Knolles’s History of the Turks. 31. Knolles, already known by a spirited translation of Bodin’s Commonwealth, published in 1610 a copious History of the Turks, bringing down his narrative to the most recent times. Johnson in a paper of the Rambler has given him the superiority over all English historians. “He has displayed all the excellencies that narration can admit. His style, though somewhat obscured by time, and vitiated by false wit, is pure, nervous, elevated, and clear.... Nothing could have sunk this author into obscurity but the remoteness and barbarity of the people whose story he relates. It seldom happens that all circumstances concur to happiness or fame. The nation which produced this great historian has the grief of seeing his genius employed upon a foreign and uninteresting subject; and that writer who might have secured perpetuity to his name by a history of his own country, has exposed himself to the danger of oblivion by recounting enterprises and revolutions of which none desire to be informed.”[583] The subject, however, appeared to Knolles, and I know not how we can say erroneously, one of the most splendid he could have selected. It was the rise and growth of a mighty nation, second only to Rome in the constancy of success, and in the magnitude of empire; a nation fierce and terrible, the present scourge of half Christendom, and though from our remoteness not very formidable to ourselves, still one of which not the bookish man in his closet or the statesman in council had alone heard, but the smith at his anvil, and the husbandman at his plough. A long decrepitude of the Turkish empire on one hand, and our frequent alliance with it on the other, have obliterated the apprehensions and interests of every kind which were awakened throughout Europe by its youthful fury and its mature strength. The subject was also new in England, yet rich in materials; various, in comparison with ordinary history, though not perhaps so fertile of philosophical observation as some others, and furnishing many occasions for the peculiar talents of Knolles. These were displayed, not in depth of thought, or copiousness of collateral erudition, but in a style and in a power of narration which Johnson has not too highly extolled. His descriptions are vivid and animated; circumstantial, but not to feebleness; his characters are drawn with a strong pencil. It is indeed difficult to estimate the merits of an historian very accurately without having before our eyes his original sources: he may probably have translated much that we admire, and he had shown that he knew how to translate. In the style of Knolles there is sometimes, as Johnson has hinted, a slight excess of desire to make every phrase effective; but he is exempt from the usual blemishes of his age; and his command of the language is so extensive, that we should not err in placing him among the first of our elder writers. Comparing as a specimen of Knolles’s manner, his description of the execution of Mustapha, son of Solyman, with that given by Robertson, where the latter historian has been as circumstantial as his limits would permit, we shall perceive that the former paints better his story, and deepens better its interest.[584]

[583] Rambler, No. 122.

[584] Knolles, p. 515. Robertson, book xi.

Raleigh’s History of the World. 32. Raleigh’s History of the World is a proof of the respect for laborious learning that had long distinguished Europe. We should expect from the prison-hours of a soldier, a courtier, a busy intriguer in state affairs, a poet and man of genius, something well worth our notice; but hardly a prolix history of the ancient world, hardly disquisitions on the site of Paradise and the travels of Cain. These are probably translated with little alteration from some of the learned writings of the Continent; they are by much the least valuable portion of Raleigh’s work. The Greek and Roman story is told more fully and exactly than by any earlier English author, and with a plain eloquence, which has given this book a classical reputation in our language, though from its length and the want of that critical sifting of facts which we now justly demand, it is not greatly read. Raleigh has intermingled political reflections, and illustrated his history by episodes from modern times, which perhaps are now the most interesting passages. It descends only to the second Macedonian war; the continuation might have been more generally valuable; but either the death of Prince Henry, as Raleigh himself tells us, or the new schemes of ambition which unfortunately opened upon his eyes, prevented the execution of the large plan he had formed. There is little now obsolete in the words of Raleigh, nor, to any great degree, in his turn of phrase; the periods, when pains have been taken with them, show that artificial structure which we find in Sydney and Hooker; he is less pedantic than most of his contemporaries, seldom low, never affected.[585]

[585] Raleigh’s History was so little known, that Warburton, in the preface to his Julian, took from it a remarkable passage without acknowledgment; and Dr. Parr, though a man of very extensive reading, extolled it as Warburton’s not knowing, what he afterwards discovered, the original source. The passage is as follows in Raleigh, Warburton of course having altered some of the expressions. “We have left it (the Roman empire) flourishing in the middle of the field, having rooted up or cut down all that kept it from the eyes and admiration of the world. But after some continuance, it shall begin to lose the beauty it had; the storms of ambition shall beat her great boughs and branches one against another; her leaves shall fall off, her limbs wither, and a rabble of barbarous nations enter the field and cut her down.” Raleigh’s History, ad finem.

Notwithstanding the praise that has been bestowed on this sentence, it is open to some censure; the simile and subject are too much confounded; a rabble of barbarous nations might be required to subvert the Roman empire, but make an odd figure in cutting down a tree. The rhythm and spirit indeed are admirable.

Daniel’s History of England. 33. Daniel’s History of England from the Conquest to the Reign of Edward III., published in 1618, is deserving of some attention on account of its language. It is written with a freedom from all stiffness, and a purity of style which hardly any other work of so early a date exhibits. These qualities are indeed so remarkable that it would require a good deal of critical observation to distinguish it even from writings of the reign of Anne; and where it differs from them (I speak only of the secondary class of works, which have not much individuality of manner), it is by a more select idiom, and by an absence of the Gallicism or vulgarity which are often found in that age. It is true that the merits of Daniel are chiefly negative; he is never pedantic or antithetical or low, as his contemporaries were apt to be; but his periods are ill constructed, he has little vigour or elegance; and it is only by observing how much pains he must have taken to reject phrases which were growing obsolete, that we give him credit for having done more than follow the common stream of easy writing. A slight tinge of archaism, and a certain majesty of expression, relatively to colloquial usage, were thought by Bacon and Raleigh congenial to an elevated style; but Daniel, a gentleman of the king’s household, wrote as the court spoke, and his facility would be pleasing if his sentences had a less negligent structure. As an historian, he has recourse only to common authorities; but his narration is fluent and perspicuous, with a regular vein of good sense, more the characteristic of his mind, both in verse and prose, than any commanding vigour.

Bacon. 34. The style of Bacon has an idiosyncracy which we might expect from his genius. It can rarely indeed happen, and only in men of secondary talents, that the language they use is not, by its very choice and collocation, as well as its meaning, the representative of an individuality that distinguishes their turn of thought. Bacon is elaborate, sententious, often witty, often metaphorical; nothing could be spared; his analogies are generally striking and novel; his style is clear, precise, forcible; yet there is some degree of stiffness about it, and in mere language he is inferior to Raleigh. The History of Henry VII., admirable as many passages are, seems to be written rather too ambitiously, and with too great an absence of simplicity.

Milton. 35. The polemical writings of Milton, which chiefly fall within this period, contain several bursts of his splendid imagination and grandeur of soul. They are, however, much inferior to the Areopagitica, or Plea for the Liberty of Unlicensed Printing. Many passages in this famous tract are admirably eloquent; an intense love of liberty and truth glows through it, the majestic soul of Milton breathes such high thoughts as had not been uttered before; yet even here he frequently sinks in a single instant, as is usual with our old writers, from his highest flights to the ground; his intermixture of familiar with learned phraseology is unpleasing, his structure is affectedly elaborate, and he seldom reaches any harmony. If he turns to invective, as sometimes in this treatise, and more in his Apology for Smectymnuus, it is mere ribaldrous vulgarity blended with pedantry; his wit is always poor and without ease. An absence of idiomatic grace, and an use of harsh inversions violating the rules of the language, distinguish, in general, the writings of Milton, and require, in order to compensate them, such high beauties as will sometimes occur.

Clarendon. 36. The History of Clarendon may be considered as belonging rather to this than to the second period of the century, both by the probable date of composition and by the nature of its style. He is excellent in everything that he has performed with care; his characters are beautifully delineated, his sentiments have often a noble gravity which the length of his periods, far too great in itself, seems to befit; but in the general course of his narration he is negligent of grammar and perspicuity, with little choice of words, and therefore sometimes idiomatic without ease or elegance. The official papers on the royal side, which are generally attributed to him, are written in a masculine and majestic tone, far superior to those of the parliament. The latter had, however, a writer who did them honour: May’s History of the Parliament is a good model of genuine English; he is plain, terse, and vigorous, never slovenly, though with few remarkable passages, and is, in style as well as substance, a kind of contrast to Clarendon.

The Icon Basilice. 37. The famous Icon Basilice, ascribed to Charles I., may deserve a place in literary history. If we could trust its panegyrists, few books in our language have done it more credit by dignity of sentiment and beauty of style. It can hardly be necessary for me to express my unhesitating conviction that it was solely written by Bishop Gauden, who, after the Restoration, unequivocally claimed it as his own. The folly and impudence of such a claim, if it could not be substantiated, are not to be presumed as to any man of good understanding, fair character, and high station, without stronger evidence than has been alleged on the other side; especially when we find that those who had the best means of inquiry, at a time when it seems impossible that the falsehood of Gauden’s assertion should not have been demonstrated, if it were false, acquiesced in his pretensions. We have very little to place against this, except secondary testimony, vague, for the most part, in itself, and collected by those whose veracity has not been put to the test like that of Gauden.[586] The style, also, of the Icon Basilice has been identified by Mr. Todd with that of Gauden, by the use of several phrases, so peculiar that we can hardly conceive them to have suggested themselves to more than one person. It is, nevertheless, superior to his acknowledged writings. A strain of majestic melancholy is well kept up; but the personated sovereign is rather too theatrical for real nature, the language is too rhetorical and amplified, the periods too artificially elaborated. None but scholars and practised writers employ such a style as this.

[586] There is only one claimant, in a proper sense, for the Icon Basilice, which is Gauden himself; the king neither appears by himself or representative. And, though we may find several instances of plagiarism in literary history (one of the grossest being the publication by a Spanish friar, under another title, of a book already in print with the name of Hyperius of Marpurg, its real author), yet I cannot call to mind any, where a man known to the world has asserted in terms his own authorship of a book not written by himself, but universally ascribed to another, and which had never been in his possession. A story is told, and, I believe, truly, that a young man assumed the credit of Mackenzie’s Man of Feeling, while it was still anonymous. But this is widely different from the case of the Icon Basilice. We have had an interminable discussion as to the Letters of Junius. But no one has ever claimed this derelict property to himself, or told the world, I am Junius.

Burton’s Anatomy of Melancholy. 38. Burton’s Anatomy of Melancholy belongs, by its systematic divisions and its accumulated quotations, to the class of mere erudition; it seems, at first sight, like those tedious Latin folios, into which scholars of the sixteenth and seventeenth centuries threw the materials of their Adversaria, or common-place books, painfully selected and arranged by the labour of many years. But writing, fortunately, in English, and in a style not by any means devoid of point and terseness, with much good sense and observation of men as well as of books, and having also the skill of choosing his quotations for their rareness, oddity, and amusing character, without losing sight of their pertinence to the subject, he has produced a work of which, as is well known, Johnson said, that it was the only one which had ever caused him to leave his bed earlier than he had intended. Johnson, who seems to have had some turn for the singularities of learning, which fill the Anatomy of Melancholy, may perhaps have raised the credit of Burton higher than his desert. He is clogged by excess of reading, like others of his age, and we may peruse entire chapters without finding more than a few lines that belong to himself. This becomes a wearisome style, and, for myself, I have not found much pleasure in glancing over the Anatomy of Melancholy. It may be added that he has been a collector of stories far more strange than true, from those records of figments, the old medical writers of the sixteenth century, and other equally deceitful sources. Burton lived at Oxford, and his volumes are apparently a great sweeping of miscellaneous literature from the Bodleian library.

Earle’s Characters. 39. John Earle, after the Restoration bishop of Worcester, and then of Salisbury, is author of “Microcosmographia, or a Piece of the Worlde discovered in Essays and Characters,” published anonymously in 1628. In some of these short characters, Earle is worthy of comparison with La Bruyère; in others, perhaps the greater part, he has contented himself with pictures of ordinary manners, such as the varieties of occupation, rather than of intrinsic character, supply. In all, however, we find an acute observation and a happy humour of expression. The chapter entitled the Sceptic is best known; it is witty, but an insult throughout on the honest searcher after truth, which could have come only from one that was content to take up his own opinions for ease or profit. Earle is always gay and quick to catch the ridiculous, especially that of exterior appearances; his style is short, describing well with a few words, but with much of the affected quaintness of that age. It is one of those books which give us a picturesque idea of the manners of our fathers at a period now become remote, and for this reason it would deserve to be read.

Overbury’s Characters. 40. But the Microcosmography is not an original work in its plan or mode of execution; it is a close imitation of the Characters of Sir Thomas Overbury. They both belong to the favourite style of apophthegm, in which every sentence is a point or a witticism. Yet the entire character so delineated produces a certain effect; it is a Dutch picture, a Gerard Dow, somewhat too elaborate. Earle has more natural humour than Overbury, and hits his mark more neatly; the other is more satirical, but often abusive and vulgar. The “Fair and Happy Milk-maid,” often quoted, is the best of his characters. The wit is often trivial and flat; the sentiments have nothing in them general, or worthy of much resemblance; praise is only due to the graphic skill in delineating character. Earle is as clearly the better, as Overbury is the more original, writer.

Jonson’s Discoveries. 41. A book by Ben Jonson, entitled “Timber, or Discoveries made upon Men and Matter,” is altogether miscellaneous, the greater part being general moral remarks, while another portion deserves notice as the only book of English criticism in the first part of the seventeenth century. The observations are unconnected, judicious, sometimes witty, frequently severe. The style is what was called pregnant, leaving much to be filled up by the reader’s reflection. Good sense and a vigorous manner of grappling with every subject will generally be found in Jonson, but he does not reach any very profound criticism. His English Grammar is said by Gifford to have been destroyed in the conflagration of his study. What we have, therefore, under that name is, he thinks, to be considered as properly the materials of a more complete work that is lost. We have, as I apprehend, no earlier grammar upon so elaborate a plan; every rule is illustrated by examples, almost to redundance; but he is too copious on what is common to other languages, and perhaps not full enough as to our peculiar idiom. Nothing else deserving of the slightest notice can be added to this book of Jonson.

Sect. II.

ON FICTION.

Cervantes—French Romances—Calprenède—Scuderi—Latin and English Works of Fiction.

Publication of Don Quixote. 42. The first part of Don Quixote was published in 1605. We have no reason, I believe, to suppose that it was written long before. It became immediately popular; and the admiration of the world raised up envious competitors, one of whom, Avellenada, published a continuation in a strain of invective against the author. Cervantes, who cannot be imagined to have ever designed the leaving his romance in so unfinished a state, took time about the second part, which did not appear till 1615.

Its reputation. 43. Don Quixote is the only book in the Spanish language which can now be said to possess much of an European reputation. It has, however, enjoyed enough to compensate for the neglect of all the rest. It is to Europe in general what Ariosto is to Italy, and Shakspeare to England; the one book to which the slightest allusions may be made without affectation, but not missed without discredit. Numerous translations and countless editions of them, in every language, bespeak its adaptation to mankind; no critic has been paradoxical enough to withhold his admiration, no reader has ventured to confess a want of relish for that in which the young and old, in every climate, have, age after age, taken delight. They have doubtless believed that they understood the author’s meaning; and, in giving the reins to the gaiety that his fertile invention and comic humour inspired, never thought of any deeper meaning than he announces, or delayed their enjoyment for any metaphysical investigation of his plan.

New views of its design. 44. A new school of criticism, however, has of late years arisen in Germany, acute, ingenious, and sometimes eminently successful in philosophical, or, as they denominate it, æsthetic analysis of works of taste, but gliding too much into refinement and conjectural hypothesis, and with a tendency to mislead men of inferior capacities for this kind of investigation into mere paradox and absurdity. An instance is supplied, in my opinion, by some remarks of Bouterwek, still more explicitly developed by Sismondi, on the design of Cervantes in Don Quixote, and which have been repeated in other publications. According to these writers, the primary idea is that of a “man of elevated character, excited by heroic and enthusiastic feelings to the extravagant pitch of wishing to restore the age of chivalry; nor is it possible to form a more mistaken notion of this work than by considering it merely as a satire, intended by the author to ridicule the absurd passion for reading old romances.”[587] “The fundamental idea of Don Quixote,” says Sismondi, “is the eternal contrast between the spirit of poetry and that of prose. Men of an elevated soul propose to themselves as the object of life to be the defenders of the weak, the support of the oppressed, the champions of justice and innocence. Like Don Quixote, they find on every side the image of the virtues they worship; they believe that disinterestedness, nobleness, courage, in short, knight errantry, are still prevalent; and with no calculation of their own powers, they expose themselves for an ungrateful world, they offer themselves as a sacrifice to the laws and rules of an imaginary state of society.”[588]

[587] Bouterwek, p. 334.

[588] Littérature du Midi, vol. iii., p. 339.

45. If this were a true representation of the scheme of Don Quixote, we cannot wonder that some persons should, as M. Sismondi tells us they do, consider it as the most melancholy book that has ever been written. They consider it also, no doubt, one of the most immoral, as chilling and pernicious in its influence on the social converse of mankind, as the Prince of Machiavel is on their political intercourse. “Cervantes,” he proceeds, “has shown us in some measure the vanity of greatness of soul and the delusion of heroism. He has drawn in Don Quixote a perfect man (un homme accompli), who is, nevertheless, the constant object of ridicule. Brave beyond the fabled knights he imitates, disinterested, honourable, generous, the most faithful and respectful of lovers, the best of masters, the most accomplished and well educated of gentlemen, all his enterprises end in discomfiture to himself, and in mischief to others.” M. Sismondi descants upon the perfections of the knight of La Mancha with a gravity which is not quite easy for his readers to preserve.

Probably erroneous. 46. It might be answered by a phlegmatic observer, that a mere enthusiasm for doing good, if excited by vanity, and not accompanied by common sense, will seldom be very serviceable to ourselves or to others; that men who, in their heroism and care for the oppressed, would throw open the cages of lions, and set galley-slaves at liberty, not forgetting to break the limbs of harmless persons whom they mistake for wrongdoers, are a class of whom Don Quixote is the real type; and that the world being much the worse for such heroes, it might not be immoral, notwithstanding their benevolent enthusiasm, to put them out of countenance by a little ridicule. This, however, is not, as I conceive, the primary aim of Cervantes; nor do I think that the exhibition of one great truth, as the predominant, but concealed, moral of a long work, is in the spirit of his age. He possessed a very thoughtful mind and a profound knowledge of humanity; yet the generalisation which the hypothesis of Bouterwek and Sismondi requires for the leading conception of Don Quixote, besides its being a little inconsistent with the valorous and romantic character of its author, belongs to a more advanced period of philosophy than his own. It will, at all events, I presume, be admitted that we cannot reason about Don Quixote except from the book, and I think it may be shown in a few words that these ingenious writers have been chiefly misled by some want of consistency which circumstances produced in the author’s delineation of his hero.

Difference between the two parts. 47. In the first chapter of this romance Cervantes, with a few strokes of a great master, sets before us the pauper gentleman, an early riser and keen sportsman, who, “when he was idle, which was most part of the year,” gave himself up to reading books of chivalry till he lost his wits. The events that follow are in every one’s recollection; his lunacy consists, no doubt, only in one idea; but this is so absorbing that it perverts the evidence of his senses, and predominates in all his language. It is to be observed, therefore, in relation to the nobleness of soul ascribed to Don Quixote, that every sentiment he utters is borrowed with a punctilious rigour from the romances of his library; he resorts to them on every occasion for precedents; if he is intrepidly brave, it is because his madness and vanity have made him believe himself unconquerable; if he bestows kingdoms, it is because Amadis would have done the same; if he is honourable, courteous, a redresser of wrongs, it is in pursuance of these prototypes, from whom, except that he seems rather more scrupulous in chastity, it is his only boast not to diverge. Those who talk of the exalted character of Don Quixote, seem really to forget that, on these subjects, he has no character at all; he is the echo of romance; and to praise him is merely to say, that the tone of chivalry, which these productions studied to keep up, and, in the hands of inferior artists, foolishly exaggerated, was full of moral dignity, and has, in a subdued degree of force, modelled the character of a man of honour in the present day. But throughout the first two volumes of Don Quixote, though in a few unimportant passages he talks rationally, I cannot find more than two in which he displays any other knowledge or strength of mind than the original delineation of the character would lead us to expect.

48. The case is much altered in the last two volumes. Cervantes had acquired an immense popularity, and perceived the opportunity, of which he had already availed himself, that this romance gave for displaying his own mind. He had become attached to a hero who had made him illustrious, and suffered himself to lose sight of the clear outline he had once traced for Quixote’s personality. Hence, we find in all this second part that, although the lunacy as to knights errant remains unabated, he is, on all other subjects, not only rational in the low sense of the word, but clear, acute, profound, sarcastic, coolheaded. His philosophy is elevated but not enthusiastic, his imagination is poetical, but it is restrained by strong sense. There are, in fact, two Don Quixotes; one, whom Cervantes first designed to draw, the foolish gentleman of La Mancha, whose foolishness had made him frantic; the other, a highly gifted, accomplished model of the best chivalry, trained in all the court, the camp, or the college could impart, but scathed in one portion of his mind by an inexplicable visitation of monomania. One is inclined to ask why this Don Quixote, who is Cervantes, should have been more likely to lose his intellects by reading romances than Cervantes himself. As a matter of bodily disease, such an event is doubtless possible; but nothing can be conceived more improper for fiction, nothing more incapable of affording a moral lesson than the insanity which arises wholly from disease. Insanity is, in no point of view, a theme for ridicule; and this is an inherent fault of the romance (for those who have imagined that Cervantes has not rendered Quixote ridiculous have a strange notion of the word); but the thoughtlessness of mankind, rather than their insensibility, for they do not connect madness with misery, furnishes some apology for the first two volumes. In proportion as we perceive below the veil of mental delusion a noble intellect, we feel a painful sympathy with its humiliation; the character becomes more complicated and interesting, but has less truth and naturalness; an objection which might also be made, comparatively speaking, to the incidents in the latter volumes, wherein I do not find the admirable probability that reigns through the former. But this contrast of wisdom and virtue with insanity in the same subject would have been repulsive in the primary delineation; as I think any one may judge by supposing that Cervantes had, in the first chapter, drawn such a picture of Quixote as Bouterwek and Sismondi have drawn for him.

49. I must, therefore, venture to think as, I believe, the world has generally thought for two centuries, that Cervantes had no more profound aim than he proposes to the reader. If the fashion of reading bad romances of chivalry perverted the taste of his contemporaries, and rendered their language ridiculous, it was natural that a zealous lover of good literature should expose this folly to the world by exaggerating its effects on a fictitious personage. It has been said by some modern writer, though I cannot remember by whom, that there was a prose side in the mind of Cervantes. There was indeed a side of calm strong sense, which some take for unpoetical. He thought the tone of those romances extravagant. It might naturally occur how absurd any one must appear who should attempt to realize in actual life the adventures of Amadis. Already a novelist, he perceived the opportunities this idea suggested. It was a necessary consequence that the hero must be represented as literally insane, since his conduct would have been extravagant beyond the probability of fiction on any other hypothesis; and from this happy conception germinated in a very prolific mind the whole history of Don Quixote. Its simplicity is perfect; no limit could be found save the author’s discretion, or sense that he had drawn sufficiently on his imagination; but the death of Quixote, which Cervantes has been said to have determined upon, lest some one else should a second time presume to continue the story, is, in fact, the only possible termination that could be given, after he had elevated the character to that pitch of mental dignity which we find in the last two volumes.

Excellence of this romance. 50. Few books of moral philosophy display as deep an insight into the mechanism of the mind as Don Quixote. And when we look also at the fertility of invention, the general probability of the events, and the great simplicity of the story, wherein no artifices are practised to create suspense, or complicate the action, we shall think Cervantes fully deserving of the glory that attends this monument of his genius. It is not merely that he is superior to all his predecessors and contemporaries. This, though it might account for the European fame of his romance, would be an inadequate testimony to its desert. Cervantes stands on an eminence below which we must place the best of his successors. We have only to compare him with Le Sage or Fielding, to judge of his vast superiority. To Scott indeed he must yield in the variety of his power; but in the line of comic romance, we should hardly think Scott his equal.

Minor novels of Cervantes. 51. The moral novels of Cervantes, as he calls them (Novellas Exemplares), are written, I believe, in a good style, but too short, and constructed with too little artifice to rivet our interest. Their simplicity and truth, as in many of the old novels, have a certain charm; but in the present age, our sense of satiety in works of fiction cannot be overcome but by excellence. |Other novels—Spanish.| Of the Spanish comic romances, in the picaresque style, several remain: Justina was the most famous. One that does not strictly belong to this lower class is the Marcos de Obregon of Espinel. This is supposed to have suggested much to Le Sage in Gil Bias; in fact, the first story we meet with is that of Mergellina the physician’s wife. The style, though not dull, wants the grace and neatness of Le Sage. This is esteemed one of the best novels that Spain has produced. |And Italian.| Italy was no longer the seat of this literature. A romance of chivalry by Marini (not the poet of that name), entitled Il Caloandro (1640), was translated but indifferently into French by Scuderi, and has been praised by Salfi as full of imagination, with characters skilfully diversified, and an interesting well-conducted story.[589]

[589] Salfi, vol. xiv., p. 88

French romances—Astrée. 52. France, in the sixteenth century, content with Amadis de Gaul and the numerous romances of the Spanish school, had contributed very little to that literature. But now she had native writers of both kinds, the pastoral and heroic, who completely superseded the models they had before them. Their earliest essay was the Astrée of D’Urfé. Of this pastoral romance the first volume was published in 1610; the second in 1620; three more came slowly forth, that the world might have due leisure to admire. It contains about 3,500 pages. It would be almost as discreditable to have read such a book through at present, as it was to be ignorant of it in the age of Louis XIII. Allusions, however, to real circumstances served in some measure to lessen the insipidity of a love-story, which seems to equal any in absurdity and want of interest. The style, and I can judge no farther, having read but a few pages, seems easy and not unpleasing; but the pastoral tone is insufferably puerile, and a monotonous solemnity makes us almost suspect that one source of its popularity was its gentle effect, when read in small portions before retiring to rest. It was, nevertheless, admired by men of erudition, like Camus and Huet, or even by men of the world like Rochefoucault.[590]

[590] Dunlop’s History of Fiction, vol. iii., p. 184. Biographie Universelle. Bouterwek, vol. v., p. 295.

Heroic romances—Gomberville. 53. From the union of the old chivalrous romance with this newer style, the courtly pastoral, sprang another kind of notion, the French heroic romance. Three nearly contemporary writers, Gomberville, Calprenède, Scuderi, supplied a number of voluminous stories, frequently historical in some of their names, but utterly destitute of truth in circumstances, characters, and manners. Gomberville led the way in his Polexandre, first published in 1632, and reaching in later editions to about 6,000 pages. “This,” says a modern writer, “seems to have been the model of the works of Calprenède and Scuderi. This ponderous work may be regarded as a sort of intermediate production between the later compositions and the ancient fables of chivalry. It has, indeed, a close affinity to the heroic romance; but many of the exploits of the hero are as extravagant as those of a paladin or knight of the round table.”[591] No romance in the language has so complex an intrigue, insomuch that it is followed with difficulty; and the author has in successive editions capriciously remodelled parts of his story, which is wholly of his own invention.[592]

[591] Dunlop, iii., 230.

[592] Biog. Univ.

Calprenède. 54. Calprenède, a poet of no contemptible powers of imagination, poured forth his stores of rapid invention in several romances more celebrated than that of Gomberville. The first, which is contained in ten octavo volumes, is the Cassandra. This appeared in 1642, and was followed by the Cleopatra, published, according to the custom of romancers, in successive parts, the earliest in 1646. La Harpe thinks this unquestionably the best work of Calprenède; Bouterwek seems to prefer the Cassandra. Pharamond is not wholly his own; five out of twelve volumes belong to one De Vaumorière, a continuator.[593] Calprenède, like many others, had but a life-estate in the temple of fame, and more happy, perhaps, than greater men, lived out the whole favour of the world, which, having been largely showered on his head, strewed no memorials on his grave. It became, soon after his death, through the satire of Boileau and the influence of a new style in fiction, a matter of course to turn him into ridicule. It is impossible that his romances should be read again; but those who, for the purposes of general criticism, have gone back to these volumes, find not a little to praise in his genius, and in some measure to explain his popularity. “Calprenède,” says Bouterwek, “belonged to the extravagant party, which endeavoured to give a triumph to genius at the expense of taste, and by that very means played into the hands of the opposite party, which saw nothing so laudable as the observation of the rules which taste prescribed. We have only to become acquainted with any one of the prolix romances of Calprenède, such, for instance, as the Cassandra, to see clearly the spirit which animates the whole invention. We find there again the heroism of chivalry, the enthusiastic raptures of love, the struggle of duty with passion, the victory of magnanimity, sincerity, and humanity over force, fraud, and barbarism, in the genuine characters and circumstances of romance. The events are skilfully interwoven, and a truly poetical keeping belongs to the whole, however extended it may be. The diction of Calprenède is a little monotonous, but not at all trivial, and seldom affected. It is like that of old romance, grave, circumstantial, somewhat in the chronicle style, but picturesque, agreeable, full of sensibility and simplicity. Many passages might, if versified, find a place in the most beautiful poem of this class.”[594]

[593] Dunlop, iii., 259.

[594] Bouterwek, vi., 230.

Scuderi. 55. The honours of this romantic literature have long been shared by the female sex. In the age of Richelieu and Mazarin, this was represented by Mademoiselle de Scuderi, a name very glorious for a season, but which unfortunately did not, like that of Calprenède, continue to be such during the whole lifetime of her who bore it. The old age of Mademoiselle de Scuderi was ignominiously treated by the pitiless Boileau; and reaching more than her ninetieth year, she almost survived her only offspring, those of her pen. In her youth she had been the associate of the Rambouillet circle, and caught, perhaps, in some measure from them, what she gave back with interest, a tone of perpetual affectation and a pedantic gallantry, which could not withstand the first approach of ridicule. Her first romance was Ibrahim, published in 1635; but the more celebrated were the Grand Cyrus and the Clelie. Each of these two romances is in ten volumes.[595] The persons chiefly connected with the Hotel Rambouillet sat for their pictures, as Persians or Babylonians, in Cyrus. Julie d’Angennes herself bore the name of Artenice, by which she was afterwards distinguished among her friends; and it is a remarkable instance not only of the popularity of these romances, but of the respectful sentiment, which, from the elevation and purity no one can deny them to exhibit, was always associated in the gravest persons with their fictions, that a prelate of eminent taste and eloquence, Fléchier, in his funeral sermon on this lady, calls her “the incomparable Artenice.”[596] Such an allusion would appear to us misplaced; but we may presume that it was not so thought. Scuderi’s romances seem to have been remarkably the favourites of the clergy; Huet, Mascaron, Godeau, as much as Fléchier, were her ardent admirers. “I find,” says the second of these, one of the chief ornaments of the French pulpit, in writing to Mademoiselle de Scuderi, “so much in your works calculated to reform the world, that in the sermons I am now preparing for the court, you will often be on my table by the side of St. Augustin and St. Bernard.”[597] In the writings of this lady we see the last footstep of the old chivalrous romance. She, like Calprenède, had derived from this source the predominant characteristics of her personages, an exalted generosity, a disdain of all selfish considerations, a courage which attempts impossibilities and is rewarded by achieving them, a love outrageously hyperbolical in pretence, yet intrinsically without passion, all, in short, that Cervantes has bestowed on Don Quixote. Love, however, or its counterfeit, gallantry, plays a still more leading part in the French romance than in its Castilian prototype; the feats of heroes, though not less wonderful, are less prominent on the canvas, and a metaphysical pedantry replaces the pompous metaphors in which the knight of sorrowful countenance had taken so much delight. The approbation of many persons, far better judges than Don Quixote, makes it impossible to doubt that the romances of Calprenède and Scuderi were better than his library. But as this is the least possible praise, it will certainly not tempt any one away from the rich and varied repast of fiction which the last and present century have spread before him. Mademoiselle de Scuderi has perverted history still more than Calprenède, and changed her Romans into languishing Parisians. It is not to be forgotten that the taste of her party, though it did not, properly speaking, infect Corneille, compelled him to weaken some of his tragedies. And this must be the justification of Boileau’s cutting ridicule upon this truly estimable woman. She had certainly kept up a tone of severe and high morality, with which the aristocracy of Paris could ill dispense; but it was one not difficult to feign, and there might be Tartuffes of sentiment as well as of religion. Whatever is false in taste is apt to be allied to what is insincere in character.

[595] Biogr. Univ. Dunlop. Bouterwek.

[596] Sermons de Fléchier, ii., 825 (edit. 1690). But probably Bossuet would not have stooped to this allusion.

[597] Biogr. Univ. Mademoiselle de Scuderi was not gifted by nature with beauty, or, as this biographer more bluntly says, étoit d’un extrême laideur. She would, probably, have wished this to have been otherwise, but carried off the matter very well, as appears by her epigram on her own picture by Nanteuil:
Nanteuil, en faisant mon image,
A de son art divin signalé le pouvoir;
Je hais mes yeux dans mon miroir,
Je les aime dans son ouvrage.

Argenis of Barclay. 56. The Argenis of Barclay, a son of the defender of royal authority against republican theories, is a Latin romance, superior to those which the Spanish or French language could boast. It has indeed always been reckoned among political allegories. That the state of France, in the last years of Henry III., is partially shadowed in it, can admit of no doubt; several characters are faintly veiled, either by anagram or Greek translation of their names; but whether to avoid the insipidity of servile allegory, or to excite the reader by perplexity, Barclay has mingled so much of mere fiction with his story, that no attempts at a regular key to the whole work can be successful, nor in fact does the fable of this romance run in any parallel stream with real events. His object seems in great measure to have been the discussion of political questions in feigned dialogue. But though in these we find no want of acuteness or good sense, they have not at present much novelty in our eyes; and though the style is really pleasing, or, as some have judged, excellent,[598] and the incidents not ill contrived, it might be hard to go entirely through a Latin romance of 700 pages, unless, indeed, we had no alternative given but the perusal of the similar works in Spanish or French. The Argenis was published at Rome in 1622; some of the personages introduced by Barclay are his own contemporaries; a proof that he did not intend a strictly historical allegory of the events of the last age. |His Euphormio.| The Euphormio of the same author resembles in some degree the Argenis but, with less of story and character, has a more direct reference to European politics. It contains much political disquisition, and one whole book is employed in a description of the manners and laws of different countries with no disguise of names.

[598] Coleridge has pronounced an ardent, and rather excessive, eulogy on the language of the Argenis, preferring it to that of Livy or Tacitus. Coleridge’s Remains, vol. i., p. 257. I cannot by any means go this length; it has struck me that the Latinity is more that of Petronius Arbiter, but I am not well enough acquainted with this writer to speak confidently. The same observation seems applicable to the Euphormio.

Campanella’s City of the Sun. 57. Campanella gave a loose to his fanciful humour in a fiction, entitled the City of the Sun, published at Frankfort in 1623, in imitation perhaps of the Utopia. The City of the Sun is supposed to stand upon a mountain situated in Ceylon, under the equator. A community of goods and women is established in this republic; the principal magistrate of which is styled Sun, and is elected after a strict examination in all kinds of science. Campanella has brought in so much of his own philosophical system, that we may presume that to have been the object of this romance. The Solars, he tells us, abstained at first from flesh, because they thought it cruel to kill animals. “But afterwards considering that it would be equally cruel to kill plants, which are not less endowed with sensation, so that they must perish by famine, they understood that ignoble things were created for the use of nobler things, and now eat all things without scruple.” Another Latin romance had some celebrity in its day, the Monarchia Solipsorum, a satire on the Jesuits in the fictitious name of Lucius Cornelius Europeus. It has been ascribed to more than one person; the probable author is one Scotti, who had himself belonged to the order.[599] This book did not seem to me in the least interesting; if it is so in any degree, it must be not as mere fiction, but as a revelation of secrets.

[599] Biogr. Univ. arts. Scotti and Inchoffer. Niceron, vols. xxxv. and xxxix.

Few books of fiction in England. 58. It is not so much an extraordinary as an unfortunate deficiency in our own literary annals, that England should have been destitute of the comic romance, or that derived from real life, to a late period; since in fact we may say the same, as has been seen, of France. The picaresque novels of Spain were thought well worthy of translation; but it occurred to no one, or no one had the gift of genius, to shift the scene, and imitate their delineation of native manners. Of how much value would have been a genuine English novel, the mirror of actual life in the various ranks of society, written under Elizabeth or under the Stuarts! We should have seen, if the execution had not been very coarse, and the delineation absolutely confined to low characters, the social habits of our forefathers better than by all our other sources of that knowledge, the plays, the letters, the traditions and anecdotes, the pictures or buildings of the time. Notwithstanding the interest all profess to take in the history of manners, our notions of them are generally meagre and imperfect; and hence, modern works of fiction are but crude and inaccurate designs when they endeavour to represent the living England of two centuries since. Even Scott, who had a fine instinctive perception of truth and nature, and who had read much, does not appear to have seized the genuine tone of conversation, and to have been a little misled by the style of Shakspeare. This is rather elaborate and removed from vulgar use by a sort of archaism in phrase and a pointed turn in the dialogue, adapted to theatrical utterance, but wanting the ease of ordinary speech.

Mundus Alter et Idem of Hall. 59. I can only produce two books by English authors in this first part of the seventeenth century which fall properly under the class of novels or romances; and of these one is written in Latin. This is the Mundus Alter et Idem of Bishop Hall, an imitation of the later and weaker volumes of Rabelais. A country in Terra Australis is divided into four regions, Crapulia, Viraginia, Moronea, and Lavernia. Maps of the whole land and of particular regions are given; and the nature of the satire, not much of which has any especial reference to England, may easily be collected. It is not a very successful effort.

Godwin’s Journey to the Moon. 60. Another prelate, or one who became such, Francis Godwin, was the author of a much more curious story. It is called the Man in the Moon, and relates the journey of one Domingo Gonzalez to that planet. This was written by Godwin, according to Antony Wood, while he was a student at Oxford.[600] By some internal proofs, it must have been later than 1599, and before the death of Elizabeth in 1603. But it was not published till 1638. It was translated into French, and became the model of Cyrano de Bergerac, as he was of Swift. Godwin himself had no prototype, as far as I know, but Lucian. He resembles those writers in the natural and veracious tone of his lays. The fiction is rather ingenious and amusing throughout; but the most remarkable part is the happy conjectures, if we must say no more, of his philosophy. Not only does the writer declare positively for the Copernican system, which was uncommon at that time, but he has surprisingly understood the principle of gravitation, it being distinctly supposed that the earth’s attraction diminishes with the distance. Nor is the following passage less curious. “I must let you understand that the globe of the moon is not altogether destitute of an attractive power; but it is far weaker than that of the earth; as, if a man do but spring upwards with all his force, as dancers do when they show their activity by capering, he shall be able to mount fifty or sixty feet high, and then he is quite beyond all attraction of the moon.” By this device Gonzalez returns from his sojourn in the latter, though it required a more complex device to bring him thither. “The moon,” he observes, “is covered with a sea, except the parts which seem somewhat darker to us, and are dry land.” A contrary hypothesis came afterwards to prevail; but we must not expect everything from our ingenious young student.

[600] Athenæ Oxonienses, vol. ii., col. 558. It is remarkable that Mr. Dunlop has been ignorant of Godwin’s claim to this work, and takes Dominic Gonzalez for the real author. Hist. of Fiction, iii. 394.

Howell’s Dodona’s Grove. 61. Though I can mention nothing else in English which comes exactly within our notions of a romance, we may advert to the Dodona’s Grove of James Howell. This is a strange allegory, without any ingenuity in maintaining the analogy between the outer and inner story, which alone can give a reader any pleasure in allegorical writing. The subject is the state of Europe, especially of England, about 1640, under the guise of animated trees in a forest. The style is like the following:—“The next morning the royal olive sent some prime elms to attend prince Rocolino in quality of officers of state; and a little after he was brought to the royal palace in the same state Elaiana’s kings used to be attended the day of their coronation.” The contrivance is all along so clumsy and unintelligible, the invention so poor and absurd, the story, if story there be, so dull an echo of well-known events, that it is impossible to reckon Dodona’s Grove anything but an entire failure. Howell has no wit, but he has abundance of conceits, flat and common-place enough. With all this he was a man of some sense and observation. His letters are entertaining, but they scarcely deserve consideration in this volume.

Adventures of Baron de Fæneste. 62. It is very possible that some small works belonging to this extensive class have been omitted, which my readers, or myself, on second consideration, might think not unworthy of notice. It is also one so miscellaneous that we might fairly doubt as to some which have a certain claim to be admitted into it. Such are the Adventures of the Baron de Fæneste, by the famous Agrippa d’Aubigné (whose autobiography, by the way, has at least the liveliness of fiction); a singular book written in dialogue, where an imaginary Gascon baron recounts his tales of the camp and the court. He is made to speak a patois not quite easy for us to understand, and not perhaps worth the while; but it seems to contain much that illustrates the state of France about the beginning of the seventeenth century. Much in this book is satirical; and the satire falls on the Catholics, whom Fæneste, a mere foolish gentleman of Gascony, is made to defend against an acute Hugonot.

CHAPTER XXV.

HISTORY OF MATHEMATICAL AND PHYSICAL SCIENCE FROM 1600 TO 1650.

Sect. I.

Invention of logarithms by Napier—New geometry of Kepler and Cavalieri—Algebra—Harriott—Descartes—Astronomy—Kepler—Galileo— Copernican system begins to prevail—Cartesian theory of the world—Mechanical discoveries of Galileo—Descartes—Hydrostatics—Optics.

State of science in 16th century. 1. In the second volume of this work, we have followed the progress of mathematical and physical science down to the close of the sixteenth century. The ancient geometers had done so much in their own province of lines and figures, that little more of importance could be effected, except by new methods extending the limits of the science, or derived from some other source of invention. Algebra had yielded a more abundant harvest to the genius of the sixteenth century; yet something here seemed to be wanting to give that science a character of utility and reference to general truth; nor had the formulæ of letters and radical signs that preceptible beauty which often wins us to delight in geometrical theorems of as little apparent usefulness in their results. Meanwhile, the primary laws, to which all mathematical reasonings, in their relation to physical science, must be accommodated, lay hidden, or were erroneously conceived; and none of these sciences, with the exception of astronomy, were beyond their mere infancy, either as to observation or theory.[601]

[601] In this chapter my obligations to Montucla are so continual that I shall make no single reference to his Histoire des Mathématiques, which must be understood to be my principal authority.

Tediousness of calculations. 2. Astronomy, cultivated in the latter part of the sixteenth century with much industry and success, was repressed, among other more insuperable obstacles, by the laborious calculations it required. The trigonometrical tables of sines, tangents, and secants, if they were to produce any tolerable accuracy in astronomical observation, must be computed to six or seven places of decimals, upon which the regular processes of multiplication and division were perpetually to be employed. The consumption of time, as well as risk of error which this occasioned, was a serious evil to the practical astronomer.

Napier’s invention of logarithms. 3. John Napier, laird of Merchiston, after several attempts to diminish this labour by devices of his invention, was happy enough to discover his famous method of logarithms. This he first published at Edinburgh, in 1614, with the title, Logarithmorum Canonis Descriptio, seu Arithmeticarum Supputationum Mirabilis Abbreviatio. He died in 1618, and in a posthumous edition, entitled Mirifici Logarithmorum Canonis Descriptio, 1618, the method of construction, which had been at first withheld, is given; and the system itself, in consequence perhaps of the suggestion of his friend Briggs, underwent some change.

Their nature. 4. The invention of logarithms is one of the rarest instances of sagacity in the history of mankind; and it has been justly noticed as remarkable, that it issued complete from the mind of its author, and has not received any improvement since his time. It is hardly necessary to say, that logarithms are a series of numbers, arranged in tables parallel to the series of natural numbers, and of such a construction, that by adding the logarithms of two of the latter we obtain the logarithm of their product; by subtracting the logarithm of one number from that of another we obtain that of their quotient. The longest processes therefore of multiplication and division are spared, and reduced to one of mere addition or subtraction.

Property of numbers discovered by Stifelius. 5. It has been supposed that an arithmetical fact, said to be mentioned by Archimedes, and which is certainly pointed out in the work of an early German writer, Michael Stifelius, put Napier in the right course for this invention. It will at least serve to illustrate the principle of logarithms. Stifelius shows that if in a geometrical progression, we add the indices of any terms in the series, we shall obtain the index of the products of those terms. Thus, if we compare the geometrical progression, 1, 2, 4, 8, 16, 32, 64, with the arithmetical one which numbers the powers of the common ratio, namely, 0, 1, 2, 3, 4, 5, 6, we see that by adding two terms of the latter progression, as 2 and 3, to which 4 and 8 correspond in the geometrical series, we obtain 5, to which 32, the product of 4 by 8, corresponds; and the quotient would be obtained in a similar manner. But though this, which becomes self-evident, when algebraical expressions are employed for the terms of a series, seemed at the time rather a curious property of numbers in geometrical progression, it was of little value in facilitating calculation.

Extended to magnitudes. 6. If Napier had simply considered numbers in themselves, as repetitions of unity, which is their only intelligible definition, it does not seem that he could ever have carried this observation upon progressive series any farther. Numerically understood, the terms of a geometrical progression proceed per saltum; and in the series 2, 4, 8, 16, it is as unmeaning to say that 3, 5, 6, 7, 9, in any possible sense, have a place, or can be introduced to any purpose, as that ½, ¼, ⅛, 1/16 or other fractions are true numbers at all.[602] The case, however, is widely different when we use numbers as merely the signs of something capable of continuous increase or decrease of space, of duration, of velocity. These are, for our convenience, divided by arbitrary intervals, to which the numerical unit is made to correspond. But as these intervals are indefinitely divisible, the unit is supposed capable of division into fractional parts, each of them a representation of the ratio which a portion of the interval bears to the whole. And thus also we must see, that as fractions of the unit bear a relation to uniform quantity, so all the integral numbers, which do not enter into the terms of a geometrical progression, correspond to certain portions of variable quantity. If a body falling down an inclined plane acquires a velocity at one point which would carry it through two feet in a second, and at a lower point one which would carry it through four feet in the same time, there must, by the nature of a continually accelerated motion, be some point between these where the velocity might be represented by the number three. Hence, wherever the numbers of a common geometrical series, like 2, 4, 8, 16, represent velocities at certain intervals, the intermediate numbers will represent velocities at intermediate intervals; and thus it may be said that all numbers are terms of a geometrical progression, but one which should always be considered as what it is—a progression of continuous, not discrete quantity, capable of being indicated by number, but not number itself.

[602] Few books of arithmetic, or even algebra, as far as I know, draw the reader’s attention at the outset to this essential distinction between discrete and continuous quantity, which is sure to be overlooked in all their subsequent reasonings. Wallis has done it very well; after stating very clearly that there are no proper numbers but integers he meets the objection, that fractions are called intermediate numbers. Concedo quidem sic responderi posse; concedo etiam numeros quos fractos vocant, sive fractiones, esse quidam uni et nulli quasi intermedios. Sed addo, quod jam transitur εις αλλο γενος. Respondetur enim non de quot, sed de quanto. Pertinet igitur hæc responsio propriè loquendo, non tam ad quantitatem discretam, seu numerum, quam ad continuam; prout hora supponitur esse quid continuum in partes divisibile, quamvis quidem harum partium ad totum ratio numeris exprimatur. Mathesis Universalis, c. 1.

By Napier. 7. It was a necessary consequence, that if all numbers could be treated as terms of a progression, and if their indices could be found like those of an ordinary series, the method of finding products of terms by addition of indices would be universal. The means that Napier adopted for this purpose were surprisingly ingenious; but it would be difficult to make them clear to those who are likely to require it, especially without the use of lines. It may suffice to say that his process was laborious in the highest degree, consisting of the interpolation of 6931472 mean proportionals between 1 and 2, and repeating a similar and still more tedious operation for all prime numbers. The logarithms of other numbers were easily obtained, according to the fundamental principle of the invention, by adding their factors. Logarithms appear to have been so called, because they are the sum of these mean ratios, λογων αριθμος.

Tables of Napier and Briggs. 8. In the original tables of Napier the logarithm of 10 was 3.0225850. In those published afterwards (1618), he changed this for 1.0000000, making of course that of 100, 2.0000000, and so forth. This construction has been followed since; but those of the first method are not wholly neglected; they are called hyperbolical logarithms, from expressing a property of that curve. Napier found a coadjutor well worthy of him in Henry Briggs, professor of geometry at Gresham college. It is uncertain from which of them the change in the form of logarithms proceeded. Briggs, in 1618, published a table of logarithms up to 1,000, calculated by himself. This was followed in 1624 by his greater work, Arithmetica Logarithmica, containing the logarithms of all natural numbers as high as 20,000, and again from 90,000 to 100,000. These are calculated to fourteen places of decimals, thus reducing the error, which strictly speaking, must always exist from the principle of logarithmical construction, to an almost infinitesimal fraction. He had designed to publish a second table, with the logarithms of sines and tangents to the 100th part of a degree. This he left in a considerably advanced state; and it was published by Gellibrand in 1633. Gunter had as early as 1620 given the logarithms of sines and tangents on the sexagesimal scale, as far as seven decimals. Vlacq, a Dutch bookseller, printed in 1628 a translation of Brigg’s Arithmetica Logarithmica, filling up the interval from 20,000 to 90,000 with logarithms calculated to eleven decimals. He published also in 1633 his Trigonometrica Artificialis, the most useful work, perhaps, that had appeared, as it incorporated the labours of Briggs and Gellibrand, but with no great regard to the latter’s fair advantage. Kepler came like a master to the subject; and observing that some foreign mathematicians disliked the theory upon which Napier had explained the nature of logarithms, as not rigidly geometrical, gave one of his own to which they could not object. But it may probably be said that the very novelty to which the disciples of the ancient geometry were averse, the introduction of the notion of velocity into mathematical reasoning, was that which linked the abstract science of quantity with nature, and prepared the way for that expansive theory of infinites which bears at once upon the subtlest truths that can exercise the understanding, and the most evident that can fall under the senses.

Kepler’s new geometry. 9. It was, indeed, at this time that the modern geometry, which, if it deviates something from the clearness and precision of the ancient, has incomparably the advantage over it in its reach of application, took its rise. Kepler was the man that led the way. He published, in 1615, his Nova Stereometria Doliorum, a treatise on the capacity of casks. In this he considers the various solids which may be formed by the revolution of a segment of a conic section round a line which is not its axis, a condition not unfrequent in the form of a cask. Many of the problems which he starts he is unable to solve. But what is most remarkable in this treatise is that he here suggests the bold idea, that a circle may be deemed to be composed of an infinite number of triangles, having their bases in the circumference, and their common apex in the centre; a cone, in like manner, of infinite pyramids, and a cylinder of infinite prisms.[603] The ancients had shown, as is well known, that a polygon inscribed in a circle, and another described about it, may, by continual bisection of their sides, be made to approach nearer to each other than any assignable differences. The circle itself lay, of course, between them. Euclid contents himself with saying that the circle is greater than any polygon that can be inscribed in it, and less than any polygon that can be described about it. The method by which they approximated to the curve space by continual increase or diminution of the rectilineal figure was called exhaustion, and the space itself is properly called by later geometers the limit. As curvilineal and rectilineal spaces cannot possibly be compared by means of superposition, or by showing that their several constituent portions could be made to coincide, it had long been acknowledged impossible by the best geometers to quadrate by a direct process any curve surface. But Archimedes had found, as to the parabola, that there was a rectilineal space, of which he could indirectly demonstrate that it was equal, that is, could not be unequal, to the curve itself.

[603] Fabroni, Vitæ Italorum, i., 272.

Its difference from the ancient. 10. In this state of the general problem, the ancient methods of indefinite approximation having prepared the way, Kepler came to his solution of questions which regarded the capacity of vessels. According to Fabroni, he supposed solids to consist of an infinite number of surfaces, surfaces of an infinity of lines, lines of infinite points.[604] If this be strictly true, he must have left little, in point of invention, for Cavalieri. So long as geometry is employed as a method of logic, an exercise of the understanding on those modifications of quantity which the imagination cannot grasp, such as points, lines, infinites, it must appear almost an offensive absurdity to speak of a circle as a polygon with an infinite number of sides. But when it becomes the handmaid of practical art, or even of physical science, there can be no other objection, than always arises from incongruity and incorrectness of language. It has been found possible to avoid the expressions attributed to Kepler; but they seem to denote in fact nothing more than those of Euclid or Archimedes; that the difference between a magnitude and its limit may be regularly diminished, till, without strictly vanishing, it becomes less than any assignable quantity, and may consequently be disregarded in reasoning upon actual bodies.