prince of the empire, was able to collect under his banner. Alas! what is the glory of man? Little the mighty count then thought that himself and all that nobility, with whom he had obtained such splendid victories, would, within a few months, be mowed down from this earthly scene by the most despised of hands.

The dialogue between the count and the Friesland deputies which then follows is very characteristic, but our limits will not admit of its insertion; we can, however, not withhold from the reader the portrait of the Bishop of Utrecht:

It was not possible for Rinaldo to enter into the cheerful mood of the bishop,* who, with the greatest ease, which, at other times, Rinaldo would have observed with admiration, fulfilled his duty as host, and found, in every dish that was served up,t matter for a witty demonstration, in which he displayed his nice taste as a gastronome, and, at the same time, his abilities as a man of the world. Whoever should have seen him, as, in the most perfect manner, he was cutting up a pigeon; and whoever should have heard him descant about woodcocks, and ringdoves, and every other sort of birds, and about the mode of stewing them with eggs and lemons, or stuffing them with milk and six yolks of eggs, and shalot, and parsley, quant. suff, or on the mode of having preserved on the journey the little animal he held on his fork, which he had done in an old charter, well greased with butter, after the object of his care had been rolled in onions, pepper, and salt, and afterwards broiled on a gridiron would little have thought that the same man, who seemed to be so wholly absorbed by the enjoyment of a nice roast, and to have made a god of his belly, had, but a moment before, gone through the most imperceptible mazes of high politics and projects of various kinds, not less difficult of execution, though of inferior importance. It is because Arkel was one of those happy (?) egotists, whose hearts always remain at rest, however active their brains may be; who, only living for themselves, have hardened their feelings against all impressions from without, and have acquired the art of banishing from their presence every unpleasant idea and importunate care, to lay hold only of that side of every circumstance which appears to them the most agreeable, and, by these means, never suffer the enjoyments of the moment to be embittered by painful recollections of the past or anxiety for the future.

Whatever idea, however, the reader may form of the bishop's character, this is certain, that the times in which he lived, and the circumstances in which he was placed, contributed much to his committing acts which indeed are justly considered as criminal, but which, after the moral standard of his age, may seem to be more excusable. John van Arkel was one of those men who appear on the stage of the world by way of exception, who are possessed of every gift, but whose hearts are constantly filled with insatiable desires: one of those dangerous beings who are devoured by an everlasting want of active movement; who look down upon common mortals with a smile of disdain, and who are not contented with an ordinary destiny; one of those geniuses who sometimes are cursed by prosperity, but considered by the poet and the philosopher with the same admiration with which they observe an ominous constellation in the firmament of heaven. In his youth he already possessed the boldness of more advanced life; his courage was as indubitable as his ambition was unbounded; his brain as fertile as his manners were courtly and elegant. He understood the art of rendering himself agreeable to those he stood in need of, just as much as that of crushing his enemies with the terrible weapons of satire and sarcasm. He was persevering in everything he undertook, and never to be deterred from a determination once taken; but as this stedfastness in doing his own will often exhibited itself even in matters * Who was, however, just then surrounded by the most perplexing difficulties. They were dining together.

of little importance, it frequently took, by a singular contrariety, the appearance of frivolity, and brought him into difficulties, under which any other man would have sunk, and become the fable of the public, but in which he only found another opportunity for displaying his inexhaustible wit, and his dexterity in profiting by every event. If, however, he principally employed his abilities in dark intrigues, and if his heart, which, naturally, was open and noble, very early enveloped itself in a triple barrier of ice, this, as we have already observed, must be chiefly attributed to circumstances. If he had been born in another epoch, he would, according to his own choice, have occupied an honourable place with the noblest heroes or the most perfect statesmen; but, in his age, it was not allowed him to be a candidate for military renown, and politics did not yet constitute a creditable science.

He had been obliged to embrace the clerical profession, while his inclinations from childhood had been bent upon the life of a soldier. His restless spirit had not permitted him, in the secluded cloister, to be contented with the observance of the monotonous and unmeaning occupations of his calling: in the career which parental constraint had assigned to him, he was resolved to make himself a name, and this even not so much from ambition as in order to deliver himself from what was most unsupportable of all to him—dependence upon others. He, therefore, had usefully employed his leisure hours, and he, who joined penetration and firmness to a most tenacious memory, had not found it difficult to attain a height at which his contemporaries considered him as a wonder, and overlooked the scandal which he gave, when, being on a visit to his parents, or otherwise, he laid hold of any opportunity that might offer to engage in the chivalrous sports of his brothers and other young noblemen; recreations which he sought to excuse by arguing that they were necessary for his health, which, he said, was impaired by his studies. In proportion, however, as he advanced in age, similar exercises, which at first had been connived at, were more severely blamed, and, at last, decidedly forbidden by the prior of his convent. The youth could bear no restraint, and more than once he felt inclined to throw aside the cowl, and enter into the world with his lance and sword alone. But he was already too much accustomed to the ease of a monastic life, and, when he considered the advantages attached to the clerical state, he concluded that he should sacrifice too much by abandoning it, and starving as a knight-errant. Yet much it cost him to give up his favourite amusements, and he therefore determined to submit apparently to the will of his superior, but to do in secret what he liked; in short, he feigned to bid adieu to all worldly thoughts, and followed up his studies more assiduously than ever; but often, when every one supposed him to be in his cell, lost in abstract meditations, or on a pilgrimage to some holy city, he assisted in disguise at hunting parties and chivalrous games, thus enjoying a pleasure which he was the more fond of because it was forbidden.

At last he attained the object of his wishes, and the influence of Count William raised him to the episcopal chair; but how great was his disappointment, when he discovered that there too he was not destined to be his own master, but the mere tool of another. This he grieved at, and he determined to free himself from this dependence also. His conduct as a bishop proved how earnest he was in this intention, and with what firmness he could prosecute it. His diocese admired a prelate who, in such early youth, sustained with so much zeal the interests of his bishopric, and every heart was filled with pain when he crowned his noble plan by his voluntary exile into France. As to him, he had attained a triple purpose: he had gained the hearts of his people; he had rendered his diocese independent of foreign influence; and he found himself in a foreign land, free and unshackled as the bird that flies in a place where no one spied his in-goings or out-goings, and where, therefore, he could yield himself up to all those amusements after which his heart panted. But, in the midst of all these pleasures, he received tidings from his brother that Count William sought to regain his influence in the diocese by every means

in his power. Then it was that the comprehensive plans which we have heard him communicate to Father Syand came to maturity. He began to be tired, too, of winning laurels at tournaments, which procured him no honour, because his name was doomed to remain unknown, and the voice of ambition smothered at last every other inclination in his breast. In order to become better acquainted with the state of things, he departed silently from Grenoble, and made, as we have seen, his arrival in Holland known but to few individuals. The tournament at Haarlem was again a temptation which he could not withstand, and on which his whole project of remaining unknown was almost wrecked. It had, however, been advantageous to him, inasmuch as it made him acquainted with Rinaldo, in whom he hoped to find a useful tool, which he might either employ or destroy as he might deem most fit; ay, destroy! for, as we have seen in his conduct towards Father Syand and the necromancer Barbanera, he did not hesitate, in order to attain his ends, to employ means which morality rejects, but which are recommended by necessity, the goddess whom, like many statesmen even of later times, he venerated as the directress of human actions.

We shall subjoin one more extract from the narrative of Count William's death.

William's valiant nobles still stood undaunted, and maintained the glory of their names. But, alas, at the same time that their numbers continually diminished, that of their assailants increased every moment: for Adelen, who hitherto had had no share in the battle, had, as soon as he received the news of the count's landing, marched with all possible speed to meet him, and now all the valour and discipline of the Hollanders were useless: not a shadow of order was any longer observed, and every one fought only for his own life. They fell one after another under the battle-axes and the bludgeous of the Frieslanders, who, with their characteristic fierceness, gave no quarter to the enemy whom they hated so much. Seven barons, all heads of the noblest families in William's dominions, twenty knights, every one of them famous for his exploits, were slain by the hands of despised boors. Terrible, especially, was Adelen. Six different times he wrested a weapon from the slain, having broken his own on the bodies of his enemies, or left it in the deep wounds which he inflicted. Yet neither the number of those he had killed, nor their glorious names, would satisfy him. He sought the Count of Holland; him he had chosen for his victim; on him he would revenge the affronts suffered at Haarlem. Whilst, roaring like a wild bull, he looked for him in all directions, he met Harcourt, who, deprived of helmet and shield, was hewing himself a passage with his sword.

"Where is. your master, accursed slave?" he cried, when he recognised him.

The only answer was a terrible blow of the knight's sword; but Adelen, having parried it, broke his right arm with his mace.

"My left remains," cried Harcourt, seizing his sword with the other arm, but, at the same time, a boor, who wielded a flail, dealt such a dreadful blow with it on the knight's head, that he fell lifeless among the numerous bodies of the slain.

"Is that cursed count then nowhere to be found?" roared Adelen, as he went along, like a lioness that is robbed of her whelps.

"Where should he be?" replied Cammingha, who just then met him; "they are all dead but one."

"Is one yet alive?" asked Adelen, with a horrible look; "where is he?" Cammingha pointed to a mound, where, formerly, the count's father had been installed as lord of Friesland. Little did William III. then think that on the same spot his valiant son would one day find his death, together with so many of his heroic followers. Adelen hastened thither, and there indeed

he saw one warrior defending himself, on the declivity of the hill, against a host of assailants. The slain bodies of his brethren at arms, and those of the Frieslanders, whom he had despatched with his own hand, formed a barrier around him which no one had passed with impunity. His helmet was knocked off, his shield broken, and his whole body so covered with blood, and mud, and dust, that it was almost impossible to see if he had armour on or not; but both his hands still wielded with astonishing power a double-edged sword, with which he kept every one at a distance.

"How is this, cowards?" cried Adelen; "do you flag? Leave me alone with him; mine be the honour of slaying the last man of the band."

With these words he penetrated through the crowd, and, suddenly approaching the foreign warrior, gave him a dreadful blow on his head.

“Take that,” he said; " and go and tell in hell who has sent thee thither.” Hourah! Long live Adelen!" cried the people, who saw the Hollander stunned by the blow.

But, although stunned, he was not wounded, for the mace had turned in the hand of the assailant. "If thou art Adelen," he said, recovering himself, although with a choked voice, "take then this last keepsake from thy lord and master."

William had not yet quite uttered these words, when he had lifted up his sword, and, with a blow louder than that of the hammer on the anvil, the blade came down on Adelen's head, penetrated the helmet, and split the scull. The impetuous Frieslander fell lifeless; but his victor tried in vain to draw back the sword from the wound, and fifty clubs, raised by his adversaries, exasperated, if possible, more than ever, by the death of their leader, instantly extended the defenceless count upon the heap of the slain.

HISTORY OF MATHEMATICS.

Aperçu historique sur l'origine et le développement des méthodes en Géométrie. (Historical Sketch of the Origin and Progress of Geometrical Methods of Reasoning.) By M. Chasles. 4to. Bruxelles. 1837.

Histoire des Sciences Mathématiques en Italie. (History of the Mathematical Sciences in Italy.) By G. Libri. 2 vols. Paris. 1838.

Since the time of Descartes, who opened such a vast field for the application of the calculus, mathematicians have been divided into two distinct classes, the Geometricians and the Algebraists; the former adhering to the cautious method of reasoning used by the Greeks, and the latter preferring the loose and artificial operation of the modern analysis. The spirit of party has likewise here, as in other instances, exercised its exclusive sway; and the number of those who are willing to admit the respective merits of both modes of proceeding, and ready, as the circumstances may require, to adopt the advantages of either, is comparatively few. The followers of the modern system, it must be confessed, have been more active and enterprising; they have not only achieved splendid conquests, and enriched science by annexing new provinces of wonderful extent, but are making con

tinual inroads upon the older departments; and, having acquired the dominion of the continent, they threaten to drive the Greek geometry from her favoured retreat in the British isles.

The study of mathematics, when rightly conducted, ought, we presume, to aim at two capital objects. It should not only lead to an intimate acquaintance with those relations of figure and quantity, which are so highly instructive, and confer such immediate and important advantages in the business of life, and the prosecution of the physical sciences; but it should also train the mind to the invaluable habits of patient attention, accurate arrangement, nice discrimination, and close reasoning. This latter advantage, with a view to general education, is the most essential. The number of those who have leisure, taste, or capacity to devote themselves to the prosecution of abstract researches, however splendid and imposing, must necessarily be very limited; but all who, in every condition of society, aspire to the liberal and cultivated exercise of their faculties, will derive inestimable benefit from that previous discipline of the understanding which the study of the mathematics appears so peculiarly calculated to bestow. On this account, we are persuaded that a young man will reap more essential and lasting advantage from an acquaintance with geometrical reasoning, than from a knowledge of Algebra. The latter may help to improve his dexterity in ciphering, and better prepare him for entering on the details of business; but the former, besides the practical skill which it cannot fail to impart, has a direct tendency to invigorate the whole of the intellectual powers, and to lay a sure and solid foundation on which to erect future superstructures. After such habits of cautious procedure and accurate discrimination are once formed, the student may safely venture into the region of modern analysis, and range with profit through that boundless domain, where so much is admirable, and so much is yet clouded with obscurity, or disfigured by hasty and careless combination.

It is with this view that we hail, with unfeigned pleasure, the first of the works whose titles stand at the head of this article. M. Chasles has performed an invaluable service to every one interested in the by-gone times of science, and we earnestly hope that his work may also serve to counteract that unfortunate tendency which prevails on the Continent, with the exception, perhaps, of Italy, to substitute, on almost every occasion, a clumsy and often obscure sort of calculation for the clear evidence and unfading beauty of the Greek geometry. This abuse of an instrument, which, when skilfully employed, affords such powerful aid in exploring the heights of science, but which is so ill adapted for reducing the elementary properties of figure, seems at last to have been perceived and tacitly admitted by several distinguished analysts abroad. The manner in which the work of M. Chasles