Otherwise.-Write the quantities to be added one after another, putting the sign + between them, and then simplify the expression by incorporating like quantities.

Note 1.-If any of the quantities be in brackets and the sign +be before the brackets, the brackets may be removed without altering the result.

29. ax3, a`x, y3, xy2, and 3by2.
29. a3-2ab3ab2 + 263, 3a — a2b — 4ab2 + 1063, 2a3
ab2 + 363.
- b3, and 5a3 - 4a2b
30. 23-

By brackets is meant the vinculum or parenthesis, already explained [Art. 21]. This is one of the most important things in the study of Algebra; its use is unlimited. If quantities be included in any manner between brackets or parentheses, If the they must be treated as a single quantity, that is, the result of the operation of the signs within the brackets is to be used instead of the quantities themselves, as a general rule. signs of the quan ties within the brackets be either plus or minus, or a combination of both, and if a factor be outside the bracket, each of the quantities within may be multiplied by that factor, preserving their signs, and the product will be the -ce; then same as if the result were multiplied by that factor. Thus, cx; or, if a + bx (a + b −c) = ax + bx c) = ex. Conversely, if the result of the quantities x (a + b within the brackets be multiplied by any factor, the result will h (a + b −c) x = be the same as if each of the quantities were multiplied by that -ce; then, ez = factor. Thus, if a + b xy( a + b −c) = -c. If several factors be employed, the same results c = n+p) = ax + bæ will take place. Thus, azy + bxy - nbcd + pbcd = bcd (m c) ay; and mbcd ·rxyz = xyz (p + q − r) = (a+b. (m-n+p) bcd; and payz +qxyz Expressions of this kind may be varied in-h, (p+q− r) xyz. definitely.

-

=

Note 2.-If the sign - be before the brackets, they cannot be removed without vitiating the result, until the signs of all the terms within the brackets be changed, viz., + into, and conversely.

EXAMPLE. TO 3bc6d + 26 — 3y, add +bg, and 2d + y +3x + b.

These may be arranged thus: 3bc6d2b-3y

5a x2+2x-5.

3a2b-6ab2

3x + 1, 2x3 + 6x2 + 5x + 3, 3x3- 2x2-x-1, and 49

c+d, and a + b + c - d
5e, and 5e6ƒ.
31. a+b+c+d, a − b + c + d, a + b
3c, 3c4d, 4d-
32. a- - 26, 26-
33. y3+2yz 3yz2, 2y3 + 2y2z + 5yz2, and 3y3 — 4y‡z — 2yz2.
S4. ax + bx, bx3- ca2, and ca3 + dx2.
35. mz2

nz, nz

pz, and 222

-2.

KEY TO EXERCISES IN LESSONS IN ALGEBRA.

EXERCISE 1.

= 37m +

h +

4 (a + b + c) — d.

EXERCISE 2.

1. The product of a and b increased by the quotient of 3 times h
a increased by the sum of b and c, and diminished by the quotient of
minus c, divided by the sum of x and y, is equal to the product of d by
divided by the sum of 6 and b.

2. If a be added to 7 times the sum of h and x, and from this sum,
the quotient of c less 6 times d, divided by the sum of twice a and 4,
multiplied by the difference of b and c.
be subtracted, the remainder will be equal to the sum of a and ǹ,

3. The difference of a and b, is to the product of a and c, as the
difference of d and 4, divided by m, is to 3 multiplied by the sum of
d, and y.

4. If the quotient of the difference between a and h, divided by the sum of 3, and b less c, be added to the quotient of the sum of d and the product of a and b, divided by twice m, the whole will be equal to the quotient of b times a multiplied by the sum of d and h, divided by a times m, lessened by the quotient of c times d divided by h increased by d times m.

14. 45a
15. 12 (a + b) + 3 (a + b), to 2 (a + b)
16. xy (a + b) + 3xy (a + b), to 2xy (a + b) − 4xy (a + b).
17. ax + aa, x + xxx, 4aa + 2x + ax, and 2ere.

18. y- yy + xy, 2xx + 10yy, to 4xy + by

19. aaa+ 4aaa, to 1 aa

20. 12yyyy - 10xx, to 20xx

LESSONS

IN ENGLISH.-XXVIII.
LATIN STEMS.

WE are about to lay before the student a large portion of the roots of the Latin language. In the study of them, he may become acquainted with the treasures of the Roman literature, and the tone and strength of the Roman mind. These lessons do not indeed, lie on the surface. Nevertheless, they are to be learnt For this purpose, the learner should by care and diligence. impress on his mind the preceding remarks, and remembering 3b (x + y) −4a (x + y) − 4 (x + y) − (x + y), to 4b (x + y) that a language is the mirror of a nation's mind, accustom 27. a (x + y) + 7a (x + y) + 5 (x + y) + 6b (x + y).

·10 (x + y).
24. −x + y + 6x (a - b) 7x, to 16y 15x (a - b) + 25.
25. — 4 (x + y) + 16 (x + y), to 15abc-
26. 5abc- 6xy + mn, a + 6abc + 14xy
3mn + abc.

15a-abc + xy

11a + 6mn, to 15xy - 17abc

Note.-As the expressions 2 (square x), y3 (cube y), etc., are used for the first time in the following exercises, the learner is referred to Art. 28:

himself to see and contemplate the Romans in their wordsthose unerring tokens of thought, those mental miniatures.

Of course it is only so much of the Latin vocabulary as exists in English that I shall set forth in these pages. The Latin

agri

cultur

agger

ali

equanimity, equilibrium.

animosity.

libration, equilibrium.

aerial, aeriform.
coeval.

agriculture.

culture.

exaggerate.

agent, agency.

actor, active.

amicable, inimical.

aliped.

altitude, exalt.

amic, imic

anim

vert

ad

ami,amor,amat amiable,amorous,amatory,

animate.

animadvert.
adequate.

ann, annu, enni annals, annual, biennial.

biped.

aquatic, aqueduct.

conduct.

arable.

artificer, artist, inert.
articulation.

asperity, exasperate.

bi

coerce.

audience, auditor.

Augeo

The meaning of many of the words given as examples the student will either know already or may deduce from the etymology. In other cases some additional aid may be required. That aid I shall supply in quotations and in such remarks as the several topics may seem to require.

"Those milks (in certain plants) have all an acrimony, though one would think they should be lenitive."-Bacon," Natural History." "Most satirists are indeed a public scourge, Their mildest physic is a farrier's purge, Their acrid temper turns, as soon as stirred,

The milk of their good purposé all to curd."-Cowper. Acer is properly that which is sharp, as the point of a spear, or the edge of a sword, that which pricks or cuts; whereas acerbus (acerbity) denotes that which is bitter to the taste. According to its derivation, edification is house-building. The spiritual house is intended, the metaphor being borrowed from the diction of the New Testament. Consult 1 Cor. iii. 9; xiv. 3; Ephes. ii. 21; iv. 12, 16.

"So that it is by the equilibre of the muscles, by the aid of a cosiderable and equipollent (equally powerful) muscular force in constant exertion, that the head maintains its erect posture."-Paley, “ Natural History."

"Government has coercion (restraint) and animadversion upon such as neglect their duty."-South,

Articulation is properly the making of articles, that is, small limbs or joints; hence dividing a flow of sound so as to produce separate and distinct sounds, that is, letters and syllables. This power belongs only to man. Accordingly, Milton, that great master of distinctive and descriptive epithets, gives as the characteristics of the human race that they articulate.

"The first of these, at least, I thought denied

To beast, whom God on their creation-day
Created mute to all articulate sound.”

Milton, "Paradise Lost."
"The former (fore) legs of this animal (the elephant) appear, when
he standeth, like pillars of flesh without any evidence of articulation.”—
Brown, "Vulgar Errors."

"Père Bougeant's third volume will give you the best idea of the Treaty of Munster, and open to you several views of the belligerent and contracting parties."-Chesterfield.

Derivatively considered, to combine is to put things together in pairs, but it is employed without this restriction to signify to put together generally.

'The impediments were - first, the negligence of the pastors; secondly, combinations, that is double benefices, when men having two cures could not sufficiently attend both."-Hales.

"Few painters have obliged us with finer scenes, or have possessed the art of combining woods, lakes, and rocks into more agreeable pictures than G. Poussin."—Hurd. c*

It is curious to see in incubation, the act of the hen in setting on her eggs, and incumbency, the condition of a clergyman sa occupant of a living, how the same stem, and very nearly the same letters, may come to signify things so very unlike.

Cadaverous comes immediately from cadaver, a corpse, and denotes the colour or complexion of a corpse. Cadaver, a corpse,

by its etymology points out the fact which denotes death, namely, falling, from cado, I fall. A dead body cannot stand.

LESSONS IN ENGLISH.

"The subject of the present chapter will be the offence of homicide, or destroying the life of man, in its several stages of guilt, arising from the particular circumstances of mitigation or aggravation which attend it."-Blackstone, "Commentaries."

Homicide, that is, in its corresponding Saxon term, manslaughter, denotes the general act of man-killing, leaving it to be decided whether the killing was or was not murder, that is, premeditated killing. Unpremeditated man-killing is generally termed manslaughter, as contradistinguished from murder. It deserves attention, that not one of these words, homicide, manslaughter, man-killing, murder (Ger. mord, murder; Fr. mort, death; and Lat. mort, death), conveys in itself the idea of "malice aforethought."

Clinical is a scientific word, and, like most of our scientific words, may have come to us from the Greek; for the Greek klino is the root of the Latin clino, and is similar to it in import. A clinical lecture is a discourse on a disease, delivered by the bedside of the patient. A clinical convert is one that is converted on his death-bed. In the early history of the churches, those were called clinici or clinical, who, wishing to have all their sins washed away at once, postponed baptism till their dying hour. See Gibson's remarks on the delay of baptism by Constantine, miscalled the Great.

"Horror stalks around

Wild staring, and his sad concomitant
Despair, of abject look."-Philip.

"I persuaded her to take, as hot as she could well drink it, every morning, a full draught of the decoction of centaury boiled in beer or ale."-Bayle.

Cordial, of Latin origin, has a corresponding word from the Saxon, that is, hearty. This is by no means a solitary case, as will appear from the ensuing list :

Latin.
Timid

Velocity

Effeminate

Edifice

Saxon, fearful.

swiftness.

womanish.
building.

fewness.

Latin.

Saxon.

Altitude

height.

Annual

yearly.

Aqueous

Auditor

watery.
hearer.

Paucity In incorporate, animadvert, and other words, the student is expected to make use of the information which he has already had supplied to him regarding prepositions in combination, as well as regarding prefixes and suffixes.

The Chinois, without cremation or urnal "Cremation, burning, is applied particularly to the ancient custom of destroying corpses by fire. interment of their bodies, make use of trees and much burning, while they plant a pine-tree by their grave.”—Brown, "Urn Burial.”

Capillary signifies that which is like hair; hence it is applied to the small vessels of the body, as the ramifications (branches) of the arteries, "the capillaries;" also to tubes; and attraction in tubes as fine as hair, is called "capillary attraction."

"A strict and succinct style is that where you can take away nothing
without losse, and that losse to be manifest."-Ben Jonson.
"To translate him line for line is impossible, because the Latin is
naturally a more succinct language than either the Italian, Spanish,
French, or even the English; which by reason of its monosyllables, is
far the most compendious of them."-Dryden.

The idea in succinct, girded, is taken from the custom prevalent
Compare
among the ancient Greeks and Romans of gathering up and
binding around the waist their long flowing robes, when they
were about to apply to any manual occupation.
Isa. viii. 9; John xiii. 4, 5.

Song of Solomon, or the Canticles," a
Some have termed the
Hebrew Epithalamium. The rage for autographs seems to have in a

ment are not known to exist.

measure subsided,

The autographs of the writers of the New Testa
The word apology sometimes signifies
The former is the older meaning of the
The monuments of Egypt are covered with hieroglyphics,
term.
The hieroglyphics of Egypt have for the most part been at length
defence rather than excuse.

deciphered. Exodus is the name borne by the second book in the
departure of the children of Israel out of the land of Egypt.

Bible.

This name was given to the book because it recounts the

To endeavour to improve yourself in composition, report tho following anecdote, as before, to a child or to a class of

children :

ESCAPE OF THE DUKE OF ALBANY.

King James III. of Scotland, after his marriage with Margaret,
Princess of Denmark, having disgusted his proud nobility by patro-;

nising and receiving into favour many persons of inferior rank, deep
-Alexander, Duke of Albany, and John, Earl of Mar-were forming
and dangerous intrigues were formed against him. By these minions
In 1482, Albany was committed to
and upstart counsellors he was speedily made aware that his brothers
the Castle of Edinburgh, where he was kept a close prisoner by those
conspiracies against him, and that the former aimed at nothing less
He had not been long in durance until he formed and
than wresting the sceptre from his hand-a fact which has since been
destruction.
Terrified by the mysterious fate of Mar,
proved by authentic documents.
matured a plan of escape, which, with desperate courage, he executed
in the following manner.
and aware that his day of trial was approaching, some of Albany's
The tower in
numerous friends in France or Scotland contrived means to acquaint
him that a small vessel, laden with Gascon wine, lay in the roadstead of
Leith, by which he might escape if he made an effort.
which he was confined was probably David's, for we are informed that
founded, where the height of the precipice seemed to bar all possi-
bility of escape." He had but one attendant (styled his chamber-
it "arose from the northern verge of the rock on which the castle is
chield) left to wait upon him, and to this trusty follower alone he
From the French vessel he received two small
revealed his intention.
runlets or barrels of wine, which luckily the castle-guard permitted to
be carried into his apartment untasted and unexamined. On opening
them in private the duke found that they contained Malvoisie, and,
what was of more importance, a strong rope and a waxen roll inclosing
an anonymous letter, urging him to lose no time in attempting to
escape, as the king's minions had determined he should die ere the
morrow's sunset; and the billet ended by an assurance that the boats

who knew that his accession to power would assuredly be their

come.

The

of the French vessel should await him at the shore of Leith.
first point to be gained was to lull the suspicions of the captain of the
guard, for which purpose the duke invited him to supper, and by
After gaming and drink-
succeeded in partially intoxicating them.
ing until the hour grew late, Albany found the moment for action had
pressing him and three of his soldiers to drink freely of the Malvoisie,
Rushing upon the captain he snatched a long dagger from his
he dispatched the intoxicated soldiers in the same manner, and, in
Having
token of his hostility and contempt (with the assistance of his
chamber-chield), he savagely threw the bodies on the great fire that
baldrick, and buried it repeatedly in his breast; then, quick as thought,
blazed in the stone fire-place of the tower; and there in their armour
secured the keys of the doors, they locked them as they retired, and
they broiled and sweltered like tortoises in iron shells.
We may imagine how the heart
proving too short, it slipped suddenly through his hands, he fell to
stealthily hurried to the wall, which they prepared to descend at the
the bottom, and there lay senseless.
mest retired part. The chamber-chield lowered himself first over the
beetling crag, which is two hundred feet in height, but the cord
Rushing back to his apartment in the tower, he
of the blood-stained Albany must have beat at this terrible crisis!
tore the sheets from his bed, twisted them into a rope, lengthened
the cord, looped it around an embrasure, and, lowering himself over
Every moment was fraught with danger, and his death or life were
the rampart, and the rugged rocks it overlooked, reached the bottom
There he found his attendant stretched on the ground,
hanging by a hair.
in safety.
with his thigh-bone broken. Unwilling to leave behind him, to the
mercy of his enemies, one who had been so faithful, Albany, with a
sentiment of gratitude which seems almost incompatible with his pre
vious ferocity, lifted him on his shoulders, and, being a man of gigantic
stature and uncommon strength, carried him thus with ease to Leith,
where they embarked without delay; and setting sail before the
rising sun brightened the German sea, cast anchor under the towers
of Dunbar, the patrimonial castle of Albany. During the whole
night nothing was known of his escape; but daylight revealed the
rope and twisted sheets hanging over the northern ramparts; there
His flight was discovered, and the half-
was immediately given an alarm, which the dreadful stench in David's
tower must have increased.
consumed corpses were found in the fire-place of his chamber.
Enraged and confounded, James III. refused to credit the intelli-
gence until he had examined the place in person.-Memorials of the
Castle of Edinburgh, pp. 52-55.