Quidve moror, si omnes uno ordine habetis
Achivos,

Idque audire sat est? iamdudum sumite poenas:

Hoc Ithacus velit, et magno mercentur Ātridae. (d) Exhibe quaeso, Sexte Clodi, exhibe librarium illud legum vestrarum, quod te aiunt eripuisse e domo et ex mediis armis turbaque nocturna tamquam Palladium sustulisse, ut praeclarum videlicet munus atque instrumentum tribunatus ad aliquem, si nanctus esses qui tuo arbitrio tribunatum gereret, deferre posses. * * An huius ille legis, quam Sex. Clodius a se inventam gloriatur, mentionem facere ausus esset, vivo Milone, ne dicam consule? De nostrum omnium —non audeo totum dicere. Videte quid ea vitii lex habitura fuerit cuius periculosa etiam reprehensio est. Et adspexit me illis quidem oculis quibus tum solebat cum omnibus omnia minabatur: movet me quippe lumen curiae. Quid? tu me tibi iratum, Sexte, putas, cuius tu inimicissimum multo crudelius etiam punitus es quam erat humanitatis meae postulare?

(e) Otia nunc istic, iunctisque ex ordine ludis
Cedunt verbosi garrula bella fori.

Usus equi nunc est, levibus nunc luditur armis,
Nunc pila, nunc celeri vertitur orbe trochus,
Nunc ubi perfusa est oleo labente iuventus,
Defessos artus Virgine tingit aqua.

Scaena viget studiisque favor distantibus ardet
Proque tribus resonant terna theatra foris.

2. Translate and explain—

(a) Quod si per furiosum illum tribunum senatui quod sentiebat perficere licuisset, novam quaestionem nullam haberemus; decernebat enim ut

veteribus legibus, tantum modo extra ordinem, quaereretur: divisa sententia est postulante nescio quo; nihil enim necesse est omnium me flagitia proferre; sic reliqua auctoritas senatus empta intercessione sublata est.

(b) Poma negat regio, nec haberet Acontius, in quo Scriberet hic dominae verba legenda suae.

(c) Nam si morte carens vacuam volat altus in auram Spiritus, et Samii sunt rata dicta senis.

3. Translate and explain the following conditional sentences, shewing clearly the force of each mood and tense:

(a) Et si fata deum, si mens non laeva fuisset, Impulerat ferro Argolicas foedare latebras, Troiaque nunc staret, Priamique arx alta.

maneres.

(b) Delitui dum vela darent, si forte dedissent.
(c)
Ni mea cura resistat,

Iam flammae tulerint inimicus et hauserit ensis. (d) Non tali auxilio, nec defensoribus istis

Tempus eget, non si ipse meus nunc afforet
Hector.

4. What account does Caesar give of the doctrines, functions, and privileges of the Druids ?

ALGEBRA.

The Board of Examiners.

1. Resolve into factors

2. If

+ ca(ca) (b − x) (b − y) (b — z)
+ ab(a - b) (c — x) (c − y) (c — ≈).

then

ax + by + cz = 0,

(a + b + c) (x2 + y2 + z2 — Qyz — Qzx — 2xy) =3ax2 + 3by2 + 3cz2

+ a(y-2)2 + b(≈ — x)2 + c(x − y)2.

3. Eliminate x, y from

4. If

axy + bx + cy + d = 0, a2xy + b2x + c2y + d2 = 0, a3xy + b3x + c3y + d3 = 0.

ax2 + by2 + cz2 = 0,
fyzgzx+hxy = 0,
lx + my + nz = 0,

prove that

where

P2 + QR = 0,

P = afmn + bgnl + chlm,
Q = bel2 + cam2 + abn2,

R=ƒ212 + g2m2 + h2n2 — 2ghmn — 2hfnl — 2fglm.

5. If

bz2 + c'y2 - 2fyz = 0,
cx2 + a'z2 - 2gzx

· ́ay2+ b'x2 - 2hxy = 0,

shew that

ƒ√ BC + g√ CA + h√ AB = μ −fgh,

where

Abe' -f2, B = ca' - g2, Cab' — h2,
abc + a'b'c'.

6. Solve the equation

√ x2 + ax +ƒ + √ x2 + bx + g

+ √x2 + cx + h = 0,

having given that

a + b + c = 0,

af + bg+ch = 0.

7. Solve the simultaneous equations.

8. If U1, U2,

....., un ben quantities whose sum is s,

and if n other quantities v1, V2, •

so that

be taken

9. Define an arithmetical progression, and prove the formulæ for the general term and for the sum of

n terms.

The sum of 2n + 1 numbers in arithmetical progression is a, and the sum of the squares of the numbers is b2. Find the numbers.

10. Find, without assuming the permutation formula, the number of combinations of n things r at a time.

Three sorts of things, n of each sort, are divided into three groups containing respectively a, b, c things where a+b+c=3n. If c > 2n shew that the number of ways of making the division is

(a + 1)(a + 2) (b + 1)(b + 2).

GEOMETRY AND TRIGONOMETRY.

The Board of Examiners.

1. Prove that to every triangle there is an orthocentre, that is, a point such that the lines joining it to the vertices are perpendicular to the opposite sides; and show that each side of the triangle is half way between the orthocentre and the point in which the perpendicular on it from the orthocentre cuts the circle circumscribing the triangle.

2. Give a geometrical construction by which a regular polygon of 2n sides can be derived from one of n sides.