side

Again, in the two triangles AG C, B G C, because side A G = GB, and side G C is common; also base A C = base CB; therefore, by Euclid I. 4, included angle A & C = included angle BG C. But these are adjacent angles which the straight line c G makes by standing on the straight line A B. Therefore, by Def. 10, each of them is a right angle. (7) This gives us at once the results of Props. IX., X., XI., and XII. of Book I.

PROPOSITION II.--In the figure of Euclid I. 2 (Fig. 2), required to draw from D a straight line D M N, cutting the circles in м and N, such that M N, the part intercepted between them, may be equal to A L or B C.

K

H

M

N

Suppose D M N to be thus drawn, then DN, DL, being radii of the same circle, will be equal; but MN, by the supposition, is equal to AL; and, by Axiom 3, if equals be taken from equals the remainders are equal. Therefore, if MN, AL be taken from DN, DL, the remainders D M, DA will be equal. Hence, if from D, as centre, we describe a circle, with DA as radius, cutting the small circle in м and joining DM, produce it to meet the large circle in N, D M N will be the line required; for, since DA, DM are radii of the same circle, DA DM (Def, 15); and, since DL, DN are radii of the same circle, DL DN. Therefore, by Axiom 3, if DA, DM are taken from DL and D N, the remainders A L, M N will be equal; that is, the part of DN intercepted between the circles will be equal to AL, and therefore equal also to B C. Q. E. F.

Fig. 2.

Corollary.-It is obvious that there will be certain limits beyond which the problem will be impossible. This will be the case when the circle described with centre D and radius DA does not cut the smaller circle. When it touches the smaller circle, there will be only one possible position for D M N, that of passing through the point of contact. When it cuts there will be two positions, as indicated in the figure by the dotted line. PROPOSITION III.-On a given base AB (Fig. 3), to describe an isosceles triangle A B C, such that each of the sides

с

A

B

Fig. 3.

A C, BC may be four times the base A B.

Produce A B both ways indefinitely to E and F, E and from BE, the greater in the side remote from A, cut off BG equal to three times BA (I. 3), and from AF on the side remote from B cut off A H equal to three times A B (I. 3), then A G will be equal to four times A B, and в H will be equal to four times B A. From centre B, at distance в H, describe a circle (Post. 3), and from centre A, at distance A &, describe another circle, and let these two circles cut in c. Join A C, B C, then A B C shall be the

triangle required. For since A C, A G are radii of the same circle, AC AG; but A G = 4 A B, therefore a C = 4 A B. Similarly BCBH 4 A B; therefore A C B c, and the triangle ABC is isosceles, and each of its sides equal to four times the base. Q. E. F.

PROPOSITION IV.-If A B C (Fig. 4) be an isosceles triangle, vertex A, and two points H, K be taken in the sides A B, A C, such that A H= AK, and if B K, CH meet in F, then AF bisects the angle B A C.

C

For in the triangles C A H, B A K, since A CA B, and AHA K, also the included angle C A B is common to the two triangles, therefore the base B K is equal to the base c H (I. 8). Again, in the triangles AC H, A B K, because A C is equal to A B and CH to BK, and also the base A H to the base A K, therefore the included angle ACH is equal to the included angle A B K (I. 4). But the whole angle ACB= whole A B C (I. 5), and, by Axiom 3, if equals be taken from equals the remainders are equal; therefore if ACH, ABK be taken from AC B, A B C, the remainders FC B, FBC will be equal, and consequently the side Fc side FB (I. 6). Then, in the two triangles CA F, BAF, because AC A B and A F is common, also base FC base FB, therefore also included angle F A C is equal to included angle FA B, that is, A F bisects the angle B A C. Q. E. D.

A

H

Fig. 4.

=

PROPOSITION V.—If A, B (Fig. 5) be two points on opposite sides of a line CD, required to find in C D a point E, such that the angle A E C may equal the angle B E C.

By means of Prop. I. we may draw A F perpendicular to CD. Produce AF to G (Post. 2), and make F G FA (I. 3). Join GB, and produce it to cut C D in E, then E is the point required. Join A E. Then, since AF FG, and FE is common to the two triangles A F E, G F E, also the included right angle A F E is equal to the included right angle G F E, therefore the base A E is equal to the base G E (I. 4). Again, because A EEG, and FE is common, also base AF= base FG, therefore in- ccluded angle A E F included angle GEF (I. 8), therefore C D bisects the angle A E B. Q. E. F.

In the present paper we have used Book I. 1-8. In our next paper we shall use Book I. 1-16, and give solutions of the following propositions :

B

Fig. 5.

PROPOSITION VI.-In the figure of Euc. I. 5, if a o at right angles to A G cut A H produced in o, H being the intersection of BG, FC, then oF shall be perpendicular to a F.

PROPOSITION VII.-If A c, the side of an isosceles triangle A B C, be bisected in D, and BD produced to E, so that DE= D B, then if A E be joined, the angle A E D shall be equal to the angle DBC.

PROPOSITION VIII.-If A B be two points on the same side of a given line CD, find in CD a point E, such that the angle AEC may be equal to the angle B E D.

PROPOSITION IX.-Given two straight lines A B, A C, intersecting in A, and another straight line D of limited length: required to form a right-angled triangle of which the base shall coincide with A C, one side shall coincide with A B, and the other side be equal to D.

PROPOSITION X.-In an isosceles triangle A B C, if AL be drawn from vertex A perpendicular to the base B C, and if AL be produced to м so that L M = LA, then shall BL be equal to

LESSONS IN ENGLISH LITERATURE.-I.

INTRODUCTION.

THE literature of England is a collection of works of art, each one of which may be studied separately, for the sake of its individual excellence, without regard to its connection with the rest, or the circumstances of its production. Such a study will develop the taste and judgment, and give pleasure in proportion to the capacity of the student; and it requires only diligence in reading, and sufficient discernment to appreciate what is read. All that a teacher can do to assist it, is to point out what are the works best worthy of study, and to call attention to some of their more prominent beauties. This service we hope to render to such students in the course of the following lessons, so far as our space permits us.

But those who would g: in the full benefit of the study of English literature must re rd it from a wider point of view. The literature of a country is one of the most instructive parts of its history. Every thoughtful student of history seeks to know not only what men have done, but what they have thought and felt. He seeks to know not merely the great external events of the period he is studying-the wars, the revolutions, the religious controversies, the social struggles-but also the motives which influenced men, the extent of their knowledge, their standard of right and wrong, their likes and dislikes: in short, he wishes to know not men's acts only, but men ; and for this he must look chiefly to the literature they have left behind them. Every student of English literature, then, ought to endeavour, in all that he reads, to read not only beautiful poetry or eloquent prose, but history as well.

It is not merely that he will find historical facts embedded in what he reads, which he might not meet with elsewhere, though this is true. He will also find such facts related often by eyewitnesses, and therefore with all that freshness and vividness of description which stimulates the imagination and impresses the memory. He will, moreover, be able to observe for himself, and at first hand, what effect was produced upon men's minds at the time by the great events of history with which he is familiar. All these things are of importance. But the connection between national history and a national literature lies much deeper still; and it is of the utmost importance that every student of literature should at the outset clearly realise it. Every one must observe that literature in England has not been like a river flowing on in a steady and unbroken course; but has ebbed and flowed like the tide, though without the regularity of the tide. In the days of Edward III., at the close of the fourteenth century, there was produced a great mass of literature, of which Chaucer's poems are the most important examples. For a century afterwards there is almost a total blank. Then began gradually the revival, which culminated in the days of Elizabeth and James I. in an amount of literary life such as has never been seen in England before or since the age of Shakespeare and the great dramatists, of Spenser and the countless contemporary poets. And the same alternation of activity and depression is to be seen throughout the whole history of our literature. But what it is important for the student to observe is, that these changes are not isolated or meaningless events. Literary activity is only one of the many forms in which an increased mental energy exhibits itself, and a period fertile in great books is sure to be a period fertile in great deeds and great changes. Thus the age which produced the poetry of Chaucer was the same in which the feudal organisation of society was broken up, the same in which the national spirit and vigour of England displayed itself in the French conquests of Edward III., the victories of Cressy and Poitiers; and the same in which Wycliffe led the first great religious reforma tion in England, the first rebellion against the superstitions of the dark ages and the corruptions of the clergy. The century of literary dearth that followed was a century of national depression, in which the country was desolated by the Wars of the Roses. The Elizabethan era, so rich in literary genius, was also the era of the revival of classical learning, of the Reformation, of the Spanish wars and the defeat of the Armada, of the voyages of Drake and the other great navigators, and of the first colonisation of America.

But not only is the amount of literary genius shown at different times seen to be very different; the character and spirit of the works produced varies not less, and this diversity is no less

VOL. IV.

closely connected with the history of the times. Thus the same exuberance of life and energy, seeking a vent for itself in every direction, which in the days of Elizabeth and her successor sent English sailors and adventurers about the world, discovering strange lands, fighting-half as lawful warriors, half as pirates -on the Spanish main, or colonising Virginia, is apparent in all the Elizabethan dramatists, and above all in Shakespeare. Their characteristics are activity of invention, freedom, and variety. And the same patriotic pride and unity of national spirit which was shown when the Armada threatened our shores is prominent in the literature of the period. It is the very keynote of at least one of Shakespeare's plays, "Henry V." But the next generation of Englishmen lived in a very different world. England was no longer a united nation. The kingCharles I.—and his people have been alienated from one another, the liberties of the nation are at stake, the civil war ensues; and the political contest is intensified and embittered by the religious differences which are so closely connected with it. The day is one in which every man is compelled to choose his side in a contest of surpassing importance; and men do choose their sides, and maintain them with rare earnestness and fidelity. And how does this change of spirit in men show itself in literature? The representative of the literature of the age is Milton. Milton in power of genius falls behind none of the Elizabethan poets, except Shakespeare himself; but in tone and spirit his works stand in the strongest contrast to theirs. Seriousness of spirit, earnestness of purpose, and an intense realisation of the presence of the unseen, are the characteristics of everything he has left us. Nor is the change less instructive in the next generation. The Commonwealth was followed by the Restoration. The cavalier party became in the ascendant. A natural reaction against the austerity of puritanism, combined with the evil example of a licentious court, introduced a tone of morality lower than anything that had ever been known in England before; and this is immediately reproduced in the literature of the day. Dryden and the series of comedians whom we shall have to describe hereafter are its chief representatives; and they stand in the most marked contrast to the writers of the previous generation, in the entire absence of any seriousness or earnestness of purpose, and in their low moral tone.

Nor is it only the changes and movements taking place within our own country, which we may see thus faithfully reflected in the literature of each age. The study of literature enlarges our view and enables us to watch the influence which one nation has exercised upon another, either by means of its living thinkers and writers, or by its older literature. Thus we all read, as matter of history, that at the time of the first great harvest of English literature, in the time of Edward III., the chief impulse to literary activity both in England and elsewhere was derived from Italy; for in Italy had but shortly before been produced the great works of Dante, Boccaccio, and Petrarch. But the extent of this influence can only be appreciated by reading Chaucer's poems, and observing how he-one of the most original of poets-is indebted for his stories, his metres, and to a large extent his style, to his Italian models. This our readers will see more fully when we come to treat of Chaucer's poems in detail. In the same way we read, as matter of history, of the great effect produced in England, as elsewhere, during the Elizabethan era, by the revived knowledge of classical literature, through study of the originals by the few, through the medium of translations with the many. But there is no way in which this influence can be more fully realised than by observing how a man like Shakespeare, who had "small Latin and less Greek," shows in his works that he was affected by it. Play after play, as “Julius Cæsar” and “Antony and Cleopatra,” is taken from classical sources; and in each he shows not only that he can follow the narrative as he read it, probably in translation, but that he had largely entered into the spirit of the time.

We have said enough to show that the student of English literature has the opportunity of reading English history in the fullest, best, and most reliable way, for he is enabled to get a step nearer to the men with whose history he is dealing than he can do by any other method. But the advantage of keeping the connection between literature and history always in view is not entirely on the side of history. We have said that the various books which go to make up the total of English literature may be studied as isolated works of art, and may be so

82

studied with both pleasure and profit. No man, for instance, could read "Hamlet" without enjoyment, whether he knows anything of Shakespeare and his times or not. But the pleasure we receive and the benefit we derive from a great work is in proportion as we understand the author's meaning; and we understand his meaning in proportion as we are able by an effort of imagination to place ourselves in his position, to see things as he saw them, and judge them as he judged them. And we shall be able to do this to a very small extent indeed if we are not fully acquainted with the circumstances under which he wrote and the influences by which he was surrounded. For all reasons, therefore, we would impress upon our readers the importance, when reading any English author, of doing so with as full a knowledge as they can obtain of his character, his history, and his times.

But in order that English literature may be studied in the manner and from the point of view which we advise, it is necessary that the student, when he enters upon the study of any work, should have the means of at once assigning to it its proper place in the catalogue of literature. This he cannot do without having the history of our literature, at least in its broader features, mapped out in his mind, knowing the sequence of the great writers, and their connection with one another, and the characteristics of each literary period. Such a knowledge is the more easily attained, because our literature easily and naturally divides itself into several well-marked periods, corresponding very closely to the most important stages in our political history. And the object of the following lessons will be to enable students of English literature to acquire this know ledge, so necessary for a thoroughly useful system of reading, as well as to direct their choice of books to read, and give them such assistance as may be possible in understanding and appreciating what they read.

In laying out the outline of a history of English literature, the first thing to be determined is the point from which to date its commencement. And as to this there is, we think, little room for hesitation. English literature, for the purposes of the student, begins with the age of Chaucer, the latter half of the fourteenth century, the reign of Edward III. Before that time there had been many works written in England, and in different languages, but it could not be said that there was any literature addressing itself to the whole people of England, or written in a language which was that of the whole people.

The population of England, as our readers are well aware, had been recruited from many sources. The oldest inhabitants of the island of whom history gives us any account were of Celtic blood, akin to the Celts of Ireland and the Highlanders of Scotland, but much more nearly akin to those now of Wales and Cornwall. They fell under the yoke of the Roman empire, and for five hundred years Roman institutions and Roman civilisation prevailed in the country. The Romans abandoned their occupation of Britain in the middle of the fifth century, but they did not leave the Britons to the enjoyment of peace or security. Immediately after, if not before, the departure of the Romans a dangerous friend, soon to become a formidable enemy, had appeared on the coasts of Britain. The Saxons, a people from the banks of the Elbe and the shores of the German Ocean, had commenced their long series of invasions. The history of the struggle between the Saxons and the Britons is lost in obscurity, but it ended in the complete subjugation of Britain under the Saxon dominion; and some form of their language-a language of the German stock, and the parent of our modern English-has ever since been the language of the great bulk of the inhabitants of this island. The Danes were the next invaders; but though they established their dominion for long, and although their tongue no doubt materially modified the dialect of those parts of England with which they had most to do, the language of the country remained substantially unchanged; and it may be said that at the date of the Norman conquest, with the exception of the Celtic-speaking districts, which we need not here consider, the language of England was one, and that was Anglo-Saxon.

But the Norman conquest brought a great change. The Normans, or Northmen, who invaded and conquered England under William of Normandy, were a Scandinavian race, nearly akin to the Danes; but during their long abode in the province of Normandy they had abandoned their original tongue, and adopted the French language, the language of those they had vanquished; and French was the language which they carried

with them into England. From this time onward there were two spoken languages in England, the Norman-French of the court and the feudal castles, and the Saxon of the mass of the people. Each of these languages had its writers, books intended for the nobles being written for the most part in French, those intended for the people in Saxon. But there was also a third kind of literature in this country. In the monasteries, which were scattered over all parts of the country, chroniclers and religious writers used Latin as their literary tongue.

We have spoken of the Saxon tongue as the parent of our modern English, and we have just spoken of the Saxon literature which preceded the period at which the history of English literature properly begins. And it may therefore be asked why we arbitrarily select a particular point of time after which we say the literature was English, while what went before was not? In answer to this, we say that we do not draw the line at the point at which we have drawn it or the ground of any sudden or marked change in the language, though the language did undergo much modification at the very period in question; but for the reason we have given above, that the Saxon or English literature before Chaucer's day was not the literature of the whole English nation, but of the English-speaking portion of the nation: in his time it became that of the nation. The changes by which the language of the first Saxon invaders has in the course of centuries been transformed into the English of our day have been very gradual; and there is no one point of time at which it can be said that Anglo-Saxon became English. But in order to the better understanding of what we shall have to say in future lessons, it is well that our readers should be acquainted with the several stages into which the progress of the language is divided by most modern scholars. It must be remembered, however, that these divisions are not always very clearly marked, and are not given in quite the same way by all the authorities. The language is said to be AngloSaxon down to the middle of the twelfth century. The name of Semi-Saxon is given to it for the next hundred years, down to the middle of the thirteenth century. From that time until the latter end of the fourteenth century it is called Old English. Then the name of Middle English is applied to the English in use down to the reign of Elizabeth. And after that period the language is said to be Modern English.

In our next lesson we shall give a brief account of the remains which have come down to us of those various forms of literature-Saxon, French, and Latin-previous to the date at which we commence the history of English literature proper.

But by the days of Edward III. the English language had completely supplanted, while it partly absorbed, the French of the Norman nobles, and had become the language of the whole nation. And that period, the age of Chaucer, is our first period in the history of English literature.

The second period extends from the death of Chaucer over & space of about a hundred years, down to the time of the first revival of literary energy under the Tudor sovereigns.

The third period extends from the first revival of literature, at the period we have mentioned, through the reigns of Elizabeth and James I., and includes within it the most brilliant portion of our literary history.

The fourth period is that which includes the reign of Charles L, the Civil War, and the Commonwealth.

The fifth period is that of the Restoration, beginning with that event, and extending down to the Revolution of 1688.

The sixth period extends from the Revolution, through the reign of Queen Anne and the earlier portion of those of the Georgee, and includes what has been habitually called the Augustan age of English literature, or the age of the correct school.

The seventh period is that which is intermediate between the last-mentioned and the great revival of romantic literature at the end of the eighteenth century.

The eighth period is that of the revival of the romantic school of literature, which began in the reign of George III, under the impulse of the same intellectual movement which immediately preceded the great French Revolution, the period to which belong Scott, Byron, and Shelley, and which may be said scarcely yet to have come to an end.

In the following course of lessons we shall treat of these periods in order, and of the principal writers belonging to each of them, examining as fully as we can the most important works of these writers.