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Les diagrammes suivants ]|lustrent la mithode. 1 2 3 1 2 3 4 5 6 It .,-'V, M ■•Ai COURSE OF INSTllUCTION IN THR rou MOJEIi ORAMMAR SCHOOL " *" ?2?^'?pttj)ir^^: (SI una d it, AND OTHEE INFORMATION WITH THE EXAMINATION PAPEES OF 186i0. ^autfioriBrli tiD i\)t Council r\l );)itblu JEnstntrtion fov dipper (fTanatia, (;^-.a•^'G,"*■ TORONTO ^Drintrli for tfjf Brpartmriit ot |)ul>Uc InBtrurttojj ]tY LOVELI, AND niBSO 180O. v'^^'^^aJT* ^*' t' ^ "^, ■ \. ,-;:?•• V' *;■,' *■• -V ■• . .if:.' ', ^ •is.*;i£^'^4Ci ""^ '^^^^ '^-^:. A :% r f'i; / / *»' S- i«f! COURSE OF INSTRUCTION m TBR MODEL GRAMMAR SCHOOL Foa ^^^tt (SimUiXf AND OTHER INFORMATION WITB TBK EXAMINATION PAPERS OF 1860. «utiori«tli &S t^' C»uii«il ot public Iiwtrurtfon for Spptr flCinatii, TORONTO: ^tlntttr for tfte ©tpavtmint of ^jJubUc Inatruction for Spper «anat«» BT I.OVELL AND eiBSON. 1860. ■' .' ■.■■ I- ■^r^-. " jPr "^/''--A "^^ ): (^ .■ .,'| J '' ty' %■ »"-»■ V j;- V |ie»4 aC iht <$dtt(ntion»t §tpwetmmt „ , / Rev. EGERTON RYERSON, D.D., Chief Superinteadent of Education for Upper Canada. Cmtndt 0( ^ttblir in^tvurtian Uv ^pptt (S>muU. Hon. SAMUEL BEALY HARRISON, Q.C., Chairman. (Church of England.) Rev. EGERTON RYERSON, D.D., Chief Superintendent of Education. Right Rev. ARMAND FRANCOIS MARIE DE CHARBONNBL, D.D., Roman Catholic Bishop of Toronto. (Successor to the late Bishop Power.) Rev. HENRY JAMES GRASETT, B.D., Rector of Toronto.' Hon. JOSEPH CURRAN MORRISON, Q.C. (Presbyterian Church of Canada.) JAMES SCOTT HOWARD, Esq. (Church of England.) Rev. JOHN JENNINGS, D.D. CUnited Presbyterian Church.) Rev. ADAM LILLIE, D.D. (Congregational College, B. N. A.) Rev. JOHN BARCLAY, D.D. (Church of Scotland.) Successor to the late Hugh Scobie, Esq. Rev. JOHN McCAUL, LL.D., President of University College. (Ex o^io Member, for Orammar School Purposet.) BEOTOR : GEORGE R. R. COCKBURN, M. A. OLASSIOAL MASTEB: REV. JOHN AMBERY, M. A. MATHBMATIOAL MASTER: FRANCIS L. CHECKLEY, SCHOLAR T. C. D. ENaUBH MASTER: BENJAMIN F. FITCH, M. A. FRENCH MASTER: M. EMILE COULON. WRITING AND JUNIOR ENGLISH MASTER: MR. ALEXANDER R. STRACHAN. DRAWING MASTER: M. ALPHONSE COULON. MUSIO MASTER: MR. HENRY F. SEFTON. FENCING, GYMNASTIC AND DRILL MASTER: CAPTAIN GOODWIN. I \ Janitor and Messenger : PATRICK o'nEILL. COURSE OF INSTRUCTION IW TUB C^l VY'. tummut 3tk$$l FOR UPPER CANADA. The Model Grammar School, established by the Council of Public Instruction for Upper (-aiiada, under the authority of the Legisla- ture (Consolidated School Act, 22 Vict, cap, Ixiv. sec. 120), is mainly intended to exemplify the best method of teaching the branches required by law to be taught in the Grammar Schools, especially Classics and Mathematics, as a model for the Grammar Schools of the country. It is also intended that the Model Grammar School shall, as far as possible, secure the advantages of a Normal Classical School to candidates for Masterships and Teacherships in the Grammar Schools. The regular curriculum of five years embraces an extended course of instruction in Latin, Greek, Mathematics, French, German, English Grammar, Literature and Composition, History and Geography, both ancient and modern, Logic, Rhetoric, and Mental Science, Natural History and Physical Science, Evidences of Revealed Religion, the usual Commercial Branches, Drawing, Music, Gymnastic, Fencing, and Drill Exercises; the more advanced Students will also attend Lectures in the various departments of Literature, Science and Art. Only one hundred pupils will 1 e admitted. Accordingly, the numbers in each class will be strictly limited, in onlcr that a due regard may be paid to the peculiar temper and disposition of each pupil, and that the utmost efficiency may be secured in the cultivation of the intellectual faculties, and the inculca- tion not only of the principles but of the practice of a high-toned morality. Every pupil must follow ihe prescribed course of instruction for his class, and pass t!>e entrance examination thereto. When the first or lowest class is being annually formed in September, this shall consist in Reading, Spelling tu dictation, and orally Writing, the simple and compound rules of Arithmetic, Simple Proportion, the elements of English Grammar, and outlines of Geography. A preference will be given to those who in addition to the preceding requirements pass an examination in the Latin Declensions, and the four Regular Conjugations. Applicants for admission to the higher classes will be subjected to an examination corresponding to the class for which tb. y arc candidates. The school contains large and well ventilated class-rooms, with ante*rooms, a library, laboratory, and a hall for assembling the whole school. The most recent improvements in school architecture and furniture have been adopted. A play-ground of nearly two acres is attached, with gymnastic apparatus, and covered sheds for exercise in wet weather. The course of instruction is so arranged as to prepare and strengthen the mind for the more severe study of each succeeding year. By the peculiar system of discipline adopted, the conduct and the application of the pupils will be regulated by motives similar to those by which our conduct in after life is influenc'l, and the various honours will be made to depend as much t>n good conduct as sound scholarship. There are four Scholastic Terms in the year, as follows : — WINTER TERM— From the 7th of January, to the Thursday before Easter. SPRING TERM— From the second Monday after Good Friday, to the fourth Friday in July. SUMMER TERM— From the end of the long Vacation, to the 31st of October. AUTUMN TERM— From the 1st of November, to the 22nd of December The following are the Adinitnon Fees : For one pupil, Ten dollars per term ; payable in advance. For two brothers, Eight dollars each, per term ; ditto. . For three or mors brothers, Six dollars each, per term ; ditto. Pupils from a distance can board in private houses sanctioned br the Council, at prices agreed upon by the parents of the pupils and the keepers of the houses. A pupil will be allowed to board in any private family, at the request of his parents. Pupils may enter at any time by passing the necessary examination. All applications for admission to be transmitted in writing to the Rev. Dr. Ryerbon, Chief Superintendent of Education. NOTICE TO GRAMMAR SCHOOL MASTERS. The vacations in the Model Grammar School have been altered, so as to allow an opportunity to Grammar School Masters of visiting the School during their own vacations. NOTICE TO CANDIDATES FOR GRAMMAR SCHOOL MASTERSHIPS. The Examination of Candidates for Grammar School Masterships takes place in the Normal School Buildings, on the first Monday In January, April, July, and October, of each year. (EommitUe of (&%amitura : THOMAS J. ROBERTSON, M.A., Chairman. Rev. WILLIAM ORMISTON, D.D. ^ Inspectors of GEORGE R. R. COCKBURN, M.A. {Grammar Schools Rev. JOHN AMBERY, M.A. ) Upper Canada. #xjimittflti0» f apns, 1860, 1 4 1 I I.— GEEEK. 3. Translate, Sophocles, (Edip. Eex. vv. 151-159, and vv. 216-229 : w Alos aSvETres c^art, Tts irore Tcs 7ro\u;(pT;(rov Ilvdaivo? dyXaa; c)3as ©j^;3as ; cKTeVa/iat ^j3«pav piva^ Sci/uuzn n-aXXwv, {)^i6 AoAte Ilatav, d/x^l croi d^ofievos, Tt fioi t^ vo)I', ^ TTcpiTcAAo/x.o'ais Sipais TrdAtv e^ai/v(r«s XP''*^ flire /Ltoi, w ^vatas tckvov *E\7ri8os> afi-ftpoTf. ^afJLa, irporrd (re kckA,oju,6vos, ffivyartp Acos, ap-fipoT *A^dva. oiTets* a 8* aiTcTs, ra/w,* cav BiKys f-in} tikvoiv he)^€(T6ai rfj vocta 6' vmjptTtivy iXKTjV XdjSoi; &v Ka.vaKov((K(riv KaKwv' dyu) $€VOS /t€V ToC Aoyou tovS* 'l^tpw^ (evos §€ TOW TrpayOhrro'i. ov yap av p,aKpav l)(yevov avros, p-r} ovk €)(wv ti (Tvp-fioKov. vw 8', varepos yap doros eis dorows rcXdu, v/Aiv Trpoffxavia Tracri KaS/ixcibt; ToSc* osTis "TToO* vp.av a.m6vT€i\ov Krjp, 'Os ovoix iiairdrr](T€v c/xov Koi fiT]Ti<» afivfiiav. Kvk\(d\I/ Se arevd^^ayv re koL wStVtoi/ oSvvymv, Xe/oo-i ij/rjXaifiowv, aTrb fih XiOov eiXe Ovpdwv, Autos 8' elvi dvprja-i KaOe^ero X'^ipe Trerdaraa-i, El Tivtt TTOV ix€T oecTcn \dpoi a-TCLxovTa 6vpa^€' OuTO) ydp TTOV /x ■^Xttct' en <^/>co-t vi^ttiov cii^ai. Avrap eyw fiovXevov ottws o)^ dpLo-ra yeVoiro, Et Ttv CTaipowriy ^avarou Xro-iv ^8' e/i,ot auroT Y^poLfirjv' irdvTa<; 6i 8oA.ovs Kai jxrJTtv v(fiaivov "fls Tc irepi ijrvx^^' /tteya yap KttKov iyyvdev r}v. 'HSe 8£ /Aoi Kara 6vfi6v apian) (fjaivero fiavXrj. Ap(T€veU(Tcn. Xvyourw, T^s eirt Kvk\w\j/ evSe, vre'Awp d6ejxi(rTia ciSos. Swrpeis aivv/xevos- 6 p.ei' ev /xeww avSpa (^epecTKef . 0) o €T€p(a e/carcppcv ir>;v ctoon-es eratpovs. Tpeis 8c CKCwrrov ^wr* oi'cs <^epov avrap eywye ( Apvetos yap c»;v, /xrjXaiv n^ aptOTOs dTrarrtov,) Tow Kara vwra Aa/3o)v, Xaavqv viro yacrrip eAucr^cts K.€ifi7)V' avrap ^cpcriv dcirou Oecnrecrioio N(i>Xejttea)s (rrpe^^ei? ix/'p.rjv rerAi^ort Bvixw. 2. Give the ordinary forms of any dialectic varieties between vv. 413 and 420. 3. Notice and explain any metrical peculiarities in vv. 413 to 442. 4. Discuss briefly the question as to vrhether the Iliad and Odyssey were the production of the same author. lit i 10 «• Parse .>,, ,,0^^,^^^ . 6- ^lace tl,e accent, «„d bearings to th f „ • /. ilowever sinee I i , »f the Greeks then, those „h„ t I' '. '"'"°°- ^' "" «»' ^t .. soon as ever their eSlT/ '" "'''"'* "">'' «»» forthwith set servants over th „ ''"''''™'»nd wh,e is spoken, 'o-n-eers .„ fearn botMht H^tTr .""^ »»«* them -o».p.«h»ents,an<,thee,erj:r:;:h:Hrt:^ and polite II.-.LATIJ\r. Translate Ovid Fasti I-587-610 Africa victorem de se voeit • «lfa t Me raisernm vfZ „ ?"""""'» ^"'''' Si petat a vict"; „t ^"? '"•'"» '""^it ! Quotnu::™!!::? "'•'"'"" ^"'"■•' Antcorvititu,o.a„,ii,; lZ:r''''"=' ^lagne, tuum nomen rer.,m «^''.-ieevi„it,nrir„~,'--"' = ttSetTTVOt irpiv yap irth of be rest ir sons poken, I them polite ^1 Nee gradus est ultra Fabios cognominis iillus ; Ilia domus meritis Maxima dicta suis. Sed taraen hiimatiia celebrantur honoribua omnes; Hie socium aummo cum Jove nomen habet. Sancta vocant augusta patres : augusta vocantur Templa, sacerdotum rite dicata raanu. (2) Explain the allusiotia ia the following words:— (a) Ceras, (b) Africa, (ff) laauras, (c?) Cretura, {e) Numantina, (/) Gei" mania, (j/) torquia, (A) corvi, (i) Magne, {k) Maxima. (3) Idibus. — Sketch the diviaion of time among the Eomana, give a tabular calendar for this month, and give the Latin for the following dates:— 5th September; 12th November; Slat De- cember ; lat January. (4) Si petat f mat. — State and illustrate by examples the doctrine of the subjui ctive mood in Latin, and compare it with the Greek. ^ (1) Translate freely, Horace I. Ode 21. Dianam tenera? dicite virginea, Intonsum, pueri, dicite Cynthium, Latonamque supremo Dilectam penitua Jovi. Vos laetam fluviis et nemorura coma, Qusecuuque aut gelido prominct Algido, Nigris aut Erymanthi Silvis aut viridis Cragi ; Vos Tempo totidem tollite laudibus Natalemque, mares, Delon Apollinia, Insignemque pharetra Fraternaque humerum lyra. Hie bellum lacrimosum, hie miseram famem Pestemque a populo et principe Ca53are iu Persas atque Britaunos Vestra motus aget prece. (2) Mark the scansion of the first four lines, and name the metre. i! 12 w) Scan and give th*» »««* • , S'etedivap„,e„,Cypri. cow '°""^"^P"'-»«™-Jo. W G»-^- a sketch of tl>» p,«, „f ,, . <^'pal writing.. "'""^ •I'-i^ta,, aje a„J of tl,ei, pri„. I-ATIN PROSE. ''•"■tiiiie in niiath^r n,,., I'riau coa,t 1,. J ^'''■'""'- J*"' ">eii- shin w^Tll *"^'^' «'"' ^•'■'»". wt. n ttf ::'■ ^'-^™" °" '^zzfzT'^^^^- -'iiieh l,.,d beeu o ■ ,, "^ '^ ' """' '"»' Pawners to B„ ""=/"''«»■ «-ATIN VERSE. W,«, all the H„o ethereal s^:' ThiS'ttrr-'-^'W'-o, Th ' „», o"ginaI proclaim. 4nap„h,ir:~„r- Soon aa the evemngsh.ide,p,.e;ai, "'antjy to the hstenine par^t, B»P-t. the story 0, her S' 18 : lines : urn, (e) prin- mlly. '^ with ■> and Cala. ibas- essel med 5end hed sof III.— ANCIENT HISTORY AND GEOGRAPHY. 1. Give an account of the legislation of Lycurgus. 2. Give an account of the legislation of Solon and contrast it with that of Servius TuUius. 3. Contrast the Spartan and Athenian constitutions, and illustrate by historical examples their effect on the Spartans and Athenians respectively. 4. State the reforms of Pericles and their permanent effect on the Athenians. 5. Compare the system of colonization of Greece, Rome, and Great Britain. 6. Sketch the career of Miltiades. 7. Explain the agrarian laws of the Gracchi, and give reasons for condemning or defending them. 8. Sketch the career of Pompey. 9. Give a short life of Hannibal. 10. Give a chronological table of the leading events in Roman History between B. C. 100 and the death of Augustus. * 11. Give a similar table of Grecian History between 500-444 B. C. 12. State briefly the causes, leading events, and results of the Pelo- ponnesiau war. (For 5th class only.) IV.~ANCIENT GEOGRAPHY. (//I the following questions always give the ancient and modern name, if known-) 1. Mention the six large basins draining Gallia Antiqua. 2. Trace the Rhodanus from its mouth to its source, and o-ive the towns in the order you pass them, and any historical or other cir- cumstances connected with each. 3. Trace the Rhenus from its source to its mouth, and give a short running commentary as you proceed on your course. 4. Give an outline map of Gaul shewing its ancient divisions, its drainage and leading towns. .5. Do the same with Italia. (). Start from Genoa and coast along to Rhegium, and state in order the divisions, and the leading towns and rivers you would pass on he western side of the Apennines. 14 v.— MODERN HISTORY AND GEOGRAPHY. 1. State the causes of the high prerogative of the crown during the reign of Henry VIII. 2. Give an account of the proceedings of the Long Parliament, and discuss briefly the ground on which you would oppose or defend the execution of Charles I. 3. Mention the circumstances which led to the Restoration. 4. Explain the Corporation Act. 5. Explain the Uniformity Act. 6. Describe the members of the Cabal Ministry and the origin of the term. 7. Give the articles of the Treaty of Dover. 8. Explain the Declaration of Indulgence. 9. Explain the Test Act. 10. Mention concisely the more immediate causes of the Rsvolution of 1688 and the permanent changes wrought in the constitution. Contrast that Revolution with those in modern times, and explain the difference. VI.— MODERN GEOGRAPHY. 11. Mention the rivers tha"; fall into the Atlantic. (12) The Baltic. (I a) The Gulf of Mexico. 14. Give seven counties in the basin of the Thames and the leading towns in each. 15. Describe the mountain systems of Europe and Asia. 16. Describe the mountain systems of North and South America. 17. Define minutely the position of the following: — (1) Stettin; (2) Cologne ; (3) Copenhagen ; (4) Amsterdam ; (.5) Brussels ; (6) Munich; (7) Perth; (8) Turin; (9) Malta ; (10) Palermo (11) Bombay; (12) Cyprus. 13 Vll.— FRENCH. (All answert to be in French.) 1.— Translate into French : Disappointed in his object, Almagro prepared to march on Cnzco, the capital, as he regarded it, of his own jurisdiction, to get possession of that city, and there make preparations to meet his adversary in the field. Sotelo was sent forward with a small corps in advance. He experienced no opposition from the now defenceless citizens; the govern- ment of this place was again restored to the hands of the men of Chili, and their young leader soon appeared at the head of his battalions, and established his winter quarters in the Inca capital. II. — Translate into English : Le dragon a plusieurs tetes et le dragon a phisieurs queues, Mon sang commence k se glacer ; Et je crou qu'k raoins on s'eflFraie. Je n'en eus toutefoiB que la peur sans le mal Jamais le corps de I'animal Ne put venir vers moi, ni trouver d'ouverture. Je rivals k cette aventure, Quand un autre dragon, qui n'avait qu'un seul chef, Et bien plus d'une queue, k passer se pre'sente, Me voilk saisi derechef D'etonnement et d'^poUvante, Ce chef passe, et le coqw, et chaque queue aussi : Rien ne les emp^cha ; I'un Jit chemin k I'antre. La Fontaine's Fables ; I-XII. 1 . Give the meaning of the Fable, fill up all the ellipses and destroy inversions. 2. Give the primitive tenses of the verbs marked in italics. III. — Translate into English i lis s'adresserent au baron de Orothusen et au chancelier Mulier ; ils leur dirent qu'ils vettaient dans le desseiri de servir de fideles gardes au roi ; et que, s'il voulait, ils le conduiraient a Andrinople, ou il pourrait parler lui-m6me au grand-seigneur. Daus le temps qu'ils fesaient cette proposition, le roi lisait des lettres qui arriraient de Constantinople, et IG que Fabrice, qui ne pouvait plus le voir, lui avait fait tcnir secr^te- ment par un jannissaire. — Charles XIL, Book Cth. 1. Give the contents of the 6th Book. 2. Translate : " He apjilies himself to his studies." 3. Give one compound tense of s'adresserent. 4. What other verb is conjugated just like direnti .5, Servir, its Present Indicative. 6. Explain the two de "lervir dn. 7. Et que, what sort of word is que here ; and by what governed ? 8. 11, who is it ? 9. State the accusatives to tenir and fait. 10. Point out all the idiomatic words or phrases. IV. — Grammatical questions. 1 . Along with the full examples for each, give the rules of the agree- ment of the past participle of an active, neuter, passive, imper- sonal and reflective verb. 2. State the place of the subject with regard to the verb, and in what it differs from the English. 3. What difference is there between c'est a voua de and d^st a vous a ; anohlir and ennohlir; atteindre une chose and aiteindre it une chose; with examples. 4. Give the plural of: Hotel-Dieu, auto-da-fe, post-scripium, basse- cour, acant-coureur, un passe partout ; with English and reasons why. 5. When do we use independent sentences : son, sa, ses, leur, leurs, or en, and the article in speaking of things. Examples. 6. Give the feminine of: tuteiir, serviteur, absotts, dissous, doux,faux, vrai ; and plural of: (jeneral, nasal, carnaval, regal, eventail, bestial. II 17 VIII.— ENGLISH LANGUAGE. (1) Analyse the following sentence : Some time thus spent, the young man grew at last into a petty anger ; that a hird whom art had never taught cleffs, moods, or notes, should vie with him for mastery, whoso study had husied many hours to perfect practice : (2) Shew what remains of inflection there are in English ; and by a comparative view of modern European tongues, that in conformity with the general law they have gradually iost their inflective power. Shew the rationale of this. What have they substituted in its place ? (3) What have we lost by the verb '* Weorthau " being dropped from our language. What have we gained by new applications of " Sceal " and " Wille " ? Give the derivations and radical mean- ings of the Auxiliary Verbs in English, German, French and Spanish. (4) Why do the modern Gothic tongues deviate less widely from their originals than the Romance languages from the Latin. (5) Give a historic view of the successive strata of the English Voca- bulary, marking as definitely as you can the dates of the several accessions. (6) Shew that the Anglo-Saxon is the base of our language. Give the eight classes of words you would consider the characteristic marks of the mother tongue of any people. (7) Give the words added to our language from the Celtic, Latin of the first and second periods The general character of the Nor- mand French accessions to our tongue, with instances. Compare these with their originals. Give the Saxon equivalents for the following, with their derivations still found in our language : — Death. — To go. — To bow. — To twist. (8) Give a few of the miscellaneous Elements iii our language. (9) Give the proximate and ultimate derivations of the following : — Desire, Chivalry, Shore, Earl, Mercy, Poltron, Curfew, Count. Souvent, Assez, Chez, Mahlir, Jamais, Noel. B li 18 IX.— C0M1»ARATIVE PHILOLOGY. (1) Divide on some principle all knoMii languages. {^2) What are the Romance languages ? Whence their name ? (.'J) What objection has been lately urged to the term "Indo-Germanic'' as applied to the family of languages it was supposed to embrace. Give the more correct term. (4) Shew in Greek,— and where they are represented — in English and French, the comparative terms for the following, accounting for the respectives changes: Vinum, Ovum, Sylva, Equus, Deus, Quatuor, Sequor, Aratrum, Sisto, Sub, Cum, Sal. (5) Explain "Grimm's Law." Shew its simplicity and utility in comparative Philology. Shew its truth by the comparison of a few German an(J English words. (G) Shew the principal Laws that regulated the transition of the Latin into the French. (7) Give instances in English and French where from the derivation of n word having been forgotten it has been introduced a second time into these languages and in a different form. /8) Shew by a comparison of the following words in various languages they must severally have had one primitive root, from which it has passed into these : " Daughter," " Tongue," ** Vmsue" " Stand." X.— ARITHMETIC. 1 . A person is obliged to transfer iJ4,000 Bank Stock, on which U per cent, interest is paid, when the price is 150^ to the 3 per cents., at 90 J ; how much does he lose or gain in annual income ? 2. Given that the area of a circle is 3.14159 times the square of the radius, find the radius of a circle whose area is G acres. 3. Find the simple interest of $924.50 for 2 years, 5 months, and 7 days, at G per cent. 19 I. Cnlculiito the diapioual of n ciibi! coiitaiiiini!; l'}A\'2't cubic inclifs. n. If a debt of 81, (!()() be payable in 2 inoiKhs, one of S'J.IOO in 4 months, uiul another of $2,000 in Oinontlis; find the true ('quatod time of payment, the rate of interest beini;; ") per cent. (a) Give the ride by which the equated time is commonly determined. (». Fiiul the true present worth of 1|S() 12.80 due 2 years hence, at (I per cent, simple interest. 7. Shew that discount as calculated by the banker, exceeds the true discount by the interest on the true discount. 8. A note for .£850, drawn Aui^ust 10th, at \ months, is discounted September 12th at 7 per cent. ; thid the amount received, 9. Prove the rule for the reduction of circulating decimals to equi- valent vnlgar fractions. 10. Convert 8G32 from the denary to tlio (piinary scale. 11. Prove the rule for pointini^, in multiplication of decimals. 12. For what sum must an insurance be effected, at 3^ per cent., on a vessel worth ^12,000, so as to cover botii the loss of the vessel and the premium paid for insurance ? 13. Denoting a given sum of money by P, and the sum to which it will amount in t years at r per cent., simple interest by A ; deduce the relation Ar=P (} + '1.) V Too/ 14. A man by the sale of his farm for ;i^9,lOO, gained a profit of 30 per cent, on the cost price. What had he paid for it ? 15. Find by duodecimal arithmetic, the area of a floor ,26 ft. 6 in. long, by 18 ft. 10 in. wide. I(). In what time will a given sum of money double itself, at o per cent., simple interest ? 17. A block of marble G ft. long, 4 ft. wide, and 3 ft. deep, cost r^ 302.40 ; what should be the width of another block, 5 ft. long, and 1 1 ft. dee]), whose value is .i?80. 90 XI. -ALGEBRA. (1) Solve ibo ciiuatiouu ;ra + y9 = 90 3 («) >/;-y;;x=y2 m , n •^ (0 - + -= a a; y r (rf) 21 22 x^ +4x 3x'-» — 8.1' .1- 3 _ (2) Find the H. C. M. of a:« + a^y — a:* y'^ — y» and X* — x^i/ — x^ y^ + y^ (3) The sum of the two digits of a certain number multiplied by the number is 36, and if 9 bo added to the number, the digits are transposed. Find the number. (4) Deduce an expression for the sum of n terms of a geometric series. (5) The sum of 2 numbers is 8, and the sum of their cubes 224 : find them. (6) Sum the series 2, 4, G, &c., to 30 terms. (7) "Write down the 6th term of {ax + x^y^ SI (8) One gallon of wino worth $8 is mixed with 160 galicns of wine worth f^.50 a gallon. — At what price per gallon must the mixed wine be sold that a profit of 16 per cent, may bo mado ? (9) Shew that 2" — 1 will represent the total number of combinations of n things taken 1, 2, 3. . . . n together, (10) Prove the Binomial Theorem when the index is a positive integer. (11) A and B walk towards each other from 2 stations 105 miles apart. A walks 15 miles the first day, 14 the second, 13 the third, and so on. B walks 12 miles the first day, 10 the second, 8 the third, &c. When will they meet ? (12) Shew that the arithmetic, geometric and harmonic means between a and c are in geometric progression. (13) A shopkeeper, by the sale of a piece of goods, realizes a profit of 10 per cent, but had he sold it ono shilling a yard less he would have lost 5 per cent. Required the cost pri'^o per yard. (14) On how many nights may a different guard of 4 men be draughted from a corps of 30 men ? (a) On how many nights would any one man in such a case be on guard ? XII.—GEOMETRY. (1) Parallelograms upon equal bases and between the same parallels, are equal. (2) To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. (3) If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rect- angle contained by the whole, and that part, together with the square, on the other part. 22 (4) To describe a square that shall be equal to a f^ivcn rcctiliueal figure. (5) The angle at the centre of a circle, is double of the angle at the circumference upon the same part of the circumference. (6) Upon a given straight line, to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle. (7) To inscribe an equilateral and equiangular pentagon in a given circle. (8) Similar triangles are to one another in the duplicate ratio of their homologous sides. (9) To describe a rectilineal figure which shall be similar to one, and equal to another rectilineal figure. (a) Given the base and vertical angle, to find the triangle whose area is a maximum. (b) If the opposite sides A B, CD, of a quadrilateral be produced to meet in the point E, and F and G be the middle points of the diagonals AC, BD, then will the triangle EFGhe one- fourth of the quadrilateral ABCD. (c) Through two given points to describe a circle, intersecting a given circle so that the chord of intersection sh.all be of a given length. XIII.— TEIGONOMETEY. (1) Given that sec. A = 1.5, find ain. A. (2) Shew that cos. (A — B) = cos. A cos. B + siu. A sin. 15. (3) Two sides of a triangular field, including an angle of 35" 10', are 12 and 15 chains in length respectively. Find the uumbti' of acres in the field, 1 acre = 10 square chains. ^PnmBIVI**!' '-)'. ' '. .'J^y^'V 23 (4) Prove the formulsD (a) Siu. 2 A = 2 tan. A 1 + tan.2A (b) Sin.2 A — 8in.2 B = sin. (A + B) sin. (A — B) r \ rv o A 1 — COS. 2 A (c) Tan= A = — -^ ^ ^ I + COS. 2 A » Tan 5 (A + B) = ^^^a + co^.B (5) In a triangle, ABC, whose sides ar*^ a. b. c, and perimeter 2 s, prove that sin. i A = ^A»-h)(s-c) ^ be be (6) From a boat I observe that the elevation of the top of a tower on a cliff is 21*^ 20', and rowing directly towards the tower for 500 yards, I now observe the elevation of the top and bottom of the tower to be 49° 3', and 41° 20', respectively. What is the height of the cliff and of the tower ? (7) In a triangle ABC, given that A B = 50 ft. B C = 20 ft. and angle A B C = 20« 15', find the remaining side and angles. Lovell and Gibson, Printers, Yonge Street, Toronto.