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κωμῳδίας δὲ φορτικῆς σοφώτερον.
ἔστιν γὰρ ἡμῖν δεσπότης ἐκεινοσὶ

ἄνω καθεύδων, ὁ μέγας, οὐπὶ τοῦ τέγους.
οὗτος φυλάττειν τὸν πατέρ ̓ ἐπέταξε νῷν,
ἔνδον καθείρξας, ἵνα θύραζε μὴ 'ξίῃ.

νόσον γὰρ ὁ πατὴρ ἀλλόκοτον αὐτοῦ νοσεῖ,
ἣν οὐδ ̓ ἂν εἰς γνοίη ποτ' οὐδ' ἂν ξυμβάλοι,
εἰ μὴ πύθοιθ ̓ ἡμῶν. ἐπεὶ τοπάζετε.

ARISTOPHANES, Vespae, 54-73.

THURSDAY, March 13, 1884. 9-12.

1. TRANSLATE into LATIN HEXAMETERS :

I see thee, mighty Lord of all, revealed

In forms of infinite diversity.

I see thee like a mass of purest light,
Flashing thy lustre everywhere around.

I see thee crowned with splendour like the sun,
Pervading earth and sky, immeasurable,
Boundless, without beginning, middle, end,
Preserver of imperishable law,

The everlasting Man; the triple world
Is awe-struck at this vision of thy form,
Stupendous, indescribable in glory.
Have mercy, God of gods; the universe
Is fitly dazzled by thy majesty,
Fitly to thee alone devotes its homage.
At thy approach the evil demons flee,
Scattered in terror to the winds of heaven.
The multitude of holy saints adore thee-
Thee, first Creator, lord of all the gods,
The ancient One, supreme Receptacle
Of all that is and is not, knowing all,
And to be known by all.

Bhagavad-gītā, xi. (Monier Williams).

2. For LATIN ELEGIACS:

Semen est sanguis Christianorum.

TERTULLIAN.

THURSDAY, March 13, 1884. 1—4.

TRANSLATE with short notes:

1.

2.

nil adeo fieri celeri ratione videtur,

quam sibi mens fieri proponit et inchoat ipsa:
ocius ergo animus quam res se perciet ulla,
ante oculos quorum in promptu natura videtur:
at quod mobile tanto operest, constare rutundis
perquam seminibus debet perquamque minutis,
momine uti parvo possint impulsa moveri.
namque movetur aqua et tantillo momine flutat,
quippe volubilibus parvisque creata figuris,
at contra mellis constantior est natura
et pigri latices magis et cunctantior actus;
haeret enim inter se magis omnis materiai
copia, nimirum quia non tam levibus extat
corporibus neque tam suptilibus atque rutundis.
namque papaveris aura potest suspensa levisque
cogere ut ab summo tibi diffluat altus acervus,
at contra lapidum conlectum ipse euru' movere
noenu potest. igitur parvissima corpora proquam
et levissima sunt, ita mobilitate fruuntur:
at contra quae cumque magis cum pondere magno
asperaque inveniuntur, eo stabilita magis sunt.
nunc igitur quoniam est animi natura reperta
mobilis egregie, perquam constare necessest
corporibus parvis et levibus atque rutundis.

LUCRETIUS III. 182-205.

vix ea legati, variusque per ora cucurrit
Ausonidum turbata fremor: ceu saxa morantur
cum rapidos amnis, fit clauso gurgite murmur
vicinaeque fremunt ripae crepitantibus undis.
ut primum placati animi et trepida ora quierunt,
praefatus divos solio rex infit ab alto:
'ante equidem summa de re statuisse, Latini,
et vellem et fuerat melius, non tempore tali
cogere concilium, cum muros adsidet hostis.
bellum importunum, cives, cum gente deorum
invictisque viris gerimus, quos nulla fatigant
proelia; nec victi possunt absistere ferro.

spem siquam ascitis Aetolum habuistis in armis,

ponite spes sibi quisque. sed haec quam angusta videtis;

cetera qua rerum iaceant perculsa ruina,

ante oculos interque manus sunt omnia vestras.

nec quemquam incuso: potuit quae plurima virtus.

esse, fuit; toto certatum est corpore regni.

nunc adeo quae sit dubiae sententia menti

3.

expediam et paucis animos adhibete docebo.
est anticus ager Tusco mihi proximus amni,
longus in occasum, finis super usque Sicanos:
Aurunci Rutulique serunt et vomere duros
exercent colles atque horum asperrima pascunt.
haec omnis regio et celsi plaga pinea montis
cedat amicitiae Teucrorum, et foederis aequas
dicamus leges sociosque in regna vocemus.
considant, si tantus amor, et moenia condant.'

VIRGIL, En. XI. 296-323.

non dices hodie quorsum haec tam putida tendant,
furcifer? Ad te, inquam. Quo pacto, pessime ? Laudas
fortunam et mores antiquae plebis, et idem,

siquis ad illa deus subito te agat, usque recuses,
aut quia non sentis, quod clamas, rectius esse,
aut quia non firmus rectum defendis, et haeres
nequiquam caeno cupiens evellere plantam.
Romae rus optas; absentem rusticus urbem
tollis ad astra levis. si nusquam es forte vocatus
ad cenam, laudas securum olus ac, velut usquam
vinctus eas, ita te felicem dicis amasque,
quod nusquam tibi sit potandum. iusserit ad se
Maecenas serum sub lumina prima venire
convivam: nemon oleum fert ocius? ecquis
audit? cum magno blateras clamore fugisque.
Mulvius et scurrae tibi non referenda precati
discedunt. Etenim fateor me, dixerit ille,
duci ventre levem, nasum nidore supinor,
imbecillus, iners, siquid vis, adde, popino.
tu cum sis quod ego et fortassis nequior, ultro
insectere velut melior, verbisque decoris
obvolvas vitium? Quid, si me stultior ipso
quingentis empto drachmis deprenderis? aufer
me vultu terrere; manum stomachumque teneto,
dum, quae Crispini docuit me ianitor, edo.

HORACE, Satires II. 7, 21-45.

illa manus quondam studiorum fida meorum
et felix domino notaque Caesaribus,
destituit primos viridis Demetrius annos:
quarta tribus lustris addita messis erat.
ne tamen ad Stygias famulus descenderet umbras,
ureret implicitum cum scelerata lues,

cavimus et domini ius omne remisimus aegro:
munere dignus erat convaluisse meo.

sensit deficiens sua praemia meque patronum
dixit ad infernas liber iturus aquas.

MARTIAL, I. 101.

FRIDAY, March 14, 1884. 9-12.

1. IF one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.

2. Write a short essay on Euclid's twelfth axiom, and the principles which may be substituted for it.

3. Find the locus of a point such that the sum of the two triangles formed by joining it with the extremities of two given finite right lines shall be given.

In what sense, or with what modification of the enunciation, will the whole of the locus found apply to the problem?

4. Define compound ratio; and prove that equiangular parallelograms have to each other the ratio which is compounded of the ratio of their sides.

5. If two planes intersect, not at right angles, and from a point in one two perpendiculars be drawn, one to the line of intersection, and the other to the second plane, the line of intersection of the planes will be perpendicular to the plane containing the two perpendiculars.

6. Show how to find the greatest common measure of two integers, pointing out methods by which the process may in particular cases be shortened.

7. If a number be divisible by each of two others which are prime to each other, it will be divisible by their product.

Hence show that the product of n consecutive integers is divisible by 1, 2, 3...n.

8. Show that the weight of a substance in pounds may be ascertained by means of weights, to be put into one scale only, of 1, 2, 22, ...2" lbs. up to 2"+1-1 pounds; but that if it be allowable to put the weights some in one scale and some in the other, then with the same number of weights, of 1, 3, 33, 33...3" lbs. respectively, the weight of a substance may be found up to (3′′+1-1) pounds.

9. Show that the simultaneous equations

x + y = a
∞"+y"=b

may be solved by quadratics if n be any integer between 1 and 6.

10. At what part of a table of common logarithms will the increment of the logarithm, regarded as integral, be the same as the increment of the number, regarded as having ciphers added to make the number of figures the same as in the mantissa?

11. Apply the binomial theorem to find √98 to 5 places of decimals.

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FRIDAY, March 14, 1884. 1-4.

1. FIND the solutions, in positive integers, of the equation

7x+13y = 88.

2. If the angles of a regular pentagon be joined in all ways, find numerically the ratios in which any one of the diagonals is divided by two of the others.

3. If coshæ = } (e* + e*), sinh x = } (* — e *), tanh x=sinh x + cosh find the relations between cosh x and sinh x, and between cosh x and tanh x.

4. A person on a known hill measures the altitude, and roughly the azimuth, of a balloon, and simultaneously notes the place of its shadow on the plain below, and the time. The position of the shadow and the height of the mountain being supposed known by reference to a map, and the position of the sun from the time, required to find the elevation of the balloon.

What is the use of roughly observing the azimuth?

5. Prove Sturm's theorem; and apply it to determine the nature of the roots of the equation

x3+qx+r=0.

6. Among parallelograms circumscribing an ellipse, those which have their sides parallel to pairs of conjugate diameters are equal to one another, and less than all others.

7. If a chord of one branch of a hyperbola be produced to meet the conjugate hyperbola, the two portions comprised each between the primitive hyperbola and its conjugate are equal to each other.

8. Find the equation of the surface which touches a system of planes each of which cuts three rectangular axes so that the sum of the squares of the intercepts is constant.

9. Find the greatest paraboloid of revolution which can be inscribed in a right cone on a circular base, the axes of revolution of the two being coincident, and the vertices turned the same way.

10. A heavy flexible and inextensible chain forming a loop rests like a necklace on a smooth vertical cone of revolution; find the tension of the chain.

height on a plane, when the ball was

11. An imperfectly elastic ball is dropped from a known so as repeatedly to rebound. From observing the time from let drop to when the motion ceases, determine the coefficient of elasticity.

12. A person standing on a bridge over a chasm lets fall a stone, and notes the time from when he let go to when he hears the impact; find the depth of the chasm, supposing the velocity of sound known, but neglecting the resistance of the air.

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