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VOLUNTARY PORTION.

1. Triangles having the same altitude are to one another as their bases.

2. Define the tangent of an angle ; express the values of tan 90°, tan 45o, tan 135o, tan 60°. Prove tan (A + B + C) =

tan (A + B) + tan C

[ – tan (A + B) tan C 3. Given three sides of a triangle, investigate a formula adapted to logarithmic computation, by means of which an angle of the triangle may be found.

Find the least angle of the triangle whose sides are 63.4, 72.2, 81.8.

4. State and prove the property by means of which the solid generated by the revolution of a given plane area round an axis may be determined. Assuming the area of a semi-circle and the content of a sphere, find the centre of gravity of the semicircle.

5. If a body be projected up a given smooth inclined plane, show how to determine the space it will describe in a given time.

An inclined plane rises 1 foot vertical for every 100 feet of length, with what velocity must a body be projected up the plane that it may describe 183-9 feet in 10 seconds, gravity being taken as 32-2 feet.

LATIN

Rev. OSBORNE GORDON, B.D.

1. Which of the Cardinal Numerals are declinable, and which not ?

2. Decline: ager, agger, caro, iter, merces, aer, tener, acer-marking the gender of the nouns substantive.

3. What are the comparatives and superlatives of: agilis, dives, externus, juvenis, senex, benevolus?

4. Give the perfect tenses and infinitive moods of : queror, fruor, fio, edo, proficiscor, mereor, nanciscor.

5. What are the derivations of : cogo, ambitio, mansuetus, facilis, importunus, eluvies?

6. Show how supines in um and u are used.

7. What cases do antecedere, juvare, lædere, imperare, moderari, meminisse, præesse, govern?

8. What is the government of verbs of asking, teaching, concealing? Give instances.

9. When is ut followed by the present, and when by the imperfect subjunctive ? Illustrate your answer by translating :

He went to Rome to see his brother.
I have come here to see you.

I came here to see you.
Translate them also without using the particle ut.

10. Parse thoroughly any one of the short sentences following:

Passages for Translation. [N.B.—Candidates are recommended to attempt

some of the short passages, before proceeding to the longer passages from authors. Not more than two of the longer passages should be attempted.]

Est igitur adolescentis, majores natu vereri, exque his deligere optimos et probatissimos, quorum consilio atque auctoritate nitatur. Ineuntis enim ætatis inscitia senum constituenda et regenda prudentia est.

Hinc rex xx stadia processit, semita propemodum invia, cui sylva imminebat, torrentesque et eluvies iter morabantur. Nullo tamen hoste obvio penetrat; tandem ad ulteriora perventum est. Præter alios fructus, quorum copia regio abundabat, pomorum ingens modus nascitur, et uberrimum gignendis uvis solum est.

Anco regnante, Lucumo vir divitiis potens Romam commigravit, cupidine maximè ac spe magni honoris.

Demarati Corinthii filius fuit, qui ob seditiones domo profugus, cum Tarquiniis forte consedisset, uxore ibi ducta duos filios genuit.

Funus interim Procedit; sequimur: ad sepulcrum venimus : In ignem posita est : fletur : interea hæc soror, Quam dixi, ad flammam accessit imprudentius Satis cum periclo: ibi tum exanimatus Pamphilus Bene dissimulatum amorem et celatum indicat.

Cæsar.

Interim ii, qui ad alteram partem oppidi, ut supra demonstravimus, munitionis canssa convenerant, primo exaudito clamore, inde etiam crebris nunciis incitati, oppidum ab Romanis teneri, præmissis equitibus, magno concursu eo contenderunt. Eorum ut quisque primus venerat, sub muro consistebat suorumque pugnantium numerum augebat. Quorum quum magna multitudo convenisset, matres familiæ, quæ paullo ante Romanis de muro manus tendebant, suos obtestari et more Gallico passum capillum ostentare liberosque in conspectum proferre cæperunt. Erat Romanis nec loco, nec numero, æqua contentio : simul, et cursu et spatio pugnæ defatigati, non facile recentes atque integros sustinebant.

Cicero. Quatuor robustos filios, quinque filias, tantam domum, tantas clientelas Appius regebat et cæcus et senex. Intentum enim animum, tamquam arcum, habebat, nec languescens succumbebat senectuti. Tenebat non modo auctoritatem, sed etiam imperium in suos; metuebant servi, verebantur liberi, carum omnes habebant: vigebat in illa domo mos patrius et disciplina. Ita enim senectus honesta est, si se ipsa defendit, si jus suum retinet, si nemini mancipata est, si usque ad extremum spiritum dominatur in suos. Ut enim adolescentem, in quo senile aliquid, sic senem, in quo est

գ aliquid adolescentis, probo : quod qui sequitur, corpore senex esse poterit, animo numquam erit. Semper enim in studiis laboribusque viventi non intelligitur, quando obrepat senectus. Ita sensim sine sensu atas senescit

nec subito frangitur, sed diuturnitate exstinguitur.

Virgil. Nox erat, et terris animalia somnus habebat: Effigies sacræ divûm Phrygiique Penates, Quos mecum ab Troja mediisque ex ignibus urbis Extuleram, visi ante oculos adstare jacentis In somnis, multo manifesti lumine, qua se Plena per insertas fundebat luna fenestras; Tum sic affari et curas his demere dictis : Quod tibi delato Ortygiam dicturus Apollo est, Hic canit, et tua nos en ultro ad limina mittit. Nos te, Dardania incensa, tuaque arma secuti, Nos tumidum sub te permensi classibus æquor, Idem venturos tollemus in astra nepotes, Imperiumque urbi dabimus : tu mænia magnis Mayna para, longumque fugæ ne linque laborem. Mutandæ sedes: non hæc tibi litora suasit Delius, aut Cretæ jussit considere, Apollo.

Horace.
O quisquis volet impias

Čædes et rabiem tollere civicam,
Si quæret Pater urbium

Subscribi statuis, indomitam audeat
Refrenare licentiam,

Clarus postgenitis ; quatenus, heu nefas !
Virtutem incolumem odimus,

Sublatam ex oculis quærimus invidi.
Quid tristes querimoniæ,

Si non supplicio culpa reciditur ?
Quid leges sine moribus

Vanæ proficiunt ? Si neque fervidis
Pars inclusa caloribus

Mundi, nec Boreæ finitimum latus,
Duratæque solo nives

Mercatorem abigunt ? Horrida callidi
Vincunt æquora navitæ ?

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