HONOUR E X A M I N A T I O N S , O.T. 1872. CXV
2. Translate into English—
LiaTEp a ii ETiKTEg, w fidrEp a r p . d.
Nv%, d X a n l a i Kal SESopKoaiv
Troivdv, K X V & ' b A a r o v g y a p Ivig ii d n i i o v Tidnaiv, TOVS dipaipovfiEvog
TtTWKa, iiarpwov u y v i a i i a Kvpiov (povov.
itrl Si TW TEQVJXEVW
TOSE jxiXog, irapaKowd, irapaipopd (ppEvoSaXrjg, • ifxvog ii, ' E p i v i w v ,
Siafxiog <ppEvwv, dcpop/iiKTog, a v o v d fiporolg.
Tovro y a p Xdj(OC S i a v r a i a d v r . d.
fiolp EirtKXwaEV ifjnricwg EXEIV, >
d v a r w v Tolaiv a v r o v p y i a i ivpnziawaiv t i d r a i o i , ro'ig biiapTEiv, '6(pp a v
y a v vTriXOr]' daviov S' OVK d y a v iXEvdEpog.
CXV1 EXAMINATION P A P E R S ,
^Eschylus the most obscure of extant writers."
Examine this statement, and give any of those causes.
7. State the main points in which the Greek drama differed from the modern drama.
8. Parse the following words, and translate and ex- plain them :—(a) KarnprvKwe, (ft) KadijaEiv, (c) alSEadEle, (d) KaTEvwxiovrai.
9. From what source does -32schylus ordinarily take his metaphors. Quote passages to prove your assertions.
10. Turn the following into Greek Iambics:—
Hearing thy voice I.came hither,
Hapless lady, in terror: struck to the soul by fear, Lest thou should'st come bearing to me any
new misfortune
In addition to the present one. Mess : Well then about thy. child
A wonderful and dread story would I tell thee.
11. Translate into Greek Prose—
So said the oracle. Now the Nile, when it overflows, floods not only the Delta, but also the tracts of country on both sides the stream which are thought to belong to Libya and Arabia, in some places reaching to the extent of two days
•journey from its banks, in some even exceeding that distance, but in others falling short of it.
HONOUR EXAMINATIONS, O.T. 1872. CXV11
S E N I O R L A T I N . Professor Strong.
TACITUS, Annals. HORACE and P E R S I U S , Satires, 1. Translate into Latin Prose—
One day when Antonius was sitting in the boat with Cleopatra he caught but little, and was vexed at her seeing his want of success. So he ordered one of his men to dive into the water and put upon his hook a fish which had been before taken. .Cleopatra, however, saw what was being done and quickly took the hint for a joke of her . own. The next day she brought a larger number
of her friends to see the fishing, and when Anto- nius let down his line, she ordered one of her divers to put on the hook a salted fish. The fish was landed, and Cleopatra playfully consoled Antonius, saying: " Well, general, you may leave fishing to us petty princes of Pharos and Canopus; your game is cities, provinces, and kingdoms."
2. Translate into English—
At Zmyrnae.i ropetita vetustate, sou Tantalus love ortus illos, sive Theseus divina et ipse stirpo,
* " sive una Amazonum condidisset, transcendere ad ea quis rnaxime fidebant in populum Romanum officiis, missa navali copia non modo externa ad bella, sed quae • in Italia tolerabantur; seque primes templum urbis Romae statuisse, M. Porcio consule, magnis quidem lain populi Romaui rebus, nondum tamen ad summum elatis, stante adhuc
CXV111
Punica urbe et validis per Asiam regibus. Simul L. Sullam testem adferebant, gravissimo in dis- crimine exercitus ob asperitatem hiemis et penu- riam vestis, cum id Zmyrnam in contionem nuntiatum foret, omnes qui adstabant detraxisse corpori tegmina nostrisque legionibus misisse.
Ita rogati sententiam patres Zmyrnaeos praetu- lere. Censuitque Vibius Marsus ut M. Lepido, cui ea provincia obvenerat, super numerum lega- retur, qui templi ^curam susciperet. Et quia Lepidus ipse deligere per modestiam abnuebat, Valerius Naso e praetoriis sorte missus est.
3. Translate into English—
Saepe oculos, memini, tangebam parvus olivo, Grandia si nollem morituri verba Catonis Dicere, non sano multum laudanda magistro, Quae pater adductis sudans audiret amicis.
Jure etenim id sumnium, quid dexter seuio ferret Scire, erat in vote; damnosa canicula quantum Raderet; angustae ,collo non fallier orcae;
Neu quis callidior buxum torquere flagello.
Hand tibi inexpertum curvos deprendere mores, Quacque docet sapiens braccatis illita Medis Porticus, insomnis quibus et detonsa juventus Invigilat, siliquis et grandi pasta polenta;
E t tibi quae Samios diduxit littera ramo Surgentem dextro monstravit limite callem.
« 4. Translate into English—
Laudas Fortunam et mores antiquae plebis ; et idem, Si quis ad ilia Deus subito te agat, usque recuses;
Aut quia non sentis quod clamas rectius esse, Aut quia non firmus rectum defendis, et haeres,
cxix Nequicquam coeno cupiens evellere plantam.
Romae rus optas, absentem rusticus urbem Tollis ad astra levis. Si nusquam es forte vocatus Ad coenam, laudas securum olus; ac, velut usquam Vinctus eas, ita te felicem dicis, amasque, Quod nusquam tibi sit potandurn. Jusserit' ad se Maecenas serum sub lumina prima venire Convivam : Nemon' oleum feret ocius ?
5. Describe the character of Tiberius, quoting Tacitus where possible.
. Explain and refer the following passages to their context:—
(a) Interim Felix intempestivis remediis delicta ac- cendebat.
(ft) Beatus Fannius ultro Delatis capsis et imagine !
(c) Varo, regustatum digito terebrare salinum Contentus perages, si vivere cum Jove tendis.
7. " Satira tota nostra est." Explain this statement, and compare and contrast the chief Roman satirists.
8. Give some account of Roman education during the time of the Empire, illustrating your remarks from Tacitus, Horace, or Persius.
9. " Hibernatque meum mare." Explain this expres- sion.
cxx EXAMINATION PAPERS,
GEOMETRY AND TRIGONOMETRY.
Professor Wilson.
1. Explain what is meant by the notation tan~'a-r, and investigate a general expression for tan_ 1l.
A
2. Investigate a formula for sin _ in terms of s\nA
D 2
and explain the four values. If sin^4 =z -5 find the four values of sin— and write down corre- sponding values of A and — .
3. Shew that sinO is intermediate in value between
03
6 and 0 - - 4
4. Assuming Demoivre's theorem in the case of a
> positive integral index, investigate an expression which will give the n values of
(cose -fV^Isiney •
5. Investigate the expression for sin9 and cos9 in ascending powers of 0 and deduce the expo- nential expressions for"these quantities.
6. Shew how to express any power of cosO in a series of first powers of cosines of multiples of 0.
Ex. cosc9
H O N O U R E X A M I N A T I O N S , O.T. 1872. CXxi
7. Find the sum of n terms of the series sin a + sin(a + ft) + sin(a + 2/3) + &c.
Hence shew that if the circumference of a circle be divided into any number of equal parts and radii drawn to the dividing points; the slim of the sines of the angles which these radii make with any fixed radius will be 0.
8. Investigate the distinguishing property of the curve in which the surface of a cone is cut by a plane oblique to the axis.
9. Shew that in any conic section the tangents at the extremities of" any focal chord intersect in the directrix. Interpret this in the case of the circle.
10. In the parabola shew that the subnormal is equal to the semilatus-rectum.
1 1 . In the ellipse shew that the rectangle under the focal distances of any point is equal to the square on the corresponding semiconjugate diameter.
12. In the hyperbola shew that C P is a mean propor- tional between (72'and CV.
ALGEBRA.
Professor Wilson.
1. Solve the equations
ax + by — c
a ' x + b ' y aaaaaaa c '
f
CXxii E X A M I N A T I O N P A P E R S ,
What must be the relations amongst the coeffi- cients
1st that these equations may be inconsistent 2nd that they may be insufficient ?
What forms will the general solutions take in each of these cases ?
2. Examine and explain the jieculiarity of the equa- tions
6 x - 9 y + z = 10 8* - I2y + 2z = 18 lOx - Voy + Sz = 26 3. Find the remainder after dividing
x" + px"-' + qxn~'> + &c. + t by x — a.
Hence shew that if a, ft, c &c. are n different values of x which satisfy the equation
x" + px"-' + • • .- + t = 0
the left hand side of this equation is identical with (x — a) (x — ft) (a- — c) . . .
and hence shew that, if two quantities A and k when substituted for x give to the left hand side of this equation values one positive and the other negative, at least one root of the equation is intermediate between h and k.
4. Resolve the expression x " — 1 into quadratic fac- tors not containing impossible coefficients.
5. Apply the method of indeterminate coefficients to expand — —-^ in ascending powers of x.
(1 — 3a;)-
HONOUR EXAMINATIONS, O.T. 1872. CXXiii 6. Apply the binomial theorem to find the coefficient
of x" in the preceding expansion.
7. Resolve each term of the series
x ' ax (1 + a;) (1 + ax) (1 + ax) (1 + a2x )
^ (I + a2a z ) ( l + a3x) +
into its partial fractions and apply the result to find the sum of n terms of the series.
8. A shelf contains 20 books of which 4 are single volumes and the others form sets of 8, 5, and 3 volumes respectively; find in how many ways the books may be arranged on the shelf, the volumes of" each set being in due order from left to right.
9. Investigate the series for (1 + x)n in ascending jiowers of n : define e and deduce the series for tf.
10. Investigate a series for log, "
11. Find the limit of
*/dz + ax + x1 — •y/a? — ax + x2 , • when a; aa= 0 v « + x — v a — x
12. A debenture of £100 is payable at the end of n years and bears interest at r per cent, per an- num : find an expression for its present value reckoning compound interest at s per cent, per annum.
/ 2
CXX1V EXAMINATION P A P E R S ,