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(5.) Deux and second are, in this case, used in differently :
FRENCH WORDS AS A MEDIUU FROM THE LATIN TO THE ENGLISN. Charles deux, Charles second,
Charles the Second.
English. (6.) In speaking of Charles the Fifth, of Germany, and of ala, a wing
aile (of old aisle) aisle the Pope Sixtus the Fifth, the obsolete word quint (fifth) auctor, originator
author is used:
bounty bos, an ox
chufe canalis, a pipe
chief LESSONS IN ENGLISH.-No. XXXIX.
carmen, a song,
charm catena, a chain,
chain By Joun R. BEARD, D.D.
computare, to rockon
count cooperire, to cover
couvrir FRENCH STEMS.
cultellus, a knife
devil The words which the English owes to the Romance lan- diabolus, Satan
deigner of this number, by far the dignari, to think worthy
deign guages are very numerous.
ivory largest portion comes from the French. This portion is too ebur, ivory
strange large to be here enumerated, though a few specimens may be extraneous, outward
feretrum, e bier
bier given. Before, however, I proceed to set down instances, let
fierce it be observed that I shall prefer those which retain some
fealty marked resemblance to their originals, or still appear in their fidelitas, fidelity
feaulté pative form.
gigas, a giant
giant gubernari, to govern gouverner
to govern ENGLISH WORDS FROM THE FRENCH .
gula, the throat
enchanter incantare, to enchant
enchant From CHEVAL, a horse (Lat. Caballus), come
enmity Chevalier, a knight.
lectarium, a bed
litter Chivalry, knigh hood.
levare, to lift
to lift Cavalier, a knight, or horseman.
lex, a laro
meagre From CHARTRE or CHARTE, a charter (Lat. carta), come
maitre Chart, a sea-map.
main Charter, a writing bestoring pririlegos.
medietas, the middle moitie
moiety Chartist, a person desirous of a new charter.
mirabile, wonderful inerseille
marvel Cartel, á writing containing stipulations, &c.
nomen, a name,
noun Cartoon, a drawing on large paper, a painting.
numerus, a number
number Cartouch, a case for balls or cartridges.
nutrix, a nurse
nourrice Cartrage or Cartridge, a case for gunpowder.
oil Cartulary, a register ; a monastic record.
paganus, a villager
peasant From BARRE, a bar (the same word), come to bar, to hinder. panarium, a basket
pannier Barricade, a fence or temporary forlification.
passus, a step
pace Barrier, a boundary, or obstacle.
poor Barring-out, a boyish game.
peregrinus, a stranger pelerin
pilgrim populus, the people
people The following are a few separate instances-bottle; brilliant; prepositus, placed orer prévost
provost escape ; engagement ; flask; forage ; fiank; guarantee; guard; presbyter, an elder
priest garnish; grimace; hash; harangue; hardy , lodge; marquis; probare, to make good prouver
prove mason ; packet; robe; wardrobe; saloon; supper; dinner; pullus, a chicken
poultry (breakfast is Saxon); tirade ; troubadour. The words which puppis, the sterni
reason denote the various officers in civil government are mostly ratio, reason
receive Norman French, as might be expected from the conquest of recipere, to receive
regnare, to rule
reign England by William the Norman: e.g., king and earl are
round Saxon, but prince, duke, marquis, baron, count, mayor, &c.,
saveur are of French origin, at least so far as the English is
tegula, a lile
traitor The ignorance of older philologists may be exemplified in traditor, a traitor
view the derivation which they gave of parliament. Parliament is a word of French extraction, from the word parler, to speak ; A careful survey of a French lictionary on the part of one the ment, as the student now knows, is merely the termina. who is skilled in derivation, would bring to light an extent of tional suffix. But the wisdom of our forefathers made ment obligation owing by the English to the French language, of into mind, and stated that the parliament was so called because which ordinary students have no idea. I subjoin a few words men there freely spoke their mind! The history of this deri- by way of specimen, taken under several letters of the vation is no better than the philology, for in the French par- alphabet liament liberty of speech was not predominant.
FRENCH WORDS IN THE ENGLISH LANGUAGE. Another instance of philological ignorance is presented in
English, Latin. these facts. Crermudgeon, which Bailey, in his Universal
adagium Etymological Dictionary" (1731), describes as meaning a cove
aquila tous hunks, a pitiful, niggardly, close-fisted fellow, Dr. Johnson
aisle derived from the French cæur-mechant (bad-heart), append. ing the words Unknown Correspondent as the authority. Dr. angle
angulus Ash, taking the English appendage as the meaning of the antre (Sbakspeare) French words, gives the etymology thus : curmudgeon from caur unknown, and mechant correspondent !!
balămum French words have been a medium by which Latin words
bilis have come into the English, the extent of our obligation to
purgos (Greek) both those languages can be known only when we have seen boutique
apotheke (Greek) specimens of this transference.
Divide between (two),
divido, I diride cage cage
among (many) caisse
dubito, I doubt сар
Dwell io, at, on,
begierig, desirous of cendre cinders cinis
Embark in, on board of, cerise
embarquer, to go into a barque cherry
cerăsus chaire chair
bellus, beautiful chaloupe sloop
mergo I dip char chariot
Employ in, on, about, employer, to put to use cheminée chimney camínus
emulus, a rival cle or clef
amor, lors coin
coigne comté county comitatus
corpus couple couple copula
Report the following extract:duel
ON THE CHOICE OF AUTHORS.
If we are to read, it is a very important rule in the conduct of the epouse
understanding, that we should accustom the mind to keep the best etain
company, by introducing it only to the best books. But there is a face
sort of vanity some men have, of talking of, and reading, obscure, face
half-forgotten authors, because it passes as a matter of course that famine
fames fardel fardeau
he who quotes authors which are so little read, must be completely
phortos (Greek) fibre
and thoroughly acquainted with those authors which are in every fibre
man's mouth. For instance, it is very common to quote Shakspeare;
but it makes a sort of stare to quote Massinger. I hare very little
credit for beinz well acquainted with Virgil; but if I quote Silius foi
Italicus, I may stand some chance of being reckoned a great schofront
lar. In short, whoever wishes to strike out of the great road, and
to make a short cut to fame, let him neglect Homer, and Virgil, gai
and Horace, and Ariosto, and Milton, and, instead of these, read
and talk of Fracastorius, Sannazarius, Lorenzini, Pastorini, and gingembre
ginger zingiber golfe
the thirty-six primary sonnetteers of Bettinelli; let him neglect
everything which the suffrage of ages has made renerable and goût
grand, and dig out of their graves a set of decayed scribblers, Many French terms are employed in English either in their whom the silent verdict of the public has fairly condemned to ever native form or slightly altered, and of these some even in France lasting oblivion. If he complains of the injustice with which they are of modern origin. We have dragoon from the name of the I have been treated, and call for a new
trial with loud and imporsoldiers with whom Louis XIV. earried on the war, which received in the estimation of men of sense, he will be sure to make some
tunate clamour, though I am afraid he will not make much progress the name of his dragonades, against his French Protestant subjects noise in the crowd, and to be dubbed a man of very curious and in order to compel them to become Catholics. From the noun extraordinary erudition.--Sydney Smith. dragoon we have the verb to dragoon into. A roué, in slang language, a black-leg, is literally a wretch who deserves to be broken on the wheel - metaphorically one who has the same manners, as
LESSONS IN GERMAN.-No. XXXIX. the courtiers of the profligate Duke of Orleans, Regent of France, who is said to have given the name to his abandoned
I. Abhängen, likewise, signifies to depend upon, to be de-
dependent. Ex.: Er führt ein abhängiges leben; he leads a de.
EXERCISE 84. vogue many Gallicisms. Most blame-worthy is this defacement and corruption of our language, when they are perpetrated by Ab’hängen, See frucht, f. fruit; Fanarienvegel, W. historians of whom better things might be expected.
Geber'den, to behave; nary-bird; practice bas been well taken off by the Spectator" in No. 183 of Athingig
, dependent; Gemächlichy, comfort. Deffnen
, to open; that work, which is strongly recommended to the perusal of those Petin'gung, f. condi
Umstand, m. circum. who possess it or can readily borrow it.
tion, stipulation; Gera're, exactly ; stance; Having read the remarks in the “ Spectator," and read also
Darsin'ivilligen, to Gera'then, to turn out, In'abhängig, indepenwhat I have written in this lesson, let the student proceed to write
dent; an essay on
Gntzwei'en, dis. Hinaus', out, out Veridmä'hen, to dis. THE FRENCH ELEMENT IN THE ENGLISH LANGUAGE.
unite, fall out, there;
dain, despise ;
Hinaus'cilen, to hasten Wohlmeinen, to mean
Fü'higkeit, f. ability; out;
well, wish well; F. R.
Folge, f. sequel, con. Hinaut'werfen, to Zu'rringlid, obtrusire. Disqualify for, qualis, of what kind
throw out; Dissatisfied with, satis, enough
Ich fann nicht tarein'willigen. I cannot agree to it. Dissent from, sentio, I feel
Er wil'ligte unverzügʻlich tarcin'. He agreed (consented) to it un. Distinct from tinctus, dycd, coloured
Diese leute stellen sich als ob sie von These people act (place then-
selves) as if they were out of
o wiederfährt' ung in unserm Leben There happens to us in our lives
EXERCISE 85. ($ 15. 2. d.) manches Glüd und (many a) much happiness and An'geben, to give, spe. Kern, m. kernel; Il n'würdigkeit, f. mandco Unglüd. many a misfortune.
Kutscher, m.coachman; worthiness, indige Go wiederfährt' Manchem mehr There happens to many a one anstrengung, f. exer. Ordnung, f. order, re.
nity; Ehre, als er verdient'. more honour than he de
tion, effort, labour; gulation; Leller, m.plate;
Bereit, ready; Stale, f. shell; Verter'ben, to spoil, Ter Vogel ijt zum Fenster þinaut'. The bird has flown out of the Beruf'
, m. calling, vo- Schwächling, m. weak. corrupt, destroy ; gefloʻgen. window.
ling, weakly per- Berzich'ten, (auf Erwas), Die Freunde entzwei'ten sich. The friends quarrelled (sepa- Beruhigen, to quiet; son ;
to resign, i. e. as a rated themselves.)
Bestim'men, to fix, de. Umíclic'ßen, toin. privilege or a claim Die Pflaume ist ein Steinobít. (The) plums are a stone-fruit. termine;
close, surround; on anything; Sie verlie'ben sich darauf', taß er They relied upon his keeping Dafür, therefore, for Umwerfen, to upset; Vor'gehen, to go before, jein Versprech'en halten würte. his promise.
go too fast; Man soll nie eher in eine Sache One should never asscnt to a Danf, m. thanks, ac- ly, irregular, con. Wagen, m. carriage; ein'willigen als bis man tisfel'be thing, before he has well
Weisheit, f. wisdom; wohl überlegt' hat.
considered it (the same.) Erret'ten, to save, res. lInterlasī'en, to leave Wesen, n. being, exisIst es nicht, als ob dieses Volt midy Is it not, as though this people eue, deliver:
off, omit, fail; tence: zum Gotte mache? (Schiller.) would make me a God? Furdit, f. fear, dread;
Zerbre'den, to break
(in pieces). 1. Dieses Jahr ist das Obst, sowie alle Früchte, wohl gerathen. 2. Dieser Baum trägt jedes Jahr sehr vieles Obst. 3. Ist alle Frucht Obst? Ich kann nichts dafür, taß ich mein It is not my fault, that I have 4. Nein, nicht alle , sondern nur solche, tie ($ 65. 2.) an Bäumen wächst. Dicie Uhr geht vor (or, zu schnell), This watch goes too fast and
Geld verlo'ren habe,
lost my money. 5. Dieser junge Maxn verläßt sidy zu viel auf seine Verwantten und zu
und jene geht nach, (or, zu lang. that (one) goes too slow. wenig auf seine eigenen Fähigkeiten. 6. &r verläßt sich darauf, daß wir
sam). ihn die nächsten Woche besuchen. 7. Er verließ fidz darauf, daß ihm Hat man mein Zimmer in Ordnung Has my room been put in
order ? Gott helfen werde.
gebracht'? 8. Wer sich zu viel auf Andere verläßt, kann leicht getäuscht werden. 9. Ich Halte (Sect. 69. II.) viel auf meine Freunde. In der Reihe seiner Schmeichler hat in the ranks of his flatterers he
er feinen wahren Freund.
has not a true friend. 10. &r yalt viel auf ein gemäßliches Leben. 11. Dieser Mann halt 8: giebt Viele, die glauben, daß in There are many who believe, zu viel auf sich und seine Klugheit, weßhalb er den Rath wohl. den meisten Fällen das Glüd over that in (the) most cases, the meinender Freunde verschmäht. 12. Nur unter dieser Beringung fann Unglüd eines Men den vom 31'. fortune or misfortune of a iờ barein willigen. 13. Im willige tarein, in so fern (Sect. 79. V.) fall ab'hänge.
man depends on chance. cf feine üblen Folgen hat. 14. Er willigte varein, ohne mit allen leben Sie wohl, mein Ferr, ant em. Parewell, sir, and please re
pfeh'len Sie mich gütigst Ihrer member me kindly to your Schwierigkeiten befannt zu sein. 15. Dieses Rind thut gerade, als ob es
lady. hier zu Hause wäre. 16. Der Matrose ftellte sich, als ob er von Sinnen wäre. 17. &r geberdet fich, als ob ihm ta& größte Unrecht widerfahren
1. Sie fönnen nichts safür, daß Sie su unglüdlicy find. 2. Er fonnte fei. 18. Dieser Mann ftellt fidy, als ob er beleitigt wäre. 19. Er stellt nichts dafür, dieses Olas zerbrochen zu ħaben. 3. Id, fann nichts dafür
4. Die Gründe dafür werde ich angeben, wenn fich wie ein Kind von fünf Jahren. 20. Der Nachbar warf den Zu- geben, als meinen Dank. dringlichen zur Thüre hinaus. 21 Der Knabe cilte zur Thüre hinaus, es verlangt werden sollte. 5. Rönnen Sie mir sagen, (Sect. 83. I.) wie als ich dieselbe öffnete. 22. Zur Thüre hinaus, wer sich entzweit! (Göthe.) viel Uhr (Sect. 25. IX.) es ist? 6. Nein, tenn meine Uhr ist stehen 23. Es hängt ganz von Umständen ab, ob ich schon nächstes Jahr nach geblieben. 7. Steht Ihre Ilhr schon lange? 8. Ja, beinahe cine Stunde. Amerifa reise oder nicht. 24. Gi hängt sehr von Imständen ab, was er 9. Meine Uhr geht zu schnell, sie geht beinahe eine halbe Stunde vor.
11. Belen Sie thur wird. 25. Gin To abhängiges Leben die Brucrn in Deutsdıland 10. Die Uhr meines Freundes geht fünf Minuten vor. führen, ein eben so unabhängiges führen sie in Amerifa. 26. Ganz unab. wohl, unt vergessen Sie nicht, mich bald wieder zu besuchen. 12. leben
Sie wohl, mein Herr! 13. Wann wollen wir zusammen Herrn N. hängig vermag fein Mensch auf Erten zu werden.
besuchen? 14. Ef þångt ganz von Ihnen ab (Sect. 81. I.), welche 1. Last year the fruit did not turn out well. 2. This tree Zeit Sie dazu bestimmen wollen, ich bin zu jeder Zeit bereit, mitzugchen. yields fruit but seldom. 3. This young gentleman relies too 15. Ei hängt vor Ihnen ab, diese Familie zu erretten eter zu verderben, much upon his abilities. 4. No, he does not rely too much upon his abilities, but he knows it is not well to be de. 16. Der Nachbar arbeitet in seinem Garten und sucht tenselben in pendent upon those of others. 5. I rely upon you that you will Ortnung zu bringen. 17. Bei Adler Anstrengung bringt er diese Sadie visit me next week. 6. Do exactly as if you were at home. nicht in Ordnung. 18. Er suchte mich in tie Reihe seiner Kameraten 7. The criminal acted as if he were out of his senses. 8. This
zu bringen. 19. Es hält schwer (Sect. 46. II.), einen unordentlichen man acts exactly as a child. 9. Where is your canary.bird ? Menschen an Ordnung zu gewöhnen. 20. Nacy vicler Müße hat er die It is flown out of the window. 10. How can I assent to a thing which is against my inclination? 11. Whoever quarrels Rechnung in Ortnung gelradt. 21. Wer an tem Fuße eines steilen shall be expelled the house. 12. It depends upon circum- Berget stehen Weibt und aus Furet vor Anstrengung denselben zu et. stances, whether I shall go to my friends. 13. Every man Eliminen unterläßt unt lieber auf tie litöne Aussicht verzichtet, ter zeigt strives to be independent. 14. Depend upon it that I shall not damit an, taß er ein Schwächling und eines solchen Genussos unwerth help you again.
ist,-und wer aus eigner Sdult in ter Mitte seiner geistigen Ausbildung SECTION LXXXII
stehen bleibt, und den süßen Kern der Weisheit entbehren will, weil eine
rauhe und Karte Scale denselben umschließt, der zeigt ebenfalls nicht Nichts or, nicht dafür fönnen, signifies "not to be in fault, or
nur seine Unwärtigfeit, denselber zu genießen, an, sondern auch, wie to blame," &c.; as, ich fann nichts dafür ; it is not my fault, or wenig er den Beruf und die Pflicht die Menschen, als eincs geistigen I cannot help it; literally, I cannot, or can nothing therefore.
Wesens, erkannt hat. Er fann nicht dafür, daß er so arm ist; he cannot help it, i. e. he is not to blame that he is so poor. So also interrogatively;
1. It is not my fault that you have had the mishap. 2. You as, fann die Welt etwas bafür, daß sich ein großer Beist in ein saled. could not give me anything for it, except his thanks. 4. He
are not to blame that the servant has broken the plate. 3. He 888 Kleid verstedt? (Rabener.) Is the world t blame, that a could not help it, he only spoke the truth. 5. Is the coachman great soul conceals itself in a plain dress? That is, Die Welt to blame, that the carriage was upset? 6. No, he is not to be tann nichts bafür.
blamed, for the horses could not be quieted. 7. Can you
til me what time it is: $. X3, wh gra lo sr. 9.'-22:14: === S Sirée : 10 fx tie bou o! sy dapat di uso my parest Jeg rin nge: 1. S. 58 1. bares il, Badami peale do Krzet, to nezve at i. Then it was azi ze: a stessa 19 355 52:et's 111: depo ka! ise pou !!
xts 54 you fread; I 22:23: le ready to accompany stata 11 5.a znz Sárzy kz23 yotte 12 kortase a more and daik, sorerty and tzt. It= 524 is: Stez tzzs za kr 12 Se seits risises, all depend on the ri. o GA
112.35 gebe zat er alle 4 Er ecz to na
3 :: ::1 otte ! 16 Sie Izrgo koka z gen SECTIOY LUXXIII.
ili lét eine 242376 15 6.23 seeria ; "es en warteten, (to understand one's self, rih * signifies to get 4.7 19. je tu ti u bezobete : 91 ans ke a jege of, to be skibed ir.. Ex : fr : 41
**lasyn Saatgag betur èz ? Si. 36 tu šetze he is ski..ed in everytisias,
! So Frezen gegaat 22 : Isza Su sic ece Et se. 1e&t 14 (literal's, it belerads its!!, i. e it is 'në 23. 24 mi tre att ta 24 ore 24. 3 certud, is sell-evidest, avsTI 6 oct phrase, “c course,
. ** *a krébez cica? 23. * Ebene en ene Stra: as a trat. Of coure." Ex : G! ett fint crê *:
24:tea lemnitiba eztietat secca 2234 Bets soos fb: From 1:1 14.0 68 geen rit of course,
a matter of course, ! m d my parents. Toe word 4 wuu awi tariet, eter ici es is jer: Eli. 27. Ta Erisse : „81r! 4* naturally, is o n und in the same manner; as, et les fan lazge gereg tes et ten zerren Sherz za Eat at ta ei 1:2141 mm ti íc Ins, of cours, it must be 10
šot babe terrestre napea 25 I4 13 raz zk tl 1. @agen answers to the English ray or t-il : to tell or et jei tean, bas mein Srata berair mata se in zizt 2: partate, however, is often e paregod is. German by ten taas heute am glad recea Bad beurtigen eie tez sikre Ex : 14 ilgte et? Wat dit! lie eay? Fat et Yhain getest? Na#miaz, eziger geicat pene 30. G: z Mimae is tz Siz: What has he told, or said to you? Tez alte Istzsie czibtc engelašca, es iei tean, tas t einen B:5 $35 eine zúhrente Oristie, the old sailor told, or related a moving (affecting) story
I. Tell me if that is your own horse: 2. Tha: farmer told
me many things about agriculture. 3. I shall not go out toII. fort is often answered in English, b: “ gone, off,", &c day unless necessity compels me. 4. You will not enter the Ex : 34 « ídca large ført? Hlas he already been gone long?
kingdom of hearen, unless you acknowledge the blessings of III. 6. kei team, tab=unless, except, &c, Ex.: Ter Bienia God. 6. My brother went off yesterday and we have heard Linn nicht mahrt zit glüdlich sein, eg íci renn, tar e tugent tait iei; notiing of him. 6. It is self-evident that without nourishment man can not be truly happy, unless he be virtuous Wahrhet, man, animals, and plants cannot exist i. My knife is gone, marlem, id faze tit: G: fei renn, 1:5 Jenant ron Neuem gebeten and none of the children know where. 8. Our money is all wette, fann er tae Reid Wettes niat It'ent;
gone. 9. I know very well how far I have to go in this matter
10. Where do you go to? 11. I am goiag to my brother. 12 EXERCISE 86
How far have you to go? 13. Just to the park. 14. What Anwalt, m. attorney, Sin'tcmmen, to come, Sterz m. jest, sport; distance have you to go? 15. About three quarters of a mile. defender;
Ctéren, to trouble, 16. He believed the time had now arrived to open his own Lahnen, to open, (as Pirl, m park; disturb;
path through life. a path), facilitate; Pflanze, f plant, ve. Türich, Turkish; Gme, n end;
Berschwen’teriid, prodicrt'gehen, to go away; Stein, shine, gal, lavish, pro
LESSONS IN ALGEBRA.-No. I
INTRODUCTION. elche zu geben haben?
to go in the matter? (how far | Aet. 1.-ALGEBRA is a general method of soleing problemas, and you are at liberty to go)
of inrestigating the relations of quantities by means of letters and Ginen vir langen (S 120. 4.) Spa How long a (pleasure) ride
signs. gier'riit haben Sie gemacht? have you taken?
ILLUSTRATION. 6. versteht sich von selbst, taß ein It is self-evident that a lazy
Prob. 1.-Suppose that a man divided 72 pounds among his three Fauler @duler feine Fortidritte scholar can make no ad.
sors in the following manner :-To A be gave a certain number of maden faun.
vancement Dieser Italie ́ner reisteht' fim auf This Italian is a judge of music gave the remainder, which was half as many pounds as A and a
pounds; to B he gave three times as many as to A ; and to c be Durit'.
received. How many pounds did he give to each : Herr M ist heute Morgen fort nact Mr. M. left (is off, this morning
1. To solve this problem arithmetically, the pupil would reason Moro- A me'rifa
for North America.
thu3 : A had a certain part, i. e., one share; s received three So weit er audy von hier wohnt. As far as he resides from here, times as much, or three sharcs ; but c bad half as much as A and
und so lange ich auch zu gehen and so great a distance as I B; bence he must have received two shares. By adding their Yabe, se boju'dhe it ihn tennoch have to walk, I, nevertheless, respective shares, the sum is siz shares, which, by the conditions of all: Inge.
visit him every day. the question, is equal to 72 pounds. If, then, 6 shares are equal Wuhin' eilen Sie so schnell? Whither are you hastening so to 72 pounds, 1 share is equal to è of 72, viz., 12 pounds, whick
is a's share. I had three times as many, viz., 36 pounds, and c 3d gehe zu dem Zahn'arzte. I am going to the dentist.
half as many pounds as both, viz., 24 pounds. Die Sache sei nun wie sie wolle, id; Well, be it (the thing) as it may 2. Now, to solve the same problem by algebra, he would use
werde ihm nicht verzei'hen, es sei I shall not forgive him, unless letters and signs, thus : benn, taß er mid; um Entsoul. he ask my pardon.
Let x represent a's share ; then by the conditions, tigung bitte
X X 3 will represent b's share ; and 1. Der Dieb ist reinc& Verbrechen$ überführt worten 1111t es rersteht
4x = 2 will represent c's share. rich von selbst, daß er l'estraft werden wirt. 2. Der Vater ist feit diesem Then 6x=72, for the whole is equal to all its parts ; and Is=12
Add together the several shares, or a's; tbus 3+3+ 25 562. Morgen fort unt bio felt noch nicht wieder zurückgefehrt, 3. Das Buchy pounds a's share ; 3x=36 pounds e's share; and 2x=24 pounds if fort und feiner dieser Schüler will ($ 83. 8. Rem.) wissen, wo es hinc's share. gefommen ist. 4. Meine Meffen sind fortgegangen, chne zu ingen wohin
Proof.–Add together the number of pounds received by each, fie gehen würdent. 5. linser Obst ist alle. (Sect, 41. III.) 6. Auch
and the sum will be equal to 72 pounds, the amount divided. noch so vieles Velt wird all, wenn man verschwenderiset ist. 7. Der represent the number of pounds which a received by ... Second, to
In this algebraic solution it will be observed: First, that we türkische Raiser Soliman II Prigte furz vor seinem Tote: , meiste Kräfte obtain B's share, we must multiply A's share by 3. This multisk
cation is represented by two lines crossing each other like a capital | If the first is less than the other, the character < is used ; as X. Third, to find o's 'share, we must take half the sum of A's and a<b, i. e., a is less than b. In both cases, the quantity towards B's share. This division is denoted by a line between two dots. which the character opens, is greater than the other. Fourth, the addition of their respective shares is denoted by another 16. A numeral figure is often prefixed to a letter. This is called cross formed by a horizontal and perpendicular line. Take another a co-efficient. It shows how often the quantity expressed by the example:
letter is to be taken. Thus 26 siguifies twice b; and 96, 9 times b, Prob. 2.-A boy wishes to lay out 96 pence for peaches and or 9 multiplied into b. oranges, and wants to get an equal number of each. He finds that The co-efficient may be either a whole number or a fraction. he must give 2 pence for a peacli, and 4 pence for an orange. How Thus fb is two-thirds of b. When the co-efficient is not expressed, many can be buy of each ?
1 is always to be understood. Thus a is the same as la, i. e., once Let x denote the number of each. Now, since the price of one a, or one timea. peach is 2 pence, the price of x peaches will be x X2 pence, or 2.1 17. The co-efficient may also be a letter, as well as a figure. In pence. For the same reason, x x 4, or 4x pence, will denote the the quantity mb, m may be considered the co-efficient of b; price of x oranges. Then will 2x-1- 4x, that is, 6x, be equal to because b is to be taken as many times as there are units in m. 96 pence by the conditions of that question, and 1x is equal to . of If m stands for then mb is six times b. In 3ube, 3 may be con96 pence, viz., 16 pence, which is the number he bought of each. sidered as the co-efficie:it of abc; 3a the co-efficient of bc; or 3ab
2. QUANTITIES in algebra are generally expressed by letters, as the co-efficient of c. in the preceding problems. Thus b may be put for 2 or 15, or any 18. A simple quantity is either a single letter or number, or other number which we may wish to express. It must not be several letters connected together evithout the signs + and inferred, however, that the letter used has no determinate value. Thus a, ab, abd, and 8b, are each of them simple quantities. Its value is fixed for the occasion or problem on which it is employed ; 19. A compound quantity consists of a number of simple quan. and remains unaltered throughout the solution of that problem. tities connected by the sign + or -. Thus a+b, d-4,6--0+ But on a different occasion, or in another problem, the same letter 3h, are each compound quantities. The members of which each may be put for any other number. Thus, in prob. 1, x was put is composed are called terms. for a's share of the money. Its value was 12 pounds, and remained 20. If there are two terms in a compound quantity, it is called a fixed through the operation. In prob. 2, a was put for the num- binomial. Thus a +b and a-6 are binomials. The latter is also ber of each kind of fruit. Its value was 16, and it remained so called a residual quantity, because it expresses the difference of through the calculation.
two quantities, or the remainder, after one is taken from the other. 3. By the term quanlity, we mean anything that can be multi. A compound quantity consisting of three terms, is sometimes called plied, divided, or measured. Thus, a live, weight, time, number, a trinomial; one of four terms, a quadrinomial, &c. &c., are called quantities.
21. When the several members of a compound quantity are to 4. The first letters of the alphabet, a, b, c, &c., used to be subjected to the saine operation, they must be connected by a express knorrn quantities ; and the list, z, y, x, &c. letters, those line ( -) called a rinculum, or by a parenthesis (). Thus which are unknown.
2-5 +c, or a
-(6+c), shows that the sun of b and c is to be 5. Known quantities are those whose values are given, or may subtracted from a. But a--hte signifies that 6 and c is to be be easily inferred from the conditions of the problem under con- subtracted from a, while e is to be added. sideration.
22. A single letter, or a number of letters, representing any 6. Unknour quantities are those whose values are not giren but quantities with their relations, is called an algebraic expression, or required.
fornia. Thus a+b + 30 is an algebraic expression. 7. Sometimes, however, the given quantities, instead of being
23. Multiplication is usually denoted by two oblique lines expressed by letters, are given in figures. 8. Besides letters and figures, it will also be seen that we use and 6 X 3 is 6 times 3, or 6 into 3. Sometimes a point is used to
crossing each other, thus X. Thus a xb is a multiplied into b; certain signs or characters in algebra to indicate the rclations of the indicate multiplication. Thus a .6 is the same as a Xb. But the quantities, or the operations which are to be performed with them, sign of multiplication is more commonly omitted, between simple instead of writing out these relations and operations in words. quantities; and the letters are connected together in the form of a Among these is the sign of addition (+), subtraction ( - ), equality word or syllable. Thus ab is the same as a . b or a xb. And =), &c. 9. Addition is represented by two lines (+), one horizontal, the is to be multiplied, a rinculum or parenthesis is used, as in the case
bede is the same as b XoXd X e. When a compound quantity other perpendicular, forming a cross, which is called plus. It
of subtraction. Thus the sum of a and b multiplied into the sun signifies “ more," or " added to." Thus a tl signifies that 6 is to be added to a. It is read a plus 6, or a added to b, or a and b.
of c and d, is atbt etd, or (a t.b) X (c+d). And 10. Sultraction is represented by a short horizontal line (-)|(6+2) X 5 is 8 X 5, or 40. But 6+2 x 5 is 6 +16, or 16. which is called minus. . Thus, a--/ signifies that 6 is to be "sub'. When the marks of parenthesis are used, the sign of multiplication is tracted” from a; and is read a minus 5, or a less b.
frequently omitted. Thus (x+y) (x --y) is (x + y) X (r—y). 11. The sign + is prefixed to quantities which are considered of them is called a factor. In the product ab, a is a factor, and
24. When two or more quantities are multiplicd together, each as positive or affirmative; and the sigu posed to be negative. For the nature of this distinction, see Arts. so is b. In the product xX(atm), a is one of the factors, and 36 and 37.
atm the other. Hence every co-efficient may be considered as a 12. The sign is generally omitted before the first or leading factor., (Art. 17.). In the product 3y, 3 is a factor as well as y. quantity, nnless it is negative; then it must always be ecritten factors are taken, which, being multiplied together, will produce
25. A quantity is said to be resolved into factors, when any When m sign is prefixed to a quantity, + is always understood. the given quantity. Thus 3ab may be resolved into the two Thus a too is the same as the t-b.
13. Sometimes both + and (the latter being put under the factors 3a and b, because 3aXb is 3a). And 5ann may be former, +) are prefixed to the sanic letter. The sign is then said be resolved into the two factors 2X24, or 3X16, or 4X12, or
resolved into the three factors 5a, and m, and n.
And 48 may to be ambiguous. Thus a + b signifies, that in certain cases, com. 6X8: or into the three factors 2X3X8, or 4X6X2, &c. prehended in a general solution, b is to be added to a, and in other 26. Division is expressed in two ways: 1st. By a horizontal cases subtracted from it.
line between two dots + , which shows that the quantity preceding Observ.-When all the signs are plus, or all minus, they are said it is to be divided by that which follows. Thus, a--c, is a to be alike; when some are plus and others minus, they are called divided by c. unlike.
2nd. Division is more commonly expressed in the form of a 14. The equality of two quantities, or sets of quantities, is expressed fraction, putting the dividend in the place of the numerator, and by two parallel lines =. Thus a+b=d, signifies that & and together are equal to d. So 8+4=16--4=10+2=7+the divisor in that of the denominator. Thus - is a divided by b. 2 + 3.
b is. When the first of the two quantities compared is greater 27. When four quantities are proportional, the proportion is than the other, the character > is placed between them. Thus expressed by points, in the same manner as in the Rule of Propora> b signifies that a is greater than b.
tion in arithmetic. Thus a:b::c:d signifies that a has to b, the