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LESSONS IN ARCHITECTURE.—XII. they may cross each other, which gives us the form of a pointed
arch; and the same being done throughout the whole extent of GOTHIC ARCHITECTURE.
the two opposite rowe, an horizontal rod, or ridge bar, being In our last lesson we spoke of the rise, decline, and fall of at the same time placed along the points of crossing, wa Gothic architecture. Its origin, like that of some other styles, I have the appearance of a Gothic arcade. Two rods from each has not been so correctly ascertained as
post in the same row are now to be to render its historical details of much
treated in like manner, so as to form interest. It is certain that it began to
similar arches in both rows, and these be employed in ecclesiastical edifices
are also to be connected by ridge bars about the time that the Goths were
crossing the longitudinal one. Having settled in Italy, and had been overcome,
now employed two rods of each corner in their turn, by the nations which super
post, and three of each intermediate seded the Romans. This system of
one, there still remain one in the former, architecture, as we have already said,
and two in the latter, which may be diskas practised during the Middle Ages,
posed of by causing them to pass diagoand continued in use till the sixteenth
nally from the corners of each rectangle, century, when it was supplanted by the
not crossing as in the former cases, but revival of the Roman style. It was then
applied side by side, so as to form a concalled Gothic from the architects and
tinued hoop or semicircle. In this man. workmen who were supposed to bave
ner all tho rods are occupied, and a frame been engaged in the planning and erect.
is produced capable of supporting thatch ing the edifices which bear this name;
or other covering. From the imitation and it was held in contempt by the fol
of a dwelling so constructed the threo lowers of Palladio, in Italy, and of Jones,
leatling characters of Gothic architecture in England. The Gothic architecture
may be traced, namely, the pointed arch, differs essentially from the Greek, both
the clustered column, and the branching in construction and appearance. In the
roof. On principles similar to these tho latter the arrangement of the materials CHURCH OF ST. ETIENNE DU MONT, PARIS. ingenious author endeavours to account depended on their strength in masses,
for the peculiarities of the Gothic winwhich required only to be put together, dows, doors, spires, etc. But it is much to be doubted whether in simple and elegant forms. In the any theory so simple and ingenious as the preceding will account former, on the contrary, small stones and for the origin of a style which emanated from the numerous and other materials, which would have been varied applications of the deemed useless by a Greek architect, arch, whether semi-circular or were employed in the construction of edi- pointed, whether composed of fices of equal strength, and sometimes segments of circles crossing even of greater magnificence than the each other, or of other curves ancient temples; for they depended as to corresponding to Hogart!'s their stability, not on the vertical pres- celebrated line of beauty, sure of columns, or the strength of lintels which was evidently traced from pillar to pillar, but on the correct by him in the ogee or cyma adjustment of the bearings and thrusts (Greek xuua, ku'-ma, a wave)
of different arches operating in various of the ancient Greek and Set directions. Moreover, the Gothic style Roman architecture, as well WINDOW OF 15TH CENTURY.
is easily distinguished from both the as in the Gothic. This curve WINDOW or 13TH CEN. Greek and the Roman styles by its slen is in the form of the letter S without its top and bottom apTURY.
der shafts and clustered pillars, its circu. 'pendages, thus ,
lar, pointed, or angular arches and groins, . In the churches of the Middle Ages, there were to be seen, its spires and pinnacles, and its decorations,
as indicated in the preceding theory, endless which excel the latter in variety, number,
groups of small columns, immense domes, and minuteness.
complicated buttresses, lofty roofs, with bell Among the theories which have been pro
turrets, and other appurtenances. The finest posed to account for the origin of this style,
examples in Europe of the Gothic, or ogival we may mention an ingenious one which has
style of architecture, are the great catheheen suggested by Sir James Hall, in his
drals of Notre-Dame at Paris, Bourges, " Essay on the Origin, Principles, and His
Amiens, Chartres, Rouen, and Rheims. This tory of Gothic Architecture." He conceives
style, as we have observed, at first pure and that the forms of this style may have been
simple, and formed of regular curves, bederived from the imitation of a rustic dwell.
came so distorted at the close of the short ing, constructed in the following manner :
period of its existence, as to lose its very Thrust two rows of posts into the ground
nature, and it then led to the invention of opposite to each other, at an interval equal
all the extravagant productions which arose to that between the posts in the rows them
from compound arches, which were only a selves, cach post rising to the height of
degradation of the original style, and which about three intervals. Apply to each post a
soon caused its abandonment. It would be eet of slender rods of willow, thrusting them
impossible to exhibit, in diagrams, the ininto the ground at its base, and tying them
numerable details in architecture and of in two places, one a little above the ground,
sculpture which the beautiful edifices of the and the other within about a third part of
Middle Ages present, all characterised by the the height, leaving them loose from this
use of the pointed arch. We give, however, point upwards, so that they may be freely
two specimens of the rich ornamentation wed in any direction. The rods may be three
which crowded the wirdows and capitals in bomber to each of the outside corner CATHEDRAL OF NOTRE DAME, PAEIS.
of the columns in the Gothic churches of posts, and five to each of the others, all being
the thirteenth and fifteenth centuries. In placed so as to cover the inside of the posts, and give it the the sixteenth century, the Greek and Roman arts and architecappearance of a bundle of rods. It will be easy now to form ture returned, but only by such a gradual transition, that for a the skeleton of a thatched roof. For this purpose let a rod length of time the pointed arch was employed in the construction from each of two opposite posts be bent at its loose top, so that of domes, and of some other important parts of the edifice, of
which the churches of St. Eustache, and of St. Étienne du Mont, Qu'est-ce que l'Italie ?
What is Italy? at Paris, are examples. In castles built at this period of the Qu'est-ce que le jardinage ?
What is gardening? Renaissance, such as those of Écouen and of Gaillon, the chapel
3. Que is used idiomatically in a number of sentences. In was Gothic, whilst the rest was classical. The ancient archi- the following it gives greater force to the expression :tecture has extended its power over the civilised world, from the Cesont de bons livres que les vôtres, Yours are indeed good books. Renaissance period to the middle part of the present century, Je dis que oui; je crois que non, I say yes; I believo not. when a reaction took place in favour of the Gothic style of architecture, especially for ecclesiastical buildings.
RÉSUME OF EXAMPLES. The severe study of the monuments of Greece and Italy in Qui sont ces messieurs qui parlent Who are those gentlemen who speak modern times, tends to preserve and extend the taste for the
à M. L.?
to Mr. L.? ancient orders of architecture, as being more durable in their ce sont mes cousins, qui viennent They are my cousins, who are just effects, more easy in their construction, and more economical De quel pays sont ces marchands ? Of orhat country are those merchants ?
arrived, in their expenditure, than the Gothic style. The recent desire Ce sont des Polonais ; ils viennent They are Poles; they are just arto restore the architectural monuments of the Gothic period,
d'arriver. has led to an extraordinary study of its ancient examples, and Ils ne sont pas Polonais ; ils sont They are not Poles'; they are Rrehas produced in some enthusiastic minds a wish to substitute Russes.
sians. this style of architecture for those which have regulated the ce ne sont pas des Polonais; ce They are not Poles; they are Ruesplendid edifices of Europe for three centuries. Without sont des Russes
sians. attempting to depreciate a style which is consitlered particularly Qu'est-ce que la Touraine ? What is Touraine ?
It is the garden of France. adapted to religious edifices, it is difficult to imagine that it will c'est le jardin de la France. prevail, for any lengthened period, over those orders of architec- Votre fenêtre no donne-t-elle pas does not your window look on the ture which, by their strength and solidity as well as massive Non, c'est sur la cour qu'elle donne. No, it looks on the yard. elegance, far surpass their resuscitated rival.
Je crois que oui; je crois que ron. I believe 80; I believe not, In one of the annexed engravings, the reader will find a representation of one of the finest examples of the true Gothic
VOCABULARY. style of architecture already mentioned, viz., the Church of Notre- Bris-er, 1, to break. Ecossais,-e, Scotch. Soieries,f.pl.,silk stufs. Dame, at Paris. This metropolitan church of the French capital Charron, m., wheels Etranger, -e, foreign. Sucre, m., sugar. is said to have been built on the ruins of a heathen temple, and
Fenêtre, f., window. Suisse, Suiss. to have been founded during the first ages of Christianity. Its Confitures, f. pl., pre- Lyon, Lyons. (chief. Surprend-re, 4, ir., to reconstruction was begun by Maurice Sully, in 1163, and the Donn-er, 1, to give, look. Roue, f., wheel.
Mouchoir, m., handker. catch, surprise.
Vol-er, 1, to steal. first stone was laid by Pope Alexander III. Jean de Chilles, master of works, undertook the south front in 1257; the north
EXERCISE 157. front was constructed in 1312, by means raised by the knight 1. Connaissez-vous ces étrangers ? 2. Oui, Monsieur, ce sont templars. Charles VII., in 1447, gave considerable sums for the les frères de notre voisin. 3. Ne sont-ils pas Écossais ? 4. Non, completion of this cathedral. The first stone of the great altar Monsieur, ils sont Suisses. 5. Ne sont-ce point des Écossais was laid in 1669, by Cardinal Noailles; and the choir, then begun qui vous ont fait présent de cette casquette ? 6. Non, Monsieur, from the designs of Mansarde, was only finished in 1714. The ce sont des Suisses. 7. N'est-ce pas votre domestique qui vous celebrated bell of Notre-Dame, the largest in France, is placed a volé du vin ? 8. Ce n'est pas lui, c'est son frère. 9. N'est-ce in the south tower; it was founded in 1685, and set up by pas lui qui a pris vos confitures ? 10. Ce n'est pas lui; ce sont Louis XIV. The cathedral was restored during the reign of ses enfants. 11. Ne sont-ce pas là les enfants que vous avez Napoleon III., the massive iron railing by which it is sur- surpris à voler votre sucre ? 12. Ce sont leurs frères. 13. Ne rounded being completed in 1868,
sont-ils pas cousins ? 14. Ils ne sont pas cousins ; ils sont In this lesson is also given a representation of one of the frères. 15. Qu'est-ce que ces soieries ? 16. Ce sont des finest examples of those churches which belong to the transi- marchandises qu'on vient de nous envoyer. 17. N'est-ce pas tion period mentioned above, namely, the Church of St. Etienne une belle ville que Lyon P 18. C'est une grande et belle ville. du Mont. This church was known by the same name in 1221. 19. N'est-ce pas là le mouchoir que vous avez perdu? 20. Je It was reconstructed about 1517; but the aisle and the south crois que oui. 21. N'est-ce pas sur le jardin que donnent vos chapel were built in 1588. The western parts were only finished fenêtres ? 22. Oui, Monsieur, c'est sur le jardin qu'elles donunder Charles IX. The communion chapel was built in 1606, nent. 23. N'est-ce pas notre charron qui a fait cette roue and Margaret of Valois, first wife of Henri IV., laid the first 24. Ce n'est pas lui qui l'a faite. 25. Ce sont nos amis qui l'ont stone of the front. These circumstances explain the mixture brisée, et c'est le menuisier qui l'a faite. of the Gothic style with that of the Renaissance which is found in this church. It is the only church in Papis furnished
EXERCISE 158. with a gallery; and is decorated with very remarkable windows, 1. Is that lady your friend's sister ? 2. No, Sir, she is a the work of Pinagrier, a celebrated artist of the sixteenth stranger. 3. Who are the two gentlemen who are speaking to century
your sister ? 4. They are Swiss gentlemen. 5. Are those the gentlemen whom you have invited ? 6. It is they (eu). 7.
Do you not know that man? 8. I know him very well; he is LESSONS IN FRENCH.-XLII.
the man who has stolen my wine. 9. What is Italy? 10. It SECTION LXXXI.-IDIOMS RELATING TO THE PRONOUNS is the garden of Europe. 11. Is not that the letter which you CE AND QUE.
intended to carry to the post-office? 12. No, Sir, it is another. 1. The pronoun ce (and not the pronouns il, elle, etc.) must 13. Is the city of Havre fine ? 14. Yes, Sir, Havre is truly a be used for he, she, they, coming before the verb to be, when large and beautiful city. 15. Is not that the man whom you that verb is followed by a noun, or an adjective used substan. have caught stealing your fruit? 16. It is not, it is another. tively, preceded by the, d, or an, by some or any understood, or
17. Is not this the cup that you have bought? 18. Yes, Sir, I
believe so. 19. Do not the windows of your room look on the by a possessive or demonstrative adjective. When the word used
street ? 20. No, Madam, they look on the garden. 21. Do n apposition with ce is plural, and in the third person, the verb is put in the plural, although ce remains unchanged not the windows of your dining-room look on the yard (cour) ? [$ 108 (2) (3)]:
22. No, Sir, they look on the lake (lac). 23. Is it that little
child who has taken your preserves ? 24. It is his brother and C'est un Polonais, He is a Pole.
sister. 25. What are those engravings? 26. They are engravCe sont des Anglais,
They are Englishmen. C'est cette dame qui m'a parlé de It is that lady who spoke to me of Scotch? 28. They are not Scotch; they are Italian. 29. Are
ings which I bought in Germany. 27. Are those gentlemen vous,
those ladies Scotch? 30. No; they are the Italian ladies who 2. Ce is used as the nominative of the verb être, in sentences came yesterday. 31. What is Marseilles ? 32. It is one of the like the following, and the conjunction que is used idiomatically finest cities in (de) France. 33. Is it not your tailor who made after it. The verb in this case is not put in the plural : that coat? 34. It is not he; it is an English tailor who made Qu'est-ce que ces enfants ? What are those children ?
it. 35. It is your friend who broke my watch.
SECTION LXXXII.-GOVERNMENT OF VERBS, ETC. vos marchandises à perte. 24. Vous et moi nous vendons tou1. In French, as in other languages, when a verb has two jours à profit. 25. Votre père, votre frère et moi, nous avons subjects in the singular, it is generally put in the plural acheté des marchandises. [$ 114 (2)]:
EXERCISE 160. L'oncle et la tante sont arrivés, The uncle and aunt are arrived. 1. Do we incommode you, my brother and I? 2. No, Sir; Votre frère et votre seur sont-ils Are your brother and sister gone ? you do not incommode us; we are very glad to see you. 3. Are partis ?
you not afraid to disturb your friend ? 4. We are afraid to 2. When a verb has two or more subjects of different persons, disturb him; he has much to do. 5. Is my foot in your way, it is put in the plural, and assumes the termination of the first Sir? 6. No, Sir; your foot is not in my way. 7. Will you and person rather than that of the second or third, and the termi- your brother go to Germany this year? 8. We intend to go nation of the second in preference to that of the third :
there, he and I. 9. He, you, and I, should write our lessons. Vous et moi irons demain à la You and I will go hunting to-mor. 10. Shonld you not, you and your friends, adapt yourselves to chasse,
circumstances ? 11. We should do so, if it were possible. 12. Vous et lui irez demain à l'école, You and he will go to school to- Do I not disturb you, Sir? 13. You do not disturb me by any
means. 14. Does not my little boy disturb you? 15. He does Sa mère et moi nous avons écrit His mother and I have written that not disturb me. 16. He disturbs nobody. 17. Does not your cette lettre,
partner sell his goods at a loss? 18. He never sells at a loss. 3. The above examples will show that, when a verb haz 19. He and I always sell at a profit. 20. Do you persist in several subjects, all of them pronouns, or partly pronouns and your resolution ? 21. Your friend and I persist in our reso.
23. artly nouns, the words moi, toi, lui, eux, are used instead of lution. 22. I never feel under constraint at your house. je, ta, il, ils. A pronoun recapitulating the others may, as
Be under no constraint (make yourself at home). 24. Are you in the last example, be placed immediately before the verb not wrong to incommode them? 25. I do not intend to incom[$ 33 (10) (11)]
mode them. 26. We do not like to incommode ourselves. 4. For further rules on this subject, see SS 114 and 115, and 27. My little boy and I will, perhaps, be in your way. 28. also the next section.
No, Sir; we are very glad of your company. 29. Do I disturb 5. Gêner corresponds in signification to the English to trouble, you? 30. No, Sir; you do not disturb us. 31. Do I disturb to incommode, to disturb, to be in the way, and to hurt (in speak- your father ? 32. No, Sir; you disturb no one. 33. Excuse ing of shoes and garments). So gêner means to constrain, or
me, Sir, if I disturb you. 34. Have you not been very lavish ? trouble one's self.
35. No, Sir; I assure you that your son and I have been very
economical. Est-ce que je vous gêne?
Am I in your stay?
KEY TO EXERCISES IN LESSONS IN FRENCH. Où irez-vous, votre frère et vous ? Where will you go, your brother and
EXERCISE 93 (Vol. II., page 10). you? Lui et moi irons en Angleterre. He and I acill go to England.
1. What has been taken from you? 2. My books, my pencils, and Vous, elle et lui, vous achèterez du You, she, and he will buy cheat.
my penknife have been taken from me. 3. Do you know who has
taken them from you? 4. I do not know the person who has taken Eaz et moi, nous nous sommes fait They and I have hurt our heads.
them from me, but I know that he lives here. 5. Have you asked mal i la tête.
for your books? 6. I have asked my cousin for them. 7. Has he Vous et lui, vous devriez vous prê. You and he should adapt yourselves returned them to you? 8. He has paid me for them. 9. Has much ter aux circonstances. to circumstances.
fruit been stolen from you this year? 10. Vegetables have been stolen Loi et moi, vous gênerons sans He and I will without doubt incom. from me, but no fruit has been stolen from me. 11. Have you paid doute. modo you.
the peasant for your hat? 12. I have not paid him for it, I have La cousine et moi, nous craignons My cousin and I fear to be in your paid the hatter for it. 13. Whom have you asked for information ? de vous gêner.
14. I have asked the traveller. 15. Do you know who has just knocked Je ne me gêne jamais chez mes I am never under constraint with
at the door? 16. It is Mr. L., who is asking for you. 17. For whom amis, my friends.
did you ask? 18. I asked for your brother. , 19. Hns your brother Ye vous génez pas; mettez vous à Be under no constraint; make your
paid all his debts ? 20. He has not paid them yet, because he has votre aise. self comfortable.
not received his income. 21. Have you paid him for what you Nous n'aimons pas à gêner les We do not like to incommode others.
bought of him? 22. I have paid him for it. 23. Have you not paid autres.
them your rent? 24. I have paid it to them. 25. They have paid Nous n'aimons pas à nous gêner. We do not like to incommode our
us for our house.
EXERCISE 94 (Vol. II., page 11).
1. Avez-vous payé votre propriétaire ? 2. Je lui ai payé mon loyer. À perte, et a loss. Nullement, by no Prodigue, prodigal, 3. Lui avez-vous payé les fenêtres que vous avez cassées ? 4. Je les À profit, tith a profit.
lui ai payées. 5. Le chapelier a-t-il payé tous ses chapeaux ? 6. I ne Bras, m., arm. Pardon, ercuse me. Société, f., con pany,
les a pas payés, il les a achetés à crédit. 7. Payez-vous tous les jours Déringer, 1, to disturb. Persist-er, 1, to persist. society.
ce que vous devez ? 8. Jo paie mon boucher toutes les semaines. 9. Econome, economical. Place, f., room.
Tous deux, both. Lui avez-vous payé sa viando? 10. Je la lui ai payée. 11. Qui arez.
vous demandé, ce matin ? 12. J'ai demandé M. votre frère. 13. EXÉRCISE 159.
Pourquoi n'avez-vous pas demandé mon père ? 14. Je sais que M. 1. Si nous restions plus longtemps ici, nous craindrions de votre père est en Angleterre. 15. A-t-on payé ses chapeaux au chapevous gêner. 2. Vous ne nous gênez nullement; votre société lier ? 16. On les lui a payés. 17. Vous a-t-on pris votre argent ? nous est très-agréable. 3. N'avez-vous pas été trop prodigues, 18. On m'a volé mou chapeau. 19. Avez-vous demandé votre argent VOM3 et votre frère ? 4. Lui et moi au contraire, nous à votre frère ? 70. Je le lui ai demandé, mais il ne peut me le rendre. avons été très-économes. 5. N'avez-vous pas tort de gêner il n'a pas d'argent de reste. 23. Avez-vous demandé de l'argent à M.
21. N'a-t-il pas d'argent ? 22. Il vient de payer toutes ses dettes, et te monsieur ? 6. Nous ne le gênons pas nous n'avons nalle-votre père ? 24. Je ne lui en ai pas demandé, je sais qu'il n'en a pas. ment envie de le gêner. 7. Est-ce que mon bras vous gêne, 25. Chez quel libraire avez-vous acheté vos livres ? 26. Je les ai Monsieur ? 8. Non, Monsieur ; j'ai assez de place, vous ne me achetés chez votre libraire. 27. Arez-vous tort de payer vos dettes ? génez pas, 9. Ne devriez-vous pas vous prêter aux circon- 28. J'ai raison de les payer. 29. Qui me demande ? 30. Le médecin stances? 10. Nous faisons, elle et moi, notre possible pour nous vous demande. 31. Qui frappe ? 32. Votre cordonnier frappe. prêter. 11. Ce jeune homme persiste-t-il dans sa résolution? 12. Nous y persistona, lui et moi. 13. Persistez-vous
EXERCISE 95 (Vol. II., page 42). tous deux à rester ici ? 14. Nous y persistons tous deux. 1. Did the banker receive much money last week? 2. He received 15. Cet homme est-il gêné dans ses affaires ? 16. Il était much. 3. As soon as you perceived your brother, did you not speak géné dans ses affaires il y a un an.
17. Ne vous gênez pas,
to him? 4. As soon as I perceived him, I spoke to him. 5. Here Monsieur. 18. Je ne me gêne jamais, Monsieur. 19. Est-ce you worn your new clothes already? 6. I have not yet wor them. que mon frère vous dérange? 20. Non, Monsieur, il ne me t'hauked him, and begged him to thank you. 9. Have you fourl your
7. When he gave you money yesterday, did you thank him? 8.1 I dérange pas. 21. Je ne voudrais pas vous déranger. 22. Par- books! 10. I have not found them yet. 11. Wen you came to see don, si je vous dérange. 23. Vous et votre associé avez vendu / us, did you not finish your affairs with my father? 12. I finished
15. Did you (Art. 54).
them then, and paid him. 13. Have you not seen your eldest sister write the terms of the subtrahend after those of the minuendo during your stay in Lyons? 14. I have not seen her. not go to bed too soon last night? 16. I went to bed late. 17. At what hour did you rise this morning? 18. I rose at five o'clock; I
Otherwise. -Put the quantity to be subtracted in brackets, generally rise early. 19. Did you not seek to escape from your prison and write it after the quantity from which it is to be subtracted, last year! 20. I have never tried to escape. 21. Have you sold your with the sign between them; then apply the Rules of property? 22. I have not sold it. 23. What have you given to the Addition. soldier? 24. I have given him nothing. 25. During his stay at B.,
EXAMPLES. we gave him all that he wished.
(1.) From 6a +96, take 3a + 4b. EXERCISE 96 (Vol. II., page 42).
Here, change the signs of the subtrahend, but not those of the
minuend, thus:1. Que reçâtes-vous la semaine dernière ! 2. Nous reçûmes cinquante francs de votre ami, et vingt-cinq de votre frère. 3. Menátes: Vous and you have the answer, 3a + 56.
6a + 9b - 3a --- 4b. Next reduce these terms, by Art. 52, votre fils à l'église hier? 4. Je ne l'y menai pas.
. vous l'année dernière? 6. Nous perdimes notra argent, nos habille- (2.) From 16h (3.) 14da (4.) — 28 (5.) — 16. (6.) — 14da ments et nos chevaux. 7. Les avez-vous cherchés ? 8. Je les ai Take 126 6da
6da cherchés, mais je ne les ai pas trouvés. 9. Parla-t-on de votre frère, hier? 10. On parla de lui et de vous. 11. Qu'est-ce que le médecin
Answer, 46 8da
8da vous a donné 12. Il ne m'a rien donné. 13. À quelle heuro votre (7.) 160 (8.) 12b (9.) 6da (10.) - 16 (11.) — 126 (12.) 6da soeur se leva-t-elle hier? 14. Elle se leva à cinq heures. 15. Vous 286 166 14da - 28 - 166 -- 14da êtes-vous levé de bonne heure ce matin? 16. Nous nous sommes levés à six heures et demie. 17. Votre cousin a-t-il vendu toutes ses pro- 125 - 46 -8da priétés ? 18. n ne les a pas vendues, il les a données à sa sour ainée. 19. Le voyageur vous a-t-il raconté ses aventures ! 20. Il me les a
(13.) + 166 (14.) + 14da (15.) — 28 (16.) — 165 (17.) - 14da racontées. 21. Cet homme a-t-il cherché à parler à votre père? 22.
+ 6da Il a cherché à lui parler. 23. Le professeur a-t-il parlé de votre frère, pendant son séjour chez vous ! 24. Il a parlé de lui, 25. Votre ami
20da a-t-il porté son habit neuf ? 26. Il ne l'a pas encore porté. 27. Avez- (18.) From 8ab, take Gry. Ans. Sab --- 6xy. vous remercié votre frère ? 28. Je l'ai remercié. 29. Qu'avez-vous donné à votre sour ainée? 30. Je ne lui ai rien donné, je n'ai rien (19.) From baay
(20.) 16aazz à lui donner. 31. Quand M. votre frère vous donna un livre, l'année Take 17ay
20ax dernière, le remerciâtes-vous ? 32. Je ne le remerciai pas. 33. Est-il tard! 34. Il n'est pas tard, il n'est que six heures. 35. Fait-il beau Answer, baay - 17ay 16aaxx -- 20ax temps ou mauvais temps? 36. Il fait très-beau temps.
(21.) 6dd + 3d - 4ddd
10dc + 2dddd + 4dy LESSONS IN ALGEBRA.-IV.
6dd + 3d - 4ddd - 10dc --- 2dddd — 4dy SUBTRACTION.
61. From these examples, it will be seen that the difference
between a positive and a negative quantity may be greater than 56. SUBTRACTION is the finding of the difference between any two either of the two quantities. In a thermometer, the difference quantities or collections of quantities.
between 28 degrees above zero, and 16 degrees below, is 44 EXAMPLES.-(1.) Charles has 5a pears, and James has 3a degrees. The difference between gaining 1,000 pounds in trade, pears. How many more pears has Charles than James ? and losing 500 pounds, is equivalent to 1,500 pounds. In this example, we wish to take 3a pears from 5a pears.
62. Proof.–Subtraction may be proved, as in arithmetic, by But subtraction is denoted by the sign -. Hence the expres- adding the remainder to the subtrahend. The sum ought to be sion 5a - 3a pears represents the answer. But 5a - 3a = 2a equal to the minuend, upon the obvious principle, that the dif. pears; which is the answer.
ference of two quantities added to one of them, is equal to the (2.) A gentleman owns a house valued at £4,500, but he is in other. debt £800. How much is he worth ?
EXAMPLES.-(1.) From 2w - 1, subtract -- xy + 7.
Proof. 57. Let us now attend to the principle upon which these Here, Minuend 2xy 1 Add - xy + 7 Subtrahend. operations are performed. Let us suppose that you open a Subtrahend
To 3.cy - 8 Remainder. book account with your neighbour, and that when cast up, the debtor side, which is considered positive, is £500, and the credit
Remainder 3xy 8
2xy-1 Minuend. side, which is considered negative, is £300. On balancing the (2.) From h + 3bæ (3.) hy ah (4.) nd --- 7by account, you find that he owes you £500-£300 = 200. Now,
Take 3h - 9bx 5hy - 6ah
5nd by if you take £50 from the positive or debtor side, it will have the same effect on the balance, as if you added £50 to the negative Answer 2h + 12b - 4hy + 5ah
- 4nd - bby or credit side; and on the other hand, if you take £50 from (5.)
(8.) the negative or credit side, it will have the same effect on 3abm
my 17 + 4ax ax + 76
3ah + azy the balance, as if you added £50 to the positive or debtor - 7abm + 6xy
4ax + 156 Tah + axy side. 58. In like manner, if, in the expression 12a --5a, you take 10abm -- 7xy
+3+ 5ax + 5ax- 86
+ 10ah 3a from 12a, it will have the same effect on the expression, as if you added 3a to 5a, and retained the negative sign in the sum; they may be united and their sum be used. Thus,
63. When there are several terms alike in the subtrahend, thus, 9a - 5a is the same as 12a - 8a. Again, if in the expres. sion 12a - 5a, you take 3a from 5a, and retain the negative sign
EXAMPLES.-(1.) From ab, subtract 3am + am + 7am in the difference, it will have the same effect on the expression, + 2am + bam. as if you added 3a to 12a ; thus, 12a --- 2a, is the same as
Here ab - 3am
7am - 2am - 6am = ab- 19am. 150 --- 5a.
Answer. 59. Hence universally, taking away a positive quantity from an
(2.) From y, subtract a +a+a +- a. Ans. y - 4a. algebraic expression is the same in effect as adding an equal
(3.) From ax-bc + 3ax + 7be, subtract 4bc-2ax + bc + 40%. negative quantity; and taking away a negative quantity is the
Answer. 2ax + be. same as adding an equal positive one.
(4.) From ad + 3dc - bx, subtract 3ad + 7bx - de + ad.
3ad 60. Upon this principle is founded the following
64. The sign —, placed before the marks of parenthesis which GENERAL RULE FOR SUBTRACTION.
include a number of quantities, requires that, when these marks Change the signs of all the quantities to be subtracted, i.e., of are removed, the signs of all the qnantities thus included should the subtrahend, or suppose them to be changed from + to, and be changed. Thus a - (b-c+d) signifies that the quantities from - to +; then if the quantities are ALIKE, unite the terms b-c and + d are to be subtracted from a. Remove the as in addition (Arts, 49, 50) ; but if the quantities are UNLIKE, parenthesis
, and the expression will then become a -- +
-zy + 7
an expression which has exactly the same meaning as the land if not King of France," had died away, and there was former.
neither rhyme nor reason in keeping up a ridiculous delusion. EXAMPLE.–From xy + d, take 7ad -- æy + d + hm. Here, Time was, however, when the assumed title represented a ty+d-(7ad - ay + d + hm) -7ad + 2xy - hm. Answer. reality; when, though not without dispute, the Kings of Eng
65. On the other hand, when a number of quantities are to be land were acknowledged to be also Kings of France. Let us introduced within the marks of parenthesis, with - immediately look for a while upon a scene whereon the mark of the English preceding it, their signs must be changed. Thus, -m +% domination was stamped with such indelible plainness that all -de + 3h=-(m-b + dx-3h).
the waters of oblivion that have flowed past it since have not EXERCISE 5.
sufficed to wash it away-a scene which will remain as an
historical memory to the end of time, and which showed, inci. 1. From bab + 75y + 18dfg, take 3xy + 4b + 8dfg.
dentally at least, this, that the English were wholly unworthy of 2. From - 35az 21ab - 37m, take - 30m - 15ab 10ax.
their position as lords of France. 3. From 9ay + 196. + 226c, take 12ay + 31bc + 50bx. 4. From xy - 10ab + 6d, take 12ab + 100 + 24xy.
At daybreak on the 30th of May, 1431, a priest entered the 5. From 7a + 6x + dy + xyz, take 3x - 4a - 389 - 17xys.
cell of a young woman at Rouen, and announced that he was 6. From 18be – 2y + 22gh, take 41xy - gh + bc.
come to prepare her for death. Not that the prisoner was ill7. From 21ax + y + ac - ay, take 4a - be + x - yz - de.
she was young, healthy, and in the full possession of her facul. 8. From 21x + 40xy - 13a, take 42 + 10ab - 5bc.
ties; the death she was to suffer was a violent one-she was to 9. From 5ay, take 2ab + 30ab + ab 4ab.
be burned alive! Burned alive at one-and-twenty! What could 10. From 5ax + 16ay, take fax - ay + 3ax + 4ay.
the poor wretch have done? She had shivered the power of 11. From a +b, take - (c + d-f+g-h-æy).
the English in France; she had, by means of an enthusiasm 12. F:om 7ab + 16xy - 7ad, take (hab - 12xy + ad).
which rendered her obnoxio":s to the clergy, roused the French 13. Introduce the following quantities within a parenthesis with immediately preceding, without altering their value; viz.,
nation from the torpor into which it had been thrown by the
- q + 8 -0-d + f + gh.
stunning blows dealt to it by Henry V. of England, and she 14. Also, ab -- cdx + df - x - y + ghf - be + xyz.
had dared to thwart the purposes and brave the anger of vin15. From 4tx + 6bbb, take Sax + 4bbb.
dictive churchmen like the Bishop of Beauvais, and the Bishop 16. From 20yy - 2y + 12aaa, take 15yy - 2y - 12aaa.
of Winchester, Cardinal Beaufort. The prisoner's name was 17. Froin – 8 (a + b) + 10 (x + y), take 2 (a + b) - 6(x + y). Jeanne Darc, or as she has been more commonly, but erro18. From 4 (a + b) 16 (x - y), take 17 (a + b) + 36 (x - y). neously, called, Joan of Arc. 19. From 2a - aa + ba, take a -4aa 6ba.
The priest's announcement took the poor maiden entirely by 20. From 2x + 3.x - xx, take 2x + 3xx + 10xxx.
surprise. A week before she had been led ont into a public 21. From 18 - 25ab + 20x + 3y, take 3x + 3y - 25ab + 1. 22. From 6 (a - y) - 17 (a + y), take 3 (a + y) - 7(a - y).
place in Rouen, and compelled in a moment of weakness, when 23. From ax - my-my-6, take bax - 6xy - ay + 46 - 709.
surrounded by enemies--not one kindly face among the crowd24. From 660 - 4b, take 20a - b - 30a - 16a - 3b + 5a.
and under circumstances of great excitement, to sign a docu25. From 6x** -a, tako 2x42% - 16.
ment disavowing and solemnly abjuring certain charges of 26. Fromx* + 4.23y + 6x?y2 + 4273 + y4, take at - 4k’y + 6x=y2 - 4xys heresy which were preferred against her; and she had been told
on that occasion that her life would now be spared, though she 27. From 4a3 - 8a* + 16a5, take 3as 4q+ + 5a".
must resign herself to a sentence of perpetual imprisonment. 28. From a + b + c, take - a + b + c.
The excuse for breaking faith with the poor girl was this, that 29. From 4a3 - 3a'x + ax - 203, take 2a3 402. - ar? - 23.
since her abjuration she had said that St. Catherine and St. 30. Take as - 31* + 3x - 1 from x3 + 3x2 + 3x + 1. 31. From ax? + by?, take rx2 – dya.
Margaret, with whom she asserted she was frequently in direct communion, had appeared to her, and rebuked her for her weak
ness in yielding to the threats of violence. KEY TO EXERCISES IN LESSONS IN ALGEBRA.
On first hearing the announcement of the priest, Jeanne's EXERCISE 4.
firmness gave way; she wept and gave vent to piteous cries, tore 1. hab + cd-4m + 7.
her hair, and appealed to "the great Judge” against the cruel 18. 7y + 9yy + 5xy 6x. 2. Sy -- die + hm - 1. 19. Saaa.
wrongs done to her; but by degrees her self-possession returned, 3. cbm + bm - 5y + x + 16. 20. 7yyyy + 12 xx.
and she listened to the ministrations of the priest, received the 4. Sam + 3xy - 11. 21. - 6 (a + b) - 12(x - y) - 13.
last sacrament from him, and announced herself ready to sub5. Jahy + 16.
22. 4(a - b) + 9a (x + y) - 6y. mit to the will of God. At nine o'clock in the morning she G. llad + 23. 15axy + 3bed.
was carried away in the hangman's cart to the market-place of 7. by + 3 (b-a) + sa.
24. 17 (x + y) 9. (a - b). Rouen, where had been already laid the funeral pyre on which 8. 6ax + xy. 25. 15abc + 2 (x + y).
the young victim was to be sacrificed. The Bishop of Beau9. 66 + 41cdf – 3xy. 26. 24x7 babe + 4mn 25a.
vais, Cardinal Beaufort, and several other prelates, with the 10. 180 + 4ax - 56x + c3cx + 363 27. ta (x + y) + 76 (x + y) = (ta English military commanders, were there, and a vast crowd had - 17xy.
+76) (x + y). 11. Sab
come out to see "the Maid of Orleans" die. - 6be + 4cd – 7y + 17mn 28. axa + a*x + xy + 3y2 + y8. + 1899 - 2ax. 29. llas - 10990 - 14ab2 + 1663.
In the centre of the market-place, about the spot where now 12. Sabe + 25abd + 5xyz. 30. 1023 - 2x + 3x - 2
stands a fountain surmounted by a figure of Jeanne Darc, the 13. 3df + 4ax + 74y + 30. 31, 2q + 2 + 2c + 2d,
stake was reared, and around it were piled the fagots. Soldiers 14. 55a + 686. 32. a
guarded the place of execution. The ceremonial of death was 15. 7(a + b). 33. 698
begun on that beautiful May morning by a sermon in which the 16. Qy (a + b).
34. (a + b + c) 23 + (b -c + d) z* crime of heresy was vehemently denonnced, then the sentence 17. 2ax + 5aa + 3x + 3xxx. 35. (m + n + 2) 22 - (n + p +1) •.
pronounced by the shepherds of the flock on the ewe lamb before them was published, and the signal was given to proclaim
the last act of the tragedy. A soldier's staff was broken and HISTORIC SKETCHES.-XXIX.
formed into a rough cross which “ the Maid” clasped to her
breast. She was then bound to the stake, the fagots were THE ENGLISH IN FRANCE.-JOAN OF ARC.
lighted, the fire leaped up around her, and after suffering the UNTIL some time after George III, had been on the throne agony indispensable to death by burning, her spirit returned to the style and title of onr kings was “ King of Great Britain, God who gave it. The English cardinal watched the whole France, and Ireland.” Even when James II. was a fugitive proceedings with unmoved face, and when his victim's life was from his kingdom, and was magnificently entertained by Louis beyond his reach he ordered her ashes and bones to be XIV. at St. Germains for a series of years, he still retained the gathered up and to be cast into the Seine. empty title of king of the country where he was dwelling as a Was it really heresy for which this poor girl suffered? Ostenguest. To be sure he was virtually as much King of France sibly it was, but had Jeanne's heresy stood alone, it would scarcely as he was King of England, but to the latter title he had much have provoked the interference of potentates like those who more than a mere pretension, and the title of King of France was “ did her to death." Upon her head, when bound to the stake, historically bound up with it. Yet in James's time (1685-1688), they fastened a cap on which was written her accusation, "reeven the echo of the old shoat of Henry V., “No King of Eng. I lapsed heretic, apostate, idolatress," but they did not write the