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(1.) Premièrement,

§ 29.-ORDINAL ADVERBS.
first;

Deuxièmement,
Secondement,

Troisièmement,

Quatrièmement, fourthly in the first Cinquièmement, fifthly place Sixièmement, sixthly

secondly

thirdly

Septièmement,

Dixièmement,

seventhly tenthly.

(2.) These, like adverbs of manner, are formed by the addition of ment to the feminine form of the adject ve. $ 30.-INDEFINITE ADJECTIVES.

(1.) The indefinite adjectives are used when anything is to

aucun,

the Spice Islands, or Moluccas, including Amboyna, thirty-two miles long, by twelve miles broad, and containing about 282 square miles; then the Philippine Islands, north of these, including Luzon and Mindanao; the former about 400 miles long, and about 100 miles broad, with a surface of about 56,000 square miles; and the latter about 300 miles long, and about 108 miles broad. North of the Philippines, is the island of Formosa, belonging to China, and the Loo-choo Islands northeast of Formosa, subject to China. North and north-east of these islands, are the Japan Islands, of which the largest is Niphon, about 800 miles long, and 100 broad; the next, Jesso, about 280 miles long, and 200 miles broad; next, Kiusiu, about 150 miles long, and 120 miles broad; and the next Sikokf, be represented or referred to in a general or indefinite manner. These islands They are,about ninety miles long, and fifty broad. include a surface of about 160,000 square miles, and form an important appendage to the continent of Asia. The other islands on the west of Asia, and in the north Pacific Ocean, In the northern ocean, are of small size and importance. there are a few islands, of which very little is known. South of India, are the Andaman and Nicobar Isles in the Bay of Bengal, and the important island of Ceylon, south-east of the Carnatic, with an area of about 24,600 square miles, and a population of about a million and a half-a fine appanage of the British crown; it is separated from the peninsula of India by the Gulf of Manara, and the strait called Palk's Passage. On the other side of Cape Comorin, the most southern point of India proper, lie the Laccadive and Maldive Islands, south-west of the Malabar coast. In the Indian Ocean, between Africa and India, lie the Seychelle Islands.

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chaque,
même,
nul,

plusieurs,

not any, not one
every, each

quel,

what

quelconque,
quelque,
tel,
tout,

whatever

some
such

all.

same

no

several

(2.) AUCUN is generally followed by a noun, with which it must agree. It is followed by ne when it comes before a

verb :-
:-

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(3.) Aucun is by the French authors sometimes used in the plural:

Ils ne peuvent souffrir aucun empire légitime, ne mettent aucunes bornes à leurs attentats.

MONTESQUIEU.

They can bear no legitimate dominion, set no bounds to their crimes.

Aucun and nul should be put in the plural only before such words as are not used in the singular, or have in the singular a different acceptation.

(4.) CHAQUE is of both genders, and is used only in the singular. It always precedes the noun, and cannot be separated from it by an adjective or by a preposition. It should never be used without a noun :

Chaque âge a ses plaisirs, chaque situation as has its pleasures, every

état a ses charmes. DELILLE.

its charms.

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(3.) When coming after the noun to denote an additional half, ni mécontent de son esprit. it agrees in gender with the noun :

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MME. DESHOULIERES.

(9.) PLUSIEURS is, of course, always in the plural. It does not vary its form:

Il faut bien qu'il y ait plusieurs raisons d'ennui, quand tout le Cette horloge sonne les heures et This clock strikes the hours and the monde est d'accord pour bailler. les demies. FLORIAN.

half-hours,

There must necessarily be several reasons for ennui, when all agree is yawning.

LESSONS IN GEOMETRY.

(10.) QUEL takes the gender and number of the noun to which it relates. It is sometimes immediately followed by its noun, from which it may be separated by one or several words:

Quel tableau ravissant présentent DELILLE. les campagnes ! Quelle invisible force a soumis l'univers ? L. RACINE. Quels son harmonieux, quals efforts ravissants,

De la reconnaissance égalent les

accents?

|

What a delightful picture the country offers!

What invisible hand has conquered the universe?

What harmonious sounds, what ravishinty strains, equal the voice of gratitude?

LESSONS IN GEOMETRY.-No. XVII.

LECTURES ON EUCLID.

COROLLARY TO PROP. IV., BOOK I.

Ir the sides A B and D E, or the sides AC and D F of the triangles ABC and D E F be produced, the angles upon the other sides of the bases of these triangles are equal.

In fig. (D), let the side A B of the triangle ABC be produced to G, and produce the side D E of the triangle DEF, so that DH shall be equal to A G, by Exercise on Prop. III. in our last lesson.

(11.) QUELCONQUE is always placed after the noun, and The angle C B G is equal to the varies only for the plural:—

Toutes les jouissances sont précédées d'un travail quelconque.

MME. CAMPAN.

Deux points quelconques étant donnés. THE ACADEMY.

(12.) QUELQUE in the sense whatever, agrees in number with

Il y a du mérite sans élévation, mais il n'y a point d'élévation sans quelque mérite.

LA ROCHEFOUCAULD. Quelques vains lauriers que promette la guerre,

On peut être héros sans ravager la terre.

BOILEAU.

All enjoyments are preceded by some sort of exertion.

Two points of some kind being
given.

of some (a certain number), or
the noun :-

There is merit without elevation,
but there is no elevation without some

merit.

Whatever vain laurels war may promise, one may be a hero without ravaging the earth.

angle FE H.

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For if the triangle A B C be applied to the triangle D E F so that the point A may be on the point B D, and the straight line AG upon the straight line D H, the point G shall coincide with the point H, because the straight line AG is, by construction, equal to the straight line D II; and AG coinciding with D H, it may be shown as in the fourth proposition, that the part A B coincides with the part DE. But the remainder BG is equal to the remainder EH (I. Axiom 3); and because the point в coincides with the point E, and the point G with the point H, therefore BG coincides with EH. Now, it may be shown as in the fourth proposition, that BC coincides with EF; therefore, BG coinciding with EH, and BC with EF, the angle C B G coincides with the angle FEH; where

(13.) Quelque having the sense of about or some or however, fore the angle C B G is equal to the angle F E H (I. Axiom 8). In

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Tout citoyen doit servir son pays; le soldat de son sang, le prêtre de LA MOTTE. son zèle. En toute chose, il faut considérer la fin. LA FONTAINE.

Every citizen should serve his
country; the soldier with his blood,
the priest with his zeal.
In everything we must consider the
end.

In the statement of this corollary, Dr. Thomson has taken it too readily for granted that the parts produced by the straight lines A B and DE would necessarily coincide when these straight lines themselves were made to coincide. This assumption is, in fact, taking for granted a corollary which Euclid has thought it necessary to demonstrate, and which is appended to the 11th Proposition of Book I., viz., that two straight lines cannot have a common segment, that is, they cannot coincide in part without coinciding altogether. Now, as this corollary cannot be assumed without demonstration, it became necessary to demonstrate the above corrollary as we have done; and this demonstration includes in it a demonstration of Euclid's very corollary to the 11th, which would otherewise require to be taken for granted. We are now prepared for the demonstration of the fifth proposition in the way laid down by Dr. Thomson, which we must confess is a great simplification of Euclid's, and well worthy of the attention of teachers who find any of their pupils unable to cross the bridge.

PROPOSITION V. THEOREM.

The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced, the angles upon the

(16.) Tout, in the sense of all, agrees in gender and number other side of the base shall be equal. with the noun to which it relates :

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Because in the two triangles A F C and A G B, the side A F is equal to (Const.) the side a G, and the side AB to (Hyp.) the side A c, the two sides FA and AC are equal to the two sides G And A B, each to each; and they contain the angle and AG B. Therefore the base FC is equal FAG common to the two triangles AFC (I. 4) to the base G B, and the triangle AFC to the triangle AG B. Also, the remaining angles of the one are equal (I. 4) to the remaining angles of the other, each to each, viz., those to which the equal sides are opposite; wherefore the angle AFC is equal to the angle AG B. Again, because the whole A F is equal to the whole A G, of which the parts A B and A C, are equal. equal (Ax. 3) to the remainder 0 G.

F

D

B

B

Therefore the remainder B F is
But the side FC was proved

to be equal to the side a B; therefore, in the two triangles BFC
and G CB, the two sides B F and F C, are equal to the two sides CG and
GB, each to each, and the angle B F C was proved to be equal to the
angle C G B. Therefore, the two triangles BFC and G C B are equal
(1.4), and the angles A B C and A CB, on the other side of the base
BC of these two triangles, are equal, by the preceding corollary;
but these are the angles at the base of the triangle ABC. And
because the triangles FBC and GCB are equal; therefore the
angles FBC and GCB opposite to the equal sides FC and GB
are also equal (I. 4); and these are the angles on the other
side of the base B C of the triangle A B C. Therefore, the angles at
the base of an isosceles triangle, &c. Q. E. D. Quod Erat A KEY TO THE EXERCISES IN THE
Demonstrandum, Which Was to be Demonstrated.

also equiangular (equal-angled). For any side being made the
base, it can be shown that any two angles at the base are equal;
therefore, all the three angles are equal to one another.
The enunciation of this fifth proposition is more clearly and
logically expressed by saying that "if two sides of a triangle be
equal to one another, the angles which are opposite to the equal sides
are also equal to one another; and, if the equal sides be produced,
the angles upon the other side of the base shall likewise be equal.”'

Fig. (E).

ANOTHER PROOF.-Dr. Thomson has inserted in his edition the following proof of this important theorem :-In fig. (E), let A B C be the isosceles triangle, of which the sides a C and C B are equal to one another; and let the angle ACB opposite the base AB, be bisected by the straight line CD, that is, divided into two equal parts, viz., the angles ACD and BC D. Because, in the two triangles ACD and BCD, the side a C is equal to the side C B, by hypothesis, and the side C D is common to the two triangles; therefore the two sides AC and CD are equal to the two sides BC and CD each to each; but the angle A CD is equal to the angle BCD, by hypothesis, therefore the base AD is equal to the base DB, and the triangle A CD to the triangle B CD; also, the remaining angles of the one are equal to the remaining angles of the other each, viz., those to which the equal sides are opposite; therefore, the angle CAD is equal to the angle CBD; and these are the angles at the base of the isosceles triangle A C D. And if the equal sides CA and CB were produced, the angles on the other side of the base would be equal, by the corollary to the fourth proposition,

as above demonstrated.

D

The only objection to the preceding demonstration, which is short and clear, and obvious to every capacity, is that in assuming the bisection of the angle ACB, we virtually employ an additional postulate, viz., "That any rectilineal angle may be divided into two equal parts." This, of course, increases the number of postulates, which Euclid was evidently desirous to avoid. Besides, it anticipates the construction of the 9th proposition of this book, where Euclid shows how to bisect a given rectilineal angle; and it was a principle with him, never to take any problem for granted of which it was possible to show the construction and demonstration.

A

Fig. (F).

C

E

BG

In

F

A THIRD PROOF.-In his notes on the fifth proposition, Dr. Thomson, as others have done before him, suggests another mode of proof, which we here insert in full for the sake of learners. fig. (F), let ACB be the isosceles triangle, of which the sides AC and CB are equal; and let the triangle ABC be applied obversely (that is, with its present face downwards) to the plane in which it is, at any point E, so as to leave a trace or outline EFG, in which EF represents the straight line A C; EG the straight line CB, and F G the straight line AB. Also the angle GEF represents the angle ACB; the angle EGF represents the angle C BA; and the angle EFG, the angle CA B. Because AC is equal to CB, by hypothesis, and that EG is equal to c B, by construction (being its trace), therefore AC is equal to EG (I. Axiom 1). In the same manner, it may be shown that C B is equal to E F. Because the angle A C B is equal to the angle G E F, by construction (being its trace); therefore in the two triangles ACB and GEF, the two sides A C and C B are equal to the two sides GE and EF, and the angle A C B is equal to the angle GEF; wherefore the two triangles are equal; and the remaining angles of the one are equal to the remaining angles of the other, &c. (I. 4). Therefore the angle C A B is equal to the angle E G F, and the angle A B C to the angle EFG. But the angle EGF is equal to the angle CBA by construction (being its trace); therefore the angle C A B is equal to the angle CBA (I. Axiom 1); and these are the angles at the base of the isosceles triangle ABC. In the same manner, it may be shown by the application of the corollary to the fourth proposition, above demonstrated, that if the equal sides CA and CB were produced, the angles below the base would also be equal.

COROLLARY.-Hence every equilateral (equal-sided) triangle is

LATIN LESSONS.

(Continued from page 343, Vol. II)

By JOHN R. BEARD, D.D.

Page 70, col. 2, vol. II.-LATIN-ENGLISH.

God has given us a mind than which nothing is more excellent, the victory cost us much blood; the mother of all good arts is wisdom, than which nothing more productive, nothing more excellent has been bestowed by the everlasting God on the life of men; God has placed the body as a (quandam) garment round the soul (God has surrounded the soul with the body as with a gar,ment), and has clothed it outwardly; those whose fathers or forefathers were distinguished by any glory (glorious deeds), endeavour for the most part to excel in the same sort of praise (praiseworthy deeds); we ought to hold our parents very dear, because by them life has been given to us; he has not conferred a benefit who unwilling has done good (who has done good unwillingly); who are more yours than those to whom you have restored safety, when they were destitute of hope? the citizens showed themselves most energetic defenders of liberty; a great multitude surrounded the orator in the market-place; eloquence has been given by nature for the safety of men; eloquence has been given by nature for the preservation of men; a wicked orator turns eloquence to the ruin and destruction of the good; what is so inhuman as to turn eloquence, given by nature for the safety and preservation of men, to the ruin and destruction of the good; pay had not been given to the soldiers for a long time; sedition arose among the soldiers; because pay had not been given for a long time, sedition arose amo.g the soldiers; you, my friend, will evince fidelity to me; I know for certain that you, my friend, will evince fidelity to me; nothing hinders us; nothing will hinder us; we may obtain a victory; I believe that nothing will stand in our way so that we may not obtain the victory (to prevent our obtaining the victory); the victory cost the death of many brave men; we did not doubt that the victory would cost the death of many brave men; will you persist in your opinion? I know not whether you will persist in your opinion.

N.B.-On page 70, col. 2, line 11, for constěti read constiti. do. do. line 12, for perstěti read perstiti.

Page 70, col. 2, vol. II.-ENGLISH-LATIN. Classem duci dedit; tibi classem dabit; censesne se fratre meo classem daturum esse? nihil pluris hominibus constitit quam avaritia; Deus mihi dedit sororem, quâ nihil mihi est carius; soror mea mihi se amantem per totam vitam praestabit; milites fortissimos se praestiterunt, sed victoria morte multorum virorum fortium constitit; nihil obstat quominus victoriam adipiscamur: victoriam, credo, adipiscemur; Socrates omnibus philosophis praestitit; quis nescit Socratem omnibus philosophis praestitisse? credis ne filium tuum omnibus sociis praestaturum esse? ingens hominum multitudo oratorem circumstat; stipendium militibus milites oriatur; perstaturusne es in sententiâ tuâ? nescio perstsnon est datum; stipendium militibus dabo; cave ne seditio inter turus ne sim in sententiâ meâ.

Page 71, col. 1, vol. II.-LATIN-ENGLISH. Nothing hinders to prevent our doing that which pleases us most; I will not oppose to prevent his reading everything; death does not deter a good man from consulting the welfare of the republic; they may interrupt me to prevent my being honoured, provided they do not interrupt to prevent the republic from being well managed by me; no pretext appeared sufficient to excuse any citizen from being present; he surrounded the bed with a broad rounds himself with soldiers; he will put his arms round your ditch; he surrounds the enemies' camp with his army; he surneck; he surrounded the city with a mound; I will endeavour to go beyond these limits with which I have surrounded myself; he gave a distinguished character to the peace; patrons have invested him with this fame.

Page 71, col. 1, vol. II.-ENGLISH-I.ATIN. Nihil impedit quominus puer bonus esse possis; famam tibi circumdabo; circumdabit mihi vestem; honorem sorori suae circumdedit; circumdate urbi ignes, quominus cives egredi non possint; quominus adsis, nulla excusatio justa est.

Page 82, col. 2, vol. II.-LATIN-ENGLISH.

N.B.-On page 82, col. 2, line 7 from bottom, for necuri read necui. do. 83, do. 1, do. 4 from top, for petire read petere. do. 83, do. 1, do. 43 do. for acipitrem read accipitrem. do. 83, do. 2, do. 8 do. for accipetri read accipitris. do. 83, do. 2, do. 9 do. for second read third. Who comes (venit)? the door creaked; the leader violently abused the soldiers; the whole city resounded with the voices of citizens exulting (exsultantium) on account the of victory gained over the enemies; come, let us go to lie down; the Romans by their arms completely subdued many tribes and nations; we are taught by the authority and command of the laws to possess regulated desires, and to restrain all passions; great springs of water gushed forth from the fountain; the wise men of the Indians devote themselves to the flames; the wise men of the Indians are burnt without a groan; the wise men of the Indians when they have devoted themselves to the flames are burned without a groan; Cicero applied himself to (studied under) Molon the philosopher; the wise man endeavours to unfold the involved idea of his mind; when you have laid open the history of the times you will find many examples both of virtues and vices; when the city was taken, every place on all sides sounded with the lamentations of women and children; we are frightened (terremur) when it has thundered (tonuit) in calm weather; we strive after what is forbidden; Augustus forbad the poems of Virgil to be burned; Augustus forbad the poems of Virgil to be burned in opposition to the modesty of his (Virgil's) will.

Page 82, col. 2, vol. II.-ENGLISH-LATIN.

Forium cardines crepuerunt; mater filium innocertem increpuit; milites per totam noctem excubuere; nautae hostium classem domabunt; ad Ciceronem me applicabo; veto te ad Aristotelem te applicare; nitemur in vetitum; tota domus hominum gemitibus aegrorum sonuit; urbs armis sonat; Jupiter nutu caeteros Deos domat; passim gemitus ploratusque sonant; leonem perdomui.

Page 83, col. 1, vol. II.-LATIN-ENGLISH.

I fear that I have revived your regret and grief by my letter; you are about to revive the past misfortunes of the republic by your wicked deeds; there is no doubt that you will revive the past misfortunes of the republic by your wicked deeds; Tantalus, touching the top of the water, is repesented by the poets as tortured by thirst; do you not know how much that talkative man has tortured me by chattering? Caius Marius, when he was flogged, at the first forbad that he should be bound, and no one before Marius is said to have been flogged unbound; husbandmen carry the coin, when cut down, into barns; unless you have restrained your desires, in vain will you endeavour to live happily; who knows not how much Cicero aided his country? not only fortune but your industry also has assisted you in your undertaking; if fortune lends our soldiers any aid, we do not doubt that we shall gain a splendid victory over the enemies; the army advanced by long marches (itineribus) to assist the blockaded (cinctos) citizens; do not sup before you have washed your hands; as you are about to wash your body, fetch pure water from the running stream.

Page 83, col. 1, vol. II.-ENGLISH-LATIN.

Pueri, expergiscimini, lavate, et quum lavissetis ad negotium se applicate; hae mulieres me garriendo enecuerunt; non dubito quin hae mulieres te garriendo enecuerint; hae puellae garrulae me garrulitate enecabunt; vetabo filium garrire; lavistine manus? age! bene manus prius lava quam accumbes; nolunt pedes lavare; patris verbum filium adjuvat; naves veniunt urbem obsidione cinctam adjutum; non est dubium quin ducis exercitus nostri brevi urbem adjuvaturus sit; secuistine pollicem? crus secui; dolorem meum refricuisti; nolens refricui dolorem tuum; fortuna fortem juvat; servus alligatur; pater vetat filium alligari.

Page 92, col. 1, vol. II.-LATIN-ENGLISH. N.B.-On page 91, col. 2, line 27 from top, for citum read citum. for citum read citum. do. 92, do. 1, do. 7 do.for connivère read connivere. Minerva taught Cicero all arts; the mingled earnestness of medesty is greatly to be admired; so many times have I been occupied, and with such important business, that I am unable (that it is not allowed to me) to breathe freely; know you not how many

toils, how many dangers, how many miseries the soldiers have sustained on their way? if virtue has restrained you from bad desires your life will be happy; Cicero having been told all things (cuncta) by the ambassadors (legatos), ordered the prætors to seize the Allobroges on the bridge; let not their minds mingle with the vices of men; the ascent to heaven is easy to the good; the less minds have mingled with and attached themselves to the errors and vices of men, the easier to them will be the ascent to heaven; the nature of the mind is simple, nor has it in it any thing mixed; we live on grapes dried in the sun; we have dried many grapes this season; Cato was of opinion that Carthage should be destroyed; every fifth year all Sicily was subjected to the census; two most pow erful cities, Carthage and Numantia, were destroyed by Scipio; no forgetfulness has ever blotted out the fame of the Greeks and Romans, nor ever will blot it out; God has filled the world with all good things, and has mixed with it nothing bad; while the general is absent the soldiers excited sedition; the slaughter having been declared to be greater than it really was (than the reality was), excited terror in the city; Catiline was calmed neither by watching nor by rest, conscience so harrased his excited mind; it was enjoined by the laws that the dead should be buried after the third day; I doubt not that you have always shunned the intimacy of impure men; I am not ignorant that you have always favoured me and mine; chickens having been cherished and hatched are anxiously watched by their mothers; will you doubt that I have always cherished the greatest affection toward you; you so embraced me, so held me in your hands, so fondled me, that I could never forget that day; Brutus and Cassius, the murderers of Caesar, caused a great war; he is ungrateful who returns thanks, when witnesses are removed; many commanders of the Romans devoted their lives (heads) to the safety of their country; in the same year three temples were publicly vowed (to be built) and consecrated.

Page 92, col. 1, vol. II.-ENGLISH-LATIN.

Cicero a Minervâ omnes artes edoctus est; cives sex templa publice voverunt; templum Veneri dedicaverunt; mater infantem fovet; mater semper liberos fovebit; uxores maritos foverunt; cave ab mulieribus impuris; militum clades per urbem magnum ploratum movit ; nescio quot labores sustinuerit; nescis quot labores sustinuerim; pater te a vitio arcuit; age patri gratias, quum te a vitio arcuerit; cave ne animus vitae sollicitudinibus se admisceat; magnum fovi in pectore meo amorem; in meo pectore magnus amor in te fotus est; quis hoc bellum movit? hostium duces hoc bellum moverunt; tua mens excita nunquam sedabitur; delete hace verba; historiam imperii ejus delevit; mala non sunt facilia deletu; pater tuus vitium delendum esse censuit.

Page 92, col. 2, vol. II.-LATIN-ENGLISH.

Teach me how I may escape these things; I did not receive the letter which should inform me what you were doing; I told you the affair; his father informs the judges concerning the injuries of your brother's reason; the judge must be informed of the cause of Augustus; your uncle will instruct you about your journey; it is fit and pleasant to teach those desirous of learning; I envy your master who for so large a fee has taught you to be wise in nothing; teach many scholars the Latin language; I must be taught to speak Greek; he taught my daughter to play on the lyre; they may the Greek language? teach these my sons music; gladly will I teach him to ride a horse and to use weapons; will you teach me teach you letters.

I

Page 92, col. 2, vol. II.-ENGLISH-LATIN.

Doce me quo modo tibi prodesse possim; filium tuam grammaticam docebunt; docui uxorem meam Latinam linguam loqui; me docent fidibus; Latinam linguam doctus est; doce eos Graece loqui; a patre doctus multa sum; musicam a sorore meâ docentur; nescio quid te doceam de belli evento; Latinam linguam docendi sunt pueri; doctus sum Graece loqui; multi discipuli a me Latinam linguam docti sunt.

THE MOUSE AND THE KITE.

A fuble by Esop.

A kite, caught in a snare, besought a little mouse to set him free by gnawing the meshes of the net (the meshes of the net being gnawed). Which being done, the liberated kite seized the mouse and devoured it. This fable shows what thanks the wicked are wont to give in return for benefits.

Les hommes sont comme les statues: il fait les voir en place.La Rochefoucauld,

Les hommes sont nés les uns pour les autres: il faut donc les instruire ou les supporter.-Idem.

La plupart des hommes ont, comme les plantes, des propriétés cachées que le hasard fait découvrir.-Idem.

ANSWERS TO CORRESPONDENTS.

The following extract from The Times of February 26, will be of some interest to a great number of our subscribers:-THE BookPOST. We are glad to find from an announcement in the Gazette that the book-post, which has now become an important channel for the diffusion of literature, will be commenced on the 1st of May between this country and the East Indies. The total charge from any part of the United Kingdom to any part of our vast Indian Empire for a book not exceeding half a pound in weight will be 6d.; not exceeding a pound, Is. ; not exceeding 21b., 23.; and not exceeding 31b. (the maximum by this post), 3s.

T. M. CROWHURST (Plymouth): Mensuration certainly.-LITTLE HARRY: Will receive forms one part of the verb to receire, viz, the future tense, will being an auxiliary verb to receive. In the question relating to Arithmetical scales, the radix is always mentioned in the name of the scale, thus: in the decimal scale, ten is the radix; from the Latin decem, ten. But, in order to make it all clear, take this table:

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A WOULD B. FARMER: Hebrew will come in its turn; Greek after Latin. A number is divisible by 8 when its three last figures are divisible by 8, because 8 is the cube of 2, and 2 is one of the factors of the number 10, the radix of the decimal scale. For 9, see p. 66, vol 1.

G. WILLIAMS (Bristol): See vol. I., p. 368, col. 2. line 20.-D. M. LANGLEY (Limerick): What he suggests will be done. We do not know the book he mentions.-T. H. (Somers town): Thanks, but too late to be acknowledged in the lessons.-SELF-TAUGHT (Duke-street) will obtain the case of mathematical instruments by applying at the office of the Society of Arts, St. John-street, Adelphi, Strand.-BYRD (Pontypool) is quite right as to the four sounds he mentions. The expense of colouring would be too great.DELTA (Barlby): See vol. II., p. 32-AIE: There is no attempt made to give the meaning of ch, as far as we can see; we think Aie is hypercritical; but we must no doubt consider this a benefit conferred on us; for

"Critics indeed are valuable men,
But hypercritics are as good again."

-R. B. W.: Greek will follow Latin. The best Greek dictionary is
Liddell and Scot's, of which there is an abridgment for the use of learners.
ERASMUS (Ashton-under-Lyne) must imitate the great man whose name
he has assumed.

E. L. M. (Holloway) will learn English composition by carefully studying our Lessons in English.-S. W. (Hull): We recommend the maps to be bound at the end of the volume to which they belong, where they can be most easily referred to.-G. GRIFFITII (Carmarthen): Under consideration. -J. D. B. wishes to know who is the publisher of a work on drawing issued by the Government School of Design.-A. T. M. should study the Lessons in Geography; his question is answered at p. 253, col. 1, line 35,

vol. II.

H. W. (Liverpool): Navigation will come in course.-W. II. HAGCOTT (Southampton): We do not know; try the members of Parliament for the northern district of burghs or for the western ditto in Scotland.-H. T. M. Dementate means infatuated, insane; meteyard, a staff of a certain length wherewith measures are taken; molar, having power to grind: nihility, nothingness, the state of being reduced to nothing; otiose, at leisure, unoc. cupied normal, according to rule, properly regulated, standard.-ALPHA (Brecon): His case is so peculiar that we can scarcely offer him our advice. We would recommend English and French, or English and Latin, to be studied together, and history, botany, &c., for recreation. Our object in inserting the Regulations of the University of London, was to give some clue or guide to the order and arrangement of studies.-T. WHITE (Codnor) and his friends will find some directions, with a splendid example as to the method of studying Euclid, in the "Self and Class Examiner in Euclid," price 3d., published by Mr. Cassell.-E. LORD (Manchester) and his friends are informed that the rule concerning "a vowel which comes before two consonants is long by position," is quite correct. To fix pencil drawings so as not to smear by contact with another leaf, pass over them a little milk and water, taking care that all the cream be first skimmed off; or a very weak solution of isinglass in water. The liquid should be passed over quickly with a flat camel's-hair brush.

R. S. W.: The value of x is found thus :

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ERRATUM.

LITERARY NOTICES.

ATHEISM CONSIDERED THEOLOGICALLY AND POLITICALLY. This Volume, consists of thirteen Lectures, by the Rev. LYMAN BEECHEE, D.D. (father of Mrs. H. B. Stowe.) These Lectures enter fully into the momentous question now at issue, or, at least, under discussion, between "Secularism" and Christianity. For close reasoning and eloquent declamation, these Lectures have rarely been surpassed. The Volume, just issued, is well printed, and is sold for 2s. 6d. bound in cloth. It is important in ordering this work, that John Cassell's edition should be specially named. GIN AND WATER; a pair of pictorial designs by Kenny Meadows, portraying the effects arising from the indulgence of those potent liquids. In the first, GIN, we have the interior of the drunkard's home, with a glimpse of the horrors which belong peculiarly to such homes; in the second, WATER, we see how comfort, cleanliness, and peace attend the steps of the temperate man. The contrast is well sustained, and the pictures-which measure 24 inches by 16 inches-cannot but be popular. We have had too many songs and pictures in praise of the drinking customs of our country, and are glad to perceive that our poets and artists are beginning to discover that they may get inspiration even out of water

"Wine, wine, thy power and praise

we

Have ever been echoed in minstrel lays; But water, I deem, hath a mightier claim To fill up a niche in the Temple of Fame!" These pictures, which should be framed and hung over every cottage chimney-piece, and on the walls of every factory, and workshop, and ragged school throughout all the land, can be obtained of every bookseller for one shilling. They are exquisitely engraved on wood, by Messrs. Henry Listen and William Measom.

THE AUTOGRAPHS FOR FREEDOM; containing, in addition to a New Story by Mrs. STOWE, authoress cf "Uncle Tom's Cabin," entitled "The Two Aliars; or, Two Pictures in One-The Altar of Liberty, or 1776; The Altar of, or 1850," a thrilling Narrative by FREDERICK DOUGLASS, entitled "The Heroic Slave;""Passages in the Life of a Slave Woman," by Annie Parker; "Placido, the Cuban Slave," by Professor W. G. Allen: "The Heroic Slave Woman," by the Rev. J. S. May, &c.; also, Contributions from the leading Writers in America on the Question of Negro Emancipation; and, on this side of the Atlantic, from the Earl of Carlisle, the Bishop of Oxford, Wilson Armistead, Joseph Sturge, &c.; with facsimiles of the Autographs of all the Contributors, Price Is., in boards; or bound in cloth, with Eight beautiful Engravings from designs by Gülbert and Willis, price Is. 61.

THE ALTAR OF THE HOUSEHOLD: a Series of Services for Domestic War

ship for every Morning and Evening in the Year; Select Portions of HF Writ, and Prayers and Thanksgivings for Particular Occasions; with an Address to Heads of Families. Edited by the Rev. John Harris, D.D., Priacipal of New College, St. John's Wood; Author of "The Great Teaeber;" "Mammon;""Pre-Adamite Earth," &c. &c., assisted by eminent contributors. The following are among the Ministers engaged in the preparation of THE ALTAR OF THE HOUSEHOLD-The Rev. J. Sherman, the Rev. W. Urwick, D.D., the Rev. W. H. Bunting, M.A., the Rev. R. Ferguson, LL.D., the Rev. F. A. Cox, D.D., LL.D., the Rev. Professer Lorimer, the Rev. Newinan Hall, B.A., the Rev. B. S. Hollis, the Rev. W. Chalmers, A.M., the Rev. J. Beanmont, M.D., the Rev. Samuel Martin, the Rev. William Brock, the Rev. John Kennedy, A..M, the Rev. William Leask, the Rev. Charles Williams, the Rev. W. W. Ewbank, A.M., the Rev. J. Stoughton, the Rev. W. Keid, the Rev. George Smith, &c. &c. The Work will be completed in Twelve Parts, one to appear on the First day of each successive month; the whole first-rate Artist. Parts I. to III. are now ready, price is. each, or in ene forming One Handsome Volume, with Frontispiece engraved on steel by a Quarterly Section, price 3s.

CASSELL'S EUCLID.-THE ELEMENTS OF GEOMETRY. Containing the First Six, and the Eleventh and Twelfth Books of Euclid. Edited by Robert Wallace, A.M., price ls. in stiff covers, or 1s. 6d. neat cloth.

THE SELF AND CLASS EXAMINER IN EUCLID, containing the Enunciations of all the Propositions and Corollaries in Cassell's Edition, for the use of Colleges, Schools, and Private Students, is now ready, price 3d.

THE ANSWERS TO ALL THE QUESTIONS IN CASSELL'S ARITHMETIC for the use of Private Students, and of Teachers and Professors who use this work in their classes, is just issued, price 3d.

THE LADIES' WORK BOOK, containing full instructions for every kind of Ladies' Work, in Point Lace, Knitting, Netting, Embroidery, Crochet, &c., forming the most splendid Book for the Work-table ever issued. This work contains an immense number of the newest Designs for Ladies' Werk, of every description, and is produced in a style perfectly unique. Pries 24.66. THE LADIES' DRAWING-ROOM BOOK, in which are introduced the choicest Engravings from the "Illustrated Exhibitor and Magazine of Art," and the" Ladies' Work Book;" the whole forming a beautiful Volume for the Drawing-room. The work is printed on fine Plate Paper, and got up in the first style of Art. Price 10s. 6d.

The PATHWAY, a Religious Magazine, price 2d. each Number, enclosed in a neat wrapper. The Fourth Volume has just commenced-Vols. 1. and II. price 2s. 3d. each, Vol. III., price 2s. 9d., neatly bound, are now ready.

UNCLE TOM'S CABIN, with Twenty-seven Illustrations on wood, by George Cruikshank, and an excellent Portrait of the Authoress-Three Editions of this popular work are now on sale at our office-a Drawing Room Edition, demy 8vo., price 4s. 6d. elegantly bound, with gilt edges; crown 8vo., neatly bound, gilt edges, 3s. 6d., or plain binding, 3s.

THE ILLUSTRATED EXHIBITOR AND MAGAZINE OF ART-The First Two Parts of a new and improved Series of this work, under the tile of the ILLUSTRATED MAGAZINE OF ART, are now ready, price One Shilling each. The Weekly Numbers are now enclosed in a neat wrapper, price 3d. In addition to numerous Engravings in the text, each number contains a £ne Engrave ing, worked on Plate Paper. With the first Part was presented a splendid View of the Interior of St. Paul's Cathedral, during the Interment of the late Duke of Wellington, printed upon fine Plate Paper, measuring eighteen inches by thirteen, in addition to four separate Engravings, and a large number of choice Illustrations, with which each Part is embelished.

Vol. II., p. 253, col. 1, line 24 from bottom, for north frigid read south Printed and Published by JOHN CASSELL, La Belle Sauvage-yard, Ludgategid. hill, London.-Mareli 19, 1853,

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