must partially depend upon the age in which they have been committed, and the nation to which the offender belongs. It would be a gross exaggeration of feelings, right in themselves, No less renowned than war's."-MILTON. were the same blame attached to usurpation And to celebrate these triumphs, the prog- or conquest among eastern nations as among ress of science and of art, the extension and Europeans; or among Europeans in the dark security of freedom, the improvement of na- ages, as all, when calmly considering their tional institutions, the diffusion of general conduct, without hesitation pronounce upon prosperity, exhausting on such pure and tyrants and conquerors in the present day. wholesome themes, all the resources of his But one consideration, oftentimes referred philosophy, all the graces of his style, giving to, is never to be admitted as an extenuahonor to whom honor is due, withholding tion, much less a defence, of unjust hostiliall incentives to misplaced interest and vi- ties-the propensity of man to war, called cious admiration, and not merely by general the incurable propensity by those who make remarks on men and on events, but by the no attempt to cure it. This is the very worst manner of describing the one and recording and most vulgar form of necessity-the dethe other, causing us to entertain the proper nying man's free will, and impiously making sentiments, whether of respect or interest, Heaven the author of our guilt; but the abor of aversion or indifference, for the various surdity is equal to the wickedness of the presubjects of the narrative. Consider for a text. The self-same topic might be used in moment what the perpetrators of the great-excuse, or in palliation of the ordinary crimes est crimes that afflict humanity propose to themselves as their reward for overrunning other countries and oppressing their own. It is the enjoyment of power, or of fame, or of both

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Unquestionably the renown of their deeds, their name being illustrious in their own day, and living after them in future ages, is, if not the uppermost thought, yet one that fills a large place in their minds. Surely, if they were well assured that every writer of genius, or even of such merit as secured his page from oblivion, and every teacher of youth, would honestly hold up to hatred and contempt acts of injustice, cruelty, treachery, whatever talents they might display, whatever success they might achieve, and that the opinions and feelings of the world would join in thus detesting, and thus scorning, it is not romantic to indulge a hope that some

of pillage and murder; nay, might be applied as well to physical as moral evil, and given as a reason against using the lightning rod to protect us from the storm, or against taking precautions to escape the venom of the snake when his rattle warns us, or the fury of the tiger when he howls in the forest. Yet, what but the proneness of men to succumb under great genius, wickedly used, can be urgued in extenuation of Napoleon's usurpation, by which he made France pay for her delivery from the anarchy and bloodshed of the republic, with the utter loss of her freedom; and in extenuation of his dreadful wars, waged to gratify an almost insane ambition, at the cost of the people's misery, and the massacre and pillage of their neighbors? From the height to which his arms had raised him of all but emperor of the west, and from the eminence so dearly purchased by the French, of having dictated terms to all the sovereigns in their own capitals-he and they were hurled. Twice they had the bitter mortification of receiving the law in their own capital from those they had once trampled upon; and his fate and their

humiliation was the work of headstrong pas- disposition more pernicious to the world, and sions blinding his reason, after extinguish- is fitted to call down a reprobation far more ing his humane feelings.

severe.

The latest and best historian of his reign The history of later times, indeed of our (M. Thiers), though filled with admiration own country, affords a contrast to the failfor his genius, and, as is natural to human ings and the vices which we have been viewweakness, leaning towards the hero of his ing, and the contemplation of which may tale, has been compelled to account for his well excite sorrow for the great genius which downfall by six capital errors, committed they perverted, and abhorrence of the misthrough lust of dominion which no conquests chievous uses to which they turned it. Of could satiate, and through the caprices our own illustrious captain and statesman, which, sooner or later, are sure to spring up who defeated all Napoleon's marshals in the in the soil of despotic power uncontrolled. cause of his country and her allies, and who Of these six errors, any one would have ended by overcoming Napoleon himself, it sufficed to shake, almost to subvert, his might not be fit to speak in this view, bepower; and every one of them had caused cause, though no one can have the least the destruction of thousands, the wretched- doubt how he would have acted in a like poness of millions. It would only be by a sition, yet he never had the opportunity of perversion of all right feelings if the spec- declining the assumption of power beyond tacle of his fate could excite our pity, or if the law. But in Washington we may conwe could regard his expulsion from France template every excellence, military and civil, amidst the execrations of the people whom applied to the service of his country and of he had plunged into slavery, misery, and mankind. A triumphant warrior unshaken discomfiture, his attempt at self-destruction, in confidence, when the most sanguine had his wretched end, a solitary prisoner in a a right to despair; a successful ruler in all remote island-as other than the just retribution by unexampled suffering for unexampled crimes; by the pride which had for self-indulgence humbled all others, being laid prostrate in its turn; by that wretchedness falling at length on himself, which, whensoever he had a purpose to serve, he never had hesitated to make others undergo. Let it be remembered that in every war which he waged, from his assumption of supreme power until his banishment to Elba, he was the aggressor; that each one was undertaken for his personal aggrandizement, with a thin disguise of national glory; the glory of France, of which he was not a native-and we have the measure of his guilt. The death of Enghien, the sufferings of Wright, the punishment of Palm (all proceeding from that excess of cruelty which fear is so apt to engender in a violent temper), and the tortures of Toussaint, are often dwelt upon because the fortunes of individuals, presenting a more definite object to the mind, strike our imagination and rouse our feelings more than wretchedness in larger masses, less distinctly perceived. The outrage upon religion by his declaring himself a Mahometan, to further his views in Egypt, and the equal outrage upon morality by the mingled force and fraud in his circumvention of the Spanish princes, have, in like manner, been singled out as peculiar subjects of reproach. But to the eye of calm reflection, the undertaking an unjustifiable war for a selfish purpose, or the persisting a day longer than necessary in a contest which was begun on right grounds, presents a more grievous object of contemplation, implies a

the difficulties of a course wholly untried; directing the formation of a new government for a great people, the first time so vast an experiment had ever been tried by man; voluntarily and unostentatiously retiring from supreme power with the veneration of all parties, of all nations, of all mankind, that the rights of men might be conserved, and that his example might never be appealed to by vulgar tyrants. It will be the duty of the historian and the sage in all ages to omit no occasion of commemorating this illustrious man; and until time shall be no more, will a test of the progress which our race has made in wisdom and in virtue, be derived, from the veneration paid to the immortal name of Washington.

But, though the offence is great of passing over the crimes of eminent men without duly expressing the abhorrence and contempt which they raise in all rational and virtuous minds, care must be taken to describe fully their merits, to set forth their great qualities, and to admit those good ones which are sometimes found even in wicked and wholly unprincipled men, and much more in those whose crimes are an exception to their general character. The truth of history and interests of justice require this candid statement; but it must be added, that the benefits are not inconsiderable which result from dwelling on these better parts, and impressing them on men's minds with the authority of great names which may influence some, while the mere example will arrest the attention of all. Thus the wickedness of Henry the Fifth's wars of mere plunder, and his feebleness in sacrificing Oldcastle, the most

distinguished person of the age, to the fury rulers, those whose cruelty and profligacy of the bigots whom he was courting, must are the detestation of all mankind-our own ever be related with a full admission, not Richard III. and the Borgias-the former is indeed of the benefits which our constitution believed upon right evidence to have comderived from the costs of his expeditions re-mitted many crimes beside those of which quiring the popular consent to his supplies, but of his great capacity as a commander, his general sincerity and frankness, so rare in princes and statesmen of those times, and his freedom, at least, from such a stain of cruelty as attaches to the memory of his uncle, the Black Prince [Note 8], whom Mr. Hume describes as a perfect character "to the hour of his death unstained by any blamable action," suppressing the massacre of 3,000 persons of both sexes and all ages at Limoges before his face in his last illness. So the unjust and sanguinary wars of Edward III. with Scotland and France must not shut our eyes to his great talents, both in the field and in government, to the mildness of his administration, and to the improvements which he effected, both in our jurisprudence and our constitution.

there can be no doubt, while just praise is not given to his capacity, his courage, and his improvement of our jurisprudence, and the mildness of his government to all but the nobles; and the Borgias have not been generally noted, as they deserved, for their talents in government, their protection of learning, and especially their promotion of the important study of jurisprudence. The caprice of historians in some sort resembles that of the vulgar, either struck by signal turpitude and regarding it as pervading generally and excluding all exception, or only viewing the exception and making it the rule of decision. A Borgia is held incapable of any good of any kind, a Lorenzo incapable of evil. Nothing can tend more to keep men in ignorance than such exaggerations; and they have the hurtful effect of intercepting the instruction which a contemplation of the real state of the facts in each case is fitted to impart.

When we describe the habitual fraud and falsehood of Elizabeth [Note 9], her maltreatment of Mary, and covert attempts to take her off by assassination, her sacrifice The ills that have proceeded from the great of Davison for obeying her commands for scourge of later days have been adverted to, the execution in order to support her false as well as the mischievous effects of the addenial of these commands,-we must at the miration which he excited, and which unsame time commemorate her great qualities happily has not ceased to inspire the people for government, by which she preserved the whom he most injured. But some of his peace of her dominions in a season of ex- great qualities it would be impossible to adtreme difficulty, from religious as well as mire too much; and though his genius may political dissensions, and her allowing no be pronounced inimitable, in some things his influence whatever in the management of example may be followed, and therefore it is public affairs to those favorites with whom fit that these should be recorded. There is in secret she led a life of indulgence little indeed an obvious expediency in dwelling scrutinized by most Protestant historians. rather upon qualities the example of which But far more princes, while justly held up may lead to imitation, than upon genius to reprobation for their tyranny, and to con- however calculated to command admiration. tempt for their sordid schemes carried into Genius, which consists in the rare gifts of execution at the public expense, in fact by rich fancy, perception of resemblances, and the plunder of their subjects, deserve just differences not apparent to ordinary minds, commendation for their encouragement of but admitted by all as soon as suggested, the arts and advancing the improvement of quick and sure judgment, and the power of their country. Instead of denying all merit not only abstracting the attention from all to Lorenzo [Note 10] dei Medici, or ascrib- objects save one, but of directing it and coning his munificence to vanity, we are only to centrating upon that one. This is what we lament that his accomplishments and his call genius: the gift of very few, and the patronage of genius should have dazzled works of which are to be admired at an awgood men, friends of liberty as well as of ful distance. The ordinary qualities which letters, and blinded them to the conduct of a diligent study and a fixed desire to excel one who enslaved his country, directed its may place more or less within the reach of resources by a series of fraudulent devices to all, are most fit to be recommended by the his own profit, treacherously intrigued to example and success of distinguished indisubvert the power of his neighbors, shed the viduals. Of these Napoleon possessed two blood of his adversaries at home, sometimes in an eminent degree; they can never be by his official tools, sometimes by delivering sufficiently kept in mind, and they are of them over to the mob, when their atrocious universal application,-the strict economy offences against him might have been surely of time, in compliance with the maxim, visited by the law. Take even the worst of "Take care of the minutes, the hours will

take care of themselves," and the habit of hatred of wickedness in their admiration of invariably mastering the whole of whatever genius and their sense of power. It is truly subject or part of a subject he considered a disinterested admiration, for they themhimself interested in being acquainted with. selves pay the price; and their oppression, The captain who carried him to Elba ex- with every suffering that misgovernment can pressed to me his astonishment at his pre- inflict, is the result of the cruelty which they cise, and as it were familiar, knowledge of did not abhor, the meanness which they did all the minute details connected with the not scorn when dazzled with the false lustre ship. I heard from one engaged in the great shed over detestable or despicable deeds of Helvetic mediation, 1802, that though the brilliant capacity crowned with victory. Nadeputies soon found how hopeless they were polcon knew how safely he might rely upon of succeeding with the First Consul, yet they this delusion, and he knew that the people felt themselves defeated in the long discus- whom he enslaved and ruined were intoxision by one more thoroughly master of all cated with the glory which he gained and the details of the complicated question than for which they so heavily paid. In one they could have believed it possible for any respect, at least, he was less to blame than foreigner to become. My illustrious friend, they; he faced the danger, if he witnessed the Duke of Wellington, had a like consum- the miseries of war; while they, in perfect mate acquaintance with whatever subject he safety, upheld him in his course to make was called upon to consider practically. the country unprofitably powerful by the Among others, may be mentioned his apply- slaughter of thousands and the misery of ing himself at once to the most minute de- millions. Surely, surely, a most sacred duty tails of any matters, however remote from is imposed upon the teachers of mankind, his professional pursuits, as I have heard Lord Glenelg describe with wonder his becoming familiar in a few days with the whole of a complicated question respecting the navigation of the Euphrates, when his lordship was minister for India; and then all military men knew how thoroughly the duke understood the whole details of regimental economy and discipline; which Napoleon did not so well know, because he cared not so much for the comforts of his men, nor was at all sparing of their lives (a principal object at all times with the duke); but he had a knowledge almost preternatural of the place where each corps, or even company, of his vast armies was to be found at any given time, because this was intimately connected with the use he might make of what he somewhat unfeelingly termed the "raw material." These examples of the rule which forbids superficial knowledge absolutely, and prescribes going to the bottom of any subject, or such part of any subject, as we intend to learn, give it the sanction of both those eminent men's experience, and show that it is recommended by their invariable success.

The effect of action and reaction upon the historian and the multitude has been adverted to. As regards the actors in the affairs of the world it is not to be overlooked; and it may even afford some extenuation of their faults. The multitude are in a measure the accomplices, if not the instigators, of those who for selfish objects, betray their interests, and work their misery or their ruin. Seduced by the spectacle of triumphant force, stricken with wonder at the mere exercise of great faculties with great success, men withdraw their eyes from the means by which the ends are attained, and lose their natural

whether historians who record or reasoners who comment upon events, to exert all their powers for weaning them from this fatal delusion-to mark, as their worst enemies, those who would cherish the feelings of mutual aversion or jealousy between nations connected by near neighborhood, which makes hostility most pernicious, and friendly intercourse most beneficial-and, above all, unceasingly to impress upon their minds the contrast between the empty renown of war, with its unspeakable horrors, and the solid glory of peace, as real as its blessings are substantial. It is said that the present ruler of France returned from his successful campaign impressed with a deep sense of these horrors, and that his wise devotion to the peaceful improvement of the country has been stimulated by the recollection of the scenes he had witnessed. Let us hope and trust that no vile flatterer will ever succeed in tempting him to abandon his course, and that he will join all virtuous and rational men in discountenancing the feelings which under his predecessor were productive of such misery to France and to the world-feelings which imposed and still impose upon all neighboring nations the heavy cost of unceasing watchfulness and preparation.

It is not enough, however, that the instructors of the people, and especially of youth, avoid propagating dangerous errors, and implanting, or encouraging in their growth, feelings hostile to the best interests of mankind. Their duty is to inculcate principles and cherish sentiments having the direct tendency to promote human happiness. Now the wisdom of ancient times, though it dealt largely with the subject of our passions, and generally with the nature of man in the ab

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