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EXAMINATION PAPERS

TFE CORNWALL COUNTY

GRAMMAR SCHOOL.

j-TTHTf], laex

Pd*^^

PEINTED BY JOHN LOVELL. AT THE CANADA DIRECTOEY OFFICE, H^
IT. NIOBOLAS BTRIBT, HONTBIAIi.

1861.

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EXAMINATION PAPERS

THE COENWALL COUNTY

GEAMMAE SCHOOL.

o-XTxa-JSi, xaei.

PEINTBD iJY JOHN LOVELL, AT THE CANADA DIRECTORY OFFICE,

1861.

€0mw»U €ttmi^ (^xmmm ^(Uttl

Bead Jfosfer.— Rev. H. W. DAVIES,

M.A., Trin. Coll., Toeonto.

Assistant Master.— R. WILSON,

Victoria College, Cobofro.

Mathematical Examiner.— ANOVS HAY, Esq.,

Normal School, Toronto.

ORDINARY EXAMINATION.

LATIN COMJrOSITION.

In the famous case of Catiline's conspiracy, as the evidence was
clear and the danger extreme, the accomplices in it were executed
notwithstanding the Porcian law ; and this was done by order of
the Senate, witho ^t either hearing them make their own defence
or admitting them to claim the right which the Valerian law gave
them, of an appeal to the people. Yet that whole proceeding was
chiefly directed by the two greatest asserters of public liberty that
ever lived — Gate and Cicero ; and Ca3sar, who opposed it on pre-
tence of its being against the Porcian law, was for that reason
suspected of being in the conspiracy.

LATIN.— II.

OVIDS FASTI. B. 1,

1. Translate 45 — 62. Explain Tria verba. Sq)tis, qui nono

rcdit. Construction of officii. Give the divisions

of the Roman month, with the derivation of their names. Write
out in full and give the corresponding days in our calendar :

Prid. Id, Jan.
A.D. xix. Kal. Feb.

2, Translate 89 — 112. With notes on Jane l\ »
Chaos, aer. Conjugate edo, disco, cano^ abeo, a

3. Translate 587 — 616. Explain atria, ceras, notai,v,
quema corona.

4. Translate 709—724. Why is 30th day of the month
written III. KAL. Explain Frondibus Actiacis, tuba, per ennet.

5. Translate and explain :

Sustinet in vidua tristia sign i domo.
Farraque mixta sale. Ora vides
Hecates in tres vergentia partes.
Janus Agonali luce piandus trit.
Traxerat aversos Cacus.
Scan lines 520—524.

LATIN.-III.

0\U) AND VIRGIL.

Certamen inter Ajaceni et Vlystem tie annis AchiUis.

1. Traaglate 34 — 42. Explain nulloque sub indlce, and give
principal parts of the verbs.

2. Translate 238—246. State difference between aut and vel.
Distinguish between sors md/ors.

3. Explain the following, with grammatical construction of those
marked *

Saxum grave Sisyphon urget. Te . . . cxpositum Lemnos
haberet. Quo successore eagitt® Herculis utuntur. VeruB
furor (giving Greek equivalent for vems and vemx). dictum
crimen. Resupinum. Manifestabit latentem. Proavos arid
pronepos (with ascending and descending scale.) Deus est in
utroque parente. Natam mactare Diangc. Vulncra ipso pulchra
loco. *Pretio objecta. *Si8 licet. Eripere *3ede Deam. Ten-
toria Rhesi. Quos *ho8ti nuper ademi. Ex praecipiti pet^ndum.

4. Write short notes on the following names: Telamon.
Pceantia proles. Palamedes, Dolon. Cylleniua. Menelaus.

VIRGIL.

5. Sketch the adventures of iEneaa as contained in the First
Book of the JEneid.

G. Translate B. I. 131—141. Explain the t«rms aposiopesis
and JimdladyK. Distinguish between fuhs and fiducia, career and
C4xrcere8.

7. Translate 172—194. Ipsa, what is the force ? Numen
what? Extemph derivation? Explain nntiqun sub rcUgione,
Distinguish between ultro and ^-pontc.

8. Translate B. II. 200—227, Give grammatical construction
of oculoB. Distinguish between cJypeus, parrm, and scutum.

U. Translate the following, and explain grammatical construc-
tion of the words in italics :

Me ne incepto desistere. Septem praestanti cot-pore nymphae.
Levat ipso tridentl. Oscula libavit natae. Nee vox hominem
Bonat. Et niulto nebulae circuf dea fudit amictu. Auro corpus
vendcbat. Non metus officio ne te certasse priorem poeniteat.
Non opis est nostrac. Vina coronaut. Instar mentis equum,
Inclusos utero Danaos ct pinea furtim laxat claustra Sinoii.
Explain this construction.

10. Parse the following words: Pergama, aethera, instamus,
implicat, digerU. Give the synonyms of the following, with their
meanings: Memini, dives, mens, tcmplum, cusis, accipio, and
opperior. Give the adverbs derived from Im and Ilk ; and dis-
tinguish between sic and Ita.

11. Why is the metre called Hexameter? What is a spon-
daic line? Scan lines 1, 2, 3, and 93, Book II., explaining
synaUepha.

LATIN.-IV.

SALLUST AND CICERO.

1. Translate Catilina Ch. LI. Omnis— fecere, giving the
synonyms of avimui^. Explain genvs poena' iiovcv, and explain
Lex Porcia.

2. Translate Ch. LII. Quare — possidct.

3. Translate Ch. LVIIL Si relinquerc— rclinquatis ; and give
the government of pace.

4. Parse the following words : pccora. prcctorki, conciderant,
occiderant, illcxcmt, mpessifc.

Explain the following, and distinguish between the synonyms :
Paticns incdicv ^paries, cxkhnirc, cvocatl, potcntia, gmidhm, egcs-
tas, dchihm, rcpudlarc, nutria wnsfructa, vlgilia\ ante diem
scxtum, a patribiis scc<;88it.

5. Give the divisions of the Roman month, derivation of names,
and express in Latin form, June 3, 10, 29, 30.

G. Translate CiCEBO IN Catilinam, Ch. L Quousquc— vcnit.
explaining iinnw — vcw, and giving derivation of immo. Ch. I i .
Cupio—moUentcM ; why vie Ipse and not me ipsum ? Conjugate
molior, molUo^ and molo.

7. Translate Ch. VIL Nullum— dcsinam ; with notes.

VIRGIL AND HORACE.

1. Translate B. VL 868— 886.

2. Translate Odes B. L XXII. 1—16. XXVIII. 7—15,
explaining allusion in Panthoidcn. XXXIV. 1—12, with notes
on sapicntio', Diespiter, per purum, tonantet.

3. Ode XXXV. Give the 4 objecta in respect of which For-
tune 18 here invoked. Explain rara Fides velata panno ; nova
incudc diffingas,

4. Book III., II. 17-24. IIL 45-62. XIL 1-12.

5. Mention other readings, arguing in favour of the one adopted.
Nunquam dimoveas. Siccis oculis. Curia expeditis. Veris in-
horruit adventus foliis. Hac arte enisus. Cohortes addidit oppi->
dis. Arma deropta vidi,

6. Translate literally and explain the grammatical forms : Nube
candentes humeros amictus. Debcs Virgilium ct finibus Atticis
reddas in columem. Scriberis Vario. P'lgnm que dereptuni
lacertis. Quinta parte sui nectaris imbuit. Multi Danialis meri.
Audax perpeti. Nisi vcntia debes ludibrium. Lucretilcm mutat
Lycaeo. Quae virginum barbara ?

7. Explain, with notc>s on the words in italics : l*artcm solldo
demere de die. Tabula votiva .... suspendisso. . . vcstimenta.
Pastor quum trahcret. Qtm sub Arcto rex gelidae nietuatur orse.
Quanta Charybdi. Trifornil chimasra. Injecto ter pulvere.
Arabum invides gazis. Mutatasque simul togae. Amystide.

Classc cita reparavit oras. Cui cervice pendet. Conmenta

domittit redemptor. Murus aiineus Auctore Phoebo. Carmine
perpetuo. Philippis versa acics. Capitis minor. Martiis caelebs
quid agam Kalendis. Nexae philyra corona'. Impotens sperarc.
Sine funibus. Praesens divus. Improbas divitias. Tribus aut
novem miscentur cyatlm pocula comniodis. Trcs prohibet supra
. . . .tangere Gratia. 8i cadit haedus.

8. Give the Greek expressions for: Erycina ridens. Urit.
Qravem stomachum. Favere Unguis, Ducere succos.

9. Write out scales for the following metres :
Auolepiadic. Do. i.(rvA(nf\roi. Archilochian. Pherecratian.

LATIN.— V.

CICERO AND LIVY.

1. What objections were made to the passing of the Manilian
law ? By whom were they principally urged, and how docs Cicero
answer them ?

2. Translate Cap. III., with notes on : Mithridatico hello supe-
riore ; uno die ; vestigalibus ; insignia victorise. Distinguish
between ceteri and reliqul, mercator and negotiator, redpere and
excipere. Who were the j'uhllcani ?

3. LiVY B. I. Translate Cap. VII. Palat'mm — occubuit.
Cap. XXIV. Fcedera to end, with not«s on fetiaUs, pater
patratus, sagmlna, and doh mulo.

HORACE AND TERENCE.

4. Translate Sat. I. 3, 69—75, 83—89. Explain Cam tristn
venere Kalendif. Euandri manihus trltum. Sat V. 25 — 3G.
Parse ^ranst, iUinere. Explain at? unguem /actus homo, quoting
a similar expression from Ars Poetica.

5. Ars Poetica. Translate 125 — 135. Explain amphora
ttrceus, jiEmilium circa ludum fahar umis, regis opus, soccus and
cothurnus. Vos plaudite^ facundia prcesens, orichalco, personce
'pallceque, magnum hqui. Vd qui prcetcxtas rcl qui docuere
togatas.

G. Give a brief sketch of the plot of this play (Andria).
Translate Act III., IV. 1—15. Translate Act V. (5. Explain
animum appuUf, immcmoris hencjici, hahet, symholum dcdif, ])(>•-
cussit illico animum, sedulo, vctcrator, arrcssrre and words formed
In the same way. Concrepuit ostium, sijcophantam, cxtemplo.

ANCIENT HISTORY.

1. Name the If kings of Rome, with the chief incidents that marlted
their respective reigns.

2. Give the history of the formation of the Consulate, mentioning the
qualifications subsequently required to attain to that office.

3. Explain the nature of the ager publicus.

4. Give a brief sketch of the Samnite Wars.

5. Give a brief sketch of the constitution of Lycurgus.

6. Compare the constitutions of Solon and Servius TuUius.

ANCIENT GEOGRAPHY.

1. Describe geographical position of Italy and Greece, with their an-
cient divisions and physical appearance. Trace the principal rivers of
Italy.

2. Give the position of the following places, mentioning for what
they are famous : — Faesulae, Patavlum, Laurentum, Lanuvium, Brundu-
sium, Venusia, Formiae, Gales, Mons Massicus, Palinurum, Antiufflj
Delphi, Tempe, Mons Lycicus, Hymettus, Mycense.)

GREEK IV

-1

EURIPIDES-
XENOPHON-

■MEDEA.
-MEMORABILIA, B. 1.

1. Sketch the plot of this play. Translate 66 — 94. Explain the for-
mation of tAw. Distinguish between el ml and Kal il. Illustrate the
use oinptv with the perfect, aorist, and present infinitive.

2; Translate 273— 293. ParsQ i^ium and i^idc. Distinguisli between
(ptTnijnai and einr/iuaai ; /Jw/iof, bpxni and niartr. Give construction of
Hphnru^ and compare that of celo. Distinguish between nvvi/(h/uu and
hpi/6o/iai. Express in Latin KciKinm^ dvi^pm' tKjU,h/i,-r.

3. Translate Memorabilia Cap. I. 2 and 3, 17—20. Conjugate b/iw/ji,
(iKDKTeivUf (pvMaau, a>ifiaivu, vofii^u. Cap. II. Translate 24 and 25.
Explain ypcKfiEadai Tiva, ypa<pii, (pi/fJ-at, ahmhXa, doaiai, nXiidovaa ayopd. By
what names did Socrates call his followers 7

GREEK III.—

■ XENOPHON.— ANABASIS, BOOK I.

' HOMER.— ILIAD, BOOK I.

\ GREEK TESTAMENT.— ST. JOHN'S GOSPEL

1. Translate Cap. II. 1 and 2, parsing the following words ;
awa?i?iayivn, npoejTriKsi, i/j.Etvav,

eiroiEiro,

2. Translate with notes Cap. IV. 3 and 4. Explain the following
words : fevof, dapecKdg, ■jzUdpov, napaadyyt/g, orddiov, aradfi6g, ar^-eyyiSec,
■KETpai i]\l(iaToi, bvovQ aMrag, aiy'Koq, b/JoUg, xo'm^. Parse Ka-ede/Mrfv, ida-
Trdvuv, uxpEhjirfv.

3. Translate Cap. IX, 7—9.
vio/xat, (tjtMu, npotrjfu, dv6dvu.

Conjugate KaraTre/irru, dTrodeiKW/ic, vwiax-

4. Explain these constructions : dia^dXUi wf Ein^ovlshoi. evvolKug

exotev nd^Euv uv e;j;uv. Distinguish between aroSiSpdaicu and

anoipEvyu. dpxetv and apxeaOai Tov]Aoyov, with Latin idiom for the former.
TovTovIf explain I and give corresponding Latin and French form of
pronoun. Give the adverbial afiBxes denoting motion to and from, and
rest in a place, and translate into Greek here, hence, hither, then, there,
thence, thither.

6, Translate Hom. Iliad I. line 130— 14T, and give the parts otnEidu,
(iaivu, 6i6u/ii, and aipsu. Explain civrovg line 4. TE-—Kai, prj Kixeiu, ^piv
with conjunctive and optative, causal and relative genitive, ekI (ppEol
df/KE, apa and pa, Dativus incommodi ; ^.osition ot /ih and 6e. When is a
question introduced by ^ ? Distinguish between accusative of cognate
and equivalent notion, and name the other accusatives of this class.

6. Translate St. John's Gospel, Cap. I. 35—43. <l>pa 6emTTj. What
hour ? Tov M.£aaiav. Explain use of article. Translate Cap. VI. 52 —
59. Explain the omission of the article with mvuv. Translate Cap.
VIII. 44 — 47. Give the two translations of the latter part of verse 44.
Distinguish between eMyx^ and imTipdu.

7, Translate EOK^/vuaev iv ypiv. kuI xdpiv dvrl xdpiTo<;. rovg iTu^ovvTa(j
(3oa( ; how do you account for the omission of the article with the
noans, while two of the Evangelists insert it ? KeppanaTdg who ? Give
its derivation. ol6ap,Ev bri aTrb Qeov k^'Xvdaq SiSdanaXog. ah el b 6t6daKa?io<;.
Explain the use of the article. Distinguish between noleu and npdaao).
Translate rb iidop to {uv. irvevfia b Qtbc b Xbyog kanv b aXt/Oivbc, why
not dA^%- ? Distinguish between AaAk and Myog. What force has //?)
as an interrogative? Give interpretation of 'Pa/3/J«, ^dudp, KT/(pdg,
B>fiEa6a. Explain vfuae rbv b^iv, b npoij>ijTrig, b apxirpi/cXivog, av Muvafjg
Jedw/tev vfilv rbv aprov m rbv ovpavov.

ORAMMAIRE FRANgATSE.

1. Comment appelle-t-on le verbe loraqu'il se pr^sente sous as
forme simple ?

2. Combien de sortes de temps dans les verbes, et en quoi se
divisent-ils ?

3. Comment se forme I'imparfait da subjoncti/f

4. Quelle diflFcJrence fait on entre ou conjonction et ou adverbe ?

5. Qu'est-ce que la cidille ?

6. Combien y a-t-il de parties dans I'analyse logique ?

7. De quel genre sont amour, cUlice et orgue ?

8. De quel genre est /oitc^re ?

9. Quand emploie-t-on simplement de au lieu de I'article devant
le substantif ?

10. Quelle difference y a-t-il entre un homme brave et ^^.n brave
nomme?

11. Quelle est la r^igle du participe passe employ d avec I'auxi-
liaire etre ? Du participe passd employe avec avoir ?

12. Quand mSme est-il adverbe ?

Analyse grammatlcale.
Parmi les productions natuvelles, qui par les relations de I'Eu-
rope avec 1' Orient ont ^t& transportdes dans nos climats se trouve
une fleur que les Turcs appellent TuUbant, et qui en Europe a
regu le nom de T'ulipe.

Verbe Courlr, 2dme Conjugaison.

Traduction de Charles XII, (par Voltaire).
Page 30. Depuis le second paragraphc jusqu'au troisieme,

FABLE DE PERRIN.

LA TULIPE ET LA ROSE.

Traduction de V Anglais en Fram^ais.
Lofty mountains, who has established you on your foundations ?
Wlio has raib^d your heads, even above the skies ? who has decked
you with verdant forests, with fruit trees, with these plants so
usCiai and so varied, with su XuauJ ugfCOubiC Sowcrs ?

SUBJECTS FOR ENGLISH

i!!

ENGLISH GRAMMAR.

1. Distinguish (according to Morell) between a syllable and a
vowel.

2. Give his divisions of Common and Abstract Nouns.

3. Form 3 sentences containing common nouns, and change them
into corresponding abstract ones.

4. Classify the Conjunctions and give the rule for determining
whether a word is an adverb, preposition, or conjunction.

5. a. Classify the Auxiliaries, and explain the composition
of this sentence " I will go."

b. Write out 6 verbs that cannot have o. passive voice.

c. Write out a sentence containing an intransitive verb, imply-
ing an active state.

d. Give the present and past indicative of run in the progressive
and empJuttic forms.

e. Define the Middle voice and give an example.

6. Give the rule respecting adverbs, and state which is the correct
expression, " The queen looks majestic " or " majestically."

7. Apply rules to the following examples, and parse the words
in italics :

The people were divided. Spring coming, the swallows
appear. Death where is thy sting ? A play of Shakspere's,
the great ^or^ I watched three hours. I was asked that ques-
tion yesterday.. He gave me a book. Satan, than whom none
higher sat.

8. a. Define a sentence, Subject, Predicate, Copula, Completion
and Extension of Predicate

b. Distinguish between a complex and compound sentence.

c. What do you mean by adjuncts ?

9. Analyze the following passiigcs and parse etymologically the
words in italics :

If death were nothing, and nought after death ;
If, when men died, at once they ceased to be ;
Returning to tlic barren womb of nothing
Whence first tlicy sprung, then might the debauchee
Untrcmbling, mouth tlie heaven.

Some dream that they can silence, when they will
The storm of passion and say " Peace, be still ;"
But " thus far and no further," wlien addressed,
To the wild waves, or wilder human breast,
Implies outhority, which never can,
And never ought to be the lot of man.

I A Ax.,.nt<'1>"'T ^'■^ nnnlvaia nf lu^nipnopn dfldllCR ruloS lOF DUnC-
i'.'i ii^wJ-.f-g "• j-^- "- ; t

tuation.

ENGLISH LANGUAGE.

1. Define language and disprove the assertion that language
has attained its present position by a gradual process of develop-
ment, and prove that it is more than a mere " accident of human
nature."

2. How does language prove man to be of divine origin ?

3. Give the grand divisions of the 2 great branches of the
Gothic language.

4. Of what is the Anglo-Saxon language composed; and give
a short sketch of the orio;in of the languase ?

5. Had the Danish invasions any effect upon the language of
Britain, and if any what was it ?

6. Trace the introduction and spread of the Norman French
language in Britain.

7. Give Craik's division of the different periods of English
literature.

8. State Trench's rule for knowing whether a word comes me-
diately or immediately from the Latin,

9. Illustrate, by examples, the difference between apoc^e and
syncope ; and state what changes take place in the vowels.

10. What do you mean by " double adaptation " ? Give ex-
amples.

11. What advantage does the literature of Greece or Rome
possess over ours ?

12. Adduce instances to prove the deterioration of language,
and quote passages containing the words in their original sense.

13. Give the derivation of the following words, and remark
upon those in italics : Accomplice, Affect, Affront^ Angel, Antic,
Art, (embracing Cunning and Craft), Ambition, Asperse, Aston-
ish, Astronomy and Astrology, Candidate, Saunter, Assassin,
Poltroon, Tribulation, Pagan, Heathen, Calamity, Vapid, Elimi-
nate, Imbecile, Plague, Sincere, Odd, Miscreant, Mob.

14. Give instances of words now used in the English language,
at hft\
nations.

that have been introduced b*' lueuns ol' iut^.'rcour'*o with uthor

NATURAL PHILOSOPHY.

1. Distinguish between a law and a property. Mention the
diflferent divisions of Natural Philosophy, and define the following
terms: — Graviti/, Inertia, Compressibility, and Elasticity.

2. State and illustrate the different kinds of motion. Prove
by examples, the truth of the formulae for finding S, T, and V.

3. State the 3 Laws of Motion and describe Atwood'g
Machine.

4. State the propositions respecting bodies projected upwards
and downwards with a given velocity.

5. State and prove the Parallelogram, Polygon and Triangle
of Forces.

G. Define the Centre of Gravity, and how it may be found by
experiment. J) Q^nQ projectile and random. When is the ran-
dom greatest in theory and practice 1

7. Deduce formula) for shewing the relation between P and W
in each of the Mechanical Powers.

In a compound lever, the short arms arc respectively J, 1, and
2 feet ; the long arms 4, (5, 8 ; a power of 2 lbs. is exerted at
the end of the longer arms. What weight can be raised ?

8. Explain the action of carriage wheels in overcoming ohstaclcs,
and illustrate by means of a figure.

9. Investigate and apply to each of the Mochanical Powers the
general law which applies to them all.

10. Explain the following terms ■.—regulators, rectilinear, rotary,
and recip 'ocating motion, fjnir and bevel gearing.

11- Define the following : — Flywheel, llniucrsal Joint, Rachet
Wheel, Eccentric Wheel.

12. What is the practical use of the Pendulum f

State the 5 conclusions respecting /V/tVtoH, and explain Friction
W1^cel8.

GEOGRAPHY.

1. Define Physical and Political Geography.

Give position and extent of the Zones ; and state the influ-
ences that modify the temperature of a place.

2. Name the Zones of Vegetation, with the characteristic plants
of each.

3. Classify the Rivers and Lakes on the surface of the Earth ;
and describe the great Equatorial Current.

4. Describe the causes of the Tides : and describe 8 different
Phases of the Moon.

5. Mention the 5 Divisions of the Human Family ; and how
are they, distributed ?

6. Describe the Physical Divisions of North and South America.

7. Mention the Empires and Kingdoms of Europe. Des-
cribe its physical divisions; name and give position of its princi-
pal Seas, Bays, Straits and Rivers, with the Countries which they
drain.

8. Name the 6 Northern Counties of England, mentioning the
Chief Towns and also for what they are noted.

9. Describe the Physical Features and Natural Divisions of
Asia, and trace the Indus, Ganges, and Amoor.

10. Mention the General Divisions of North and South
America, with their respective positions. What rivers drain the
Eastern and Western slopes of North America ?

11. Mention the ancient Divisions of Europe, State position
of Mesopotamia, Syria, Asia Minor, with any famous cities in
them.

12. State position of Newcastle, Canterbury, Manchester,Covcn-
try, Rouen, Aix-la-Chapolle, Constantinople, Corunna, Moscow,
Bombay, Palermo, Palmyra, Cabul, Aden, Trinidad; mentioning
anything inte.ofiting respecting them.

'M i

FRENCH HISTORY.

From the Accession of Louis XV, i. D. 17U to the Treaty of

Amiens, 1S02.

1. Give an account of the Mississippi Scheme ; the war of the
Austrian Succession ; and state briefly what you know of Maure-
pas, Turgot, Malesherbes and Necker.

2. Sketch briefly the characters of Maria Antoinette and Louis,
XVI ; and describe fully the Notables and the Farmer-Generals.

3. Describe fully the States-General of Franco, the Verification
of Powers and the National Assembly.

4. Describe the Sections, the National Guard, and the taking of
the Bastile ; and explain the system of Assignats ; with a full
description of the great changes effected by the Assembly.

5. Give a brief description of the Girondists, the massacres in
the prisons, and the trial and execution of the kincr

6. State briefly what you know of tlic following ;— The Clubs,
Egalite, the Maximum, the Girondists, and the war in La Vendee!

7. Give the characters of Robespierre, 3Iarat, and Danton, and
describe briefly the Reign of Terror and the full of the Terrorists.

^ 8. Describe briefly the state of France at the death of Robes-
pierre, and give a sketch of tlie Directory, Napoleon, the Italian
War, and the Expedition to Egypt.

9. Sketch briefly the characters of Fouche, Tallryand and Sieyes.

10. Describe fully the Council of Five Hundred ; the Consulate ;
the Passage of the Great St. Bernard ; and give a sliort account
of the battle of Marengo, and the Treaty of Amiens.

'■ 111

ARITHMETIC, I & II.

1. Explain fully by examples the four simple rules, and show
how they may be resolved into two.

2. Give the rules for the following, with examples: — Minuend
and Difference given, to find Subtrahend ; Product and one Fac-
tor to find the other ; Divisor and Quotient to find Dividend ;
Dividend and Quotient to find Divisor.

3. State and prove by examples the four general principles of
Division.

4. Define Reciprocal, Measure, Multiple, and prove fully the
rule for finding the G. C. M. and L. C. M.

5. Give full definitions, with examples, of all the different
kinds of Fractions ; explain the use of Numerator and Denomi-
nator ; and prove fully the rules for the following : — To reduce
an Improper Fraction to a whole or mixed number, and the oppo-
site ; to reduce Fractions to their lowest terms, and when are
Fractions so reduced ?

6. Prove fully the rules for the Addition, Subtraction, Multi-
plication, and Division of Common Fractions in all the cases
which can arise.

7. Define Decimal Fractions, with examples ; explain their sys-
tem of Notation and Numeration, and how they are more conve-
nient than Common Fractions.

8. Define a Rcpctend, explaining the difi'erent kinds, and the
manner of reducing them to their equivalent Vulgar Fractions ;
and find the value of •4ili;i. Prove the rule for Multiplication
and Division of Decimals.

0. Give and prove fully the rules for the Reduction, Ascending
and Descending, of Decimal and Composite Numbers.

4,V

10. Add together -/-, | of 3 A of

oi' 2 J, and

20}

Find the

value of J of ^ of I of 8^ of

by ,V of _^*-

- X

jojs

128

Find the value of

Divide A of A of

X 'H

X 43.

11. Supposing a meteor should appear so high that it could be
seen at once by the inliabitants of Boston 71° 3', of Washington
77° 43', and of the Sandwich Islands 155°, west longitude ; if
the time be 47 minutes past 11 o'clock of December 81,4t, 18(10,
at Washington, wliat will be tlio time at Boston and at the Sand-
wich Islands ?

1; "

ARITHMETIC.

1. Define Vulgar and Decimal Fractions, and prove fully
the rules for the Addition, Subtraction, Multiplication, and Divi-
sion of each. Define the different kinds of Ratio, and Propor-
tion. Prove fully that product of means equals product of
extremes ; and the rule for finding any term of a Proportion,
three being given.

2. Define Alligation Medial and Alternate, and prove
the rule for the solution of questions in Alligation Aftcrnate.
Explain Exchange, giving the nominal and commercial values
of the pound sterling, and explain the expressions a^j^ar, at a
premium, at a discount.

3. Define, with examples, Involution and Evolution.

Shew that the cube of every number of it digits has either 3 n 2

3 n — 1, or 3 n digits ; and hence deduce the rule for pointing
in the Cube root. Extract the Cube v ot of 18608G7, and ex-
plain fully the several steps in the process.

4. Define Arithmetical and Geometrical I'rogression.
Explain the different terms employed, and deduce an algebraic
formula for each letter in both kinds of Progression.

5. Distinguish between I'krmutations and Combinations,
and prove fully the formula; for n things taken 2, 3, 4, and r at a
time, and hence for n things taken all together.

(J. Define the following : — Parallelogram, Rhombus,
Rhomboid, Trapezoid, Triangle, Circle. Give and explain
fully the rules fi)r finding their areas,

7. Solve the following : — How many cubic miles in the E;iith?
Wliat are the solid contents of a pyramid wlioae base is 4 foot
Bquare, and the perpendicular height }) feet ? How many wine-
gallons in a cask the bung diameter of which is 3G inclies, the
head-diameter 27 inclies, and the length 45 inches ?

ALGEBRA.

1. Define a Fraction. State and prove the rule for the Mul-
tiplication and Division of one Fraction by another.

2. State your reasons for preferring the expressions H. CM.
to G. C. M. Investigate the rule for finding L. C. M.

3. State the dificrencc between an identical equation and a
conditional equation. What do you mean by the dimensions of
an equation ? Prove the truth of the rule respecting Transpo-
sition. Prove that an Equation of the first degree can have only
one root.

4. Define simultaneous equations. State the three methods of
solving them, and apply them to the example

4 X + 3 y = 22 ; 5 ,r, — 7 ;/ = 6.

5. Investigate the rule for extracting the square root of an
Algebraical quantity, and apply it to the example

4.x* — 12x«+ 5.x2+ Gx+ 1.

6. Define a Surd. Investigate the formulae — = , or

an a n~m '

a m-nj a -P = — ; a- >^ bn — (ah)i; ; I ci^\. = air,.
If a + V6 = 33 + Vy, then a = x and V6 = Vy«

EUCLID AND TRIGONOMETRY.

1. Define a point negatively and positiveh/. State the divisions
o£ a problem and a fhenrem. Distinguish between (it>ec« and i«-
direct demonstration. What do you mean by one proposition
being the converse of another? Enunciate those that are the
converse of IV., V., XIII., XIX., of Book I.

2. Enunciate and prove the following propositions in Book I •
v., XXIX., XLVIII., and the corollaries of the XXXII.

3. Prove Book II. : VI., XIII., and apply Algebraic proof to
the corollary of the 5th.— Book III. : XXXIT. ; Book IV. : X.

1. Distinguish between positive and negative angles, and draw
an angle in the third quadrant.

2. Define Complement and Supplement, and prove the formuljc
E = F — ~. and F = E + — . Prove that the sum of the n

10'

angles of any rectilineal figure = (n — 2) 180, and that the
angle subtended by each side of a polygon is or ac-

cording to its position.

A 6

3. Deduce the following formulae : $ = j^tt, A = —180, and

180

give the result when 6=1. State when the formula 6 = ~

r
may be used, and prove that tlie area of a circle whoso radius is
E, is ttE^.

4. State by letters and words all the Trigonometrical Ratios of
an angle, naming the reciprocals, and prove the following : —

sin ^ cos . „ ,
tan = — , cot — - -r-, sm2 + cos^ = 1, sec2
cos sin '

1 + tan2

r and

cosec2 = 1 + cot2 , and that if tan = -7-, sin = -: " —

cos = ■ ■

Vaa + />a

5. Deduce the formulae for the sine, cosine, &c. of SO'', 45°,
and 60°. Express the sine in terms of sec. and cotan. Given
sec = 4, find sine and versed sine.

6. If ni m' bo '' . number of minutes in any angle, estimated

in English and French .systems respectively, shew that — = -..

w 27

7. The angles of a right angled triangle are in A P: find
them.

8. There are two polygons such that the diflFerence of the sums
of their interior angles is four right angles, and the ratio of the

aarnn no ^ . Q . RwxA 4-V.^ ^..».U„. ..<• ,.:.J.... ;„ 1, X.""-., il

.-.wii"- Ttrr T.- , tj . HUM liiv iiuiuf,~v;i •^•j rnj;c3 ill cav'U. iuz.\nx:ns viic

interior angles in French inea.sure.

MISCELLANEOUS QUESTIONS.

1. Prove the rule for Siihtraction in Algebra. Assuming the
truth of that for the multiplication of powera, deduce one for
their division.

2. Find the G. C. M. of 2,r' — 8x + 12x' — 8x' + 2x, and
3yf — 6x' + 3x, and the L. C. M. of 6;c' — x — 1 and 2x' +

3x — 2.

a 1

Simplify 6+ c ; 1 — x ; according as x = < or > 1.

3. Solve the following equations : —

(1). J___L_ = J_--i-.

1—2 X— 4 1—6 a;— 8
(2). (a:+l)'^={6 — (1— x)}x— 2.

(3). x = 4y, i (2x + Ti/) — 1 = ? (2a: — Cy + 1).

4. A and B play at bowls, and A bets B three shillings to two
Upon every game ; after a certain number of games it appears
that A has won three shillings, but had A bet 5s. to 2s., and lost
one game more out of the same number, he would have lost thirty
shillings. How many games did they play ?

5. Find the product of

(10

,-J

,-i

and

G. Add together -0015 of lOs., 2'0615 of 10s. 6d., and 1'04 of
2s. 6d., and express the whole as the decimal of a pound.

7. If 2G4 men, in 5 days of 12 hours each, can dig a trench
240 yards long, 3 wide, and 2 deep, in how many days of 9
hours long will 24 men dig a trench 420 yards long, 5 wide, and 3
deep ?

8. How many cord feet of wood in a load 7 feet long, 3 feet
wide, and 3J feet high ?

9. L=z 117, d = 8, n = 15 ; find a. What annuity in 20
years, at 6 per cent., simjyle interest, will amount to $1570 ?

10. What is the value of 1 + i + iV + &c. V

11. If the contents of a triangle arc 600 rods, and the base 75
rods, what is its altitude ? How many square inches of leather
will cover a ball 3^ inches in diameter ?

12. What is the difference between the perimeter of a square
19* miles on each side, and its inscribed circle ?