3. Munere, of munus, a neuter noun of the third declension.

Ocioris, genitive singular of ocior an adjective in the comparative degree. Positive wanting; superlative ocissimus.

Arsurus, nominative singular, masculine of arsurus, the future participle, active of the verb ardeo, of the second conjugation. Ardeo, arsi, arsum, Ardere.

Poteretur. 3rd person singular. imperfect subjunctive, of potior, a deponent verb of the fourth conjugaton, Potior, potitus sum, potiri.

Illuxerit, 3rd person singular, perfect subjunctive active of lugeo (or luceo) a verb of the second conjugation. Lugeo, luxi, lugere, or luceo, luxi, lucere.

Praecipiti, dative, singular of praeceps, an adjective of one termination in the positive degree. Cognitus, albative, plural of cognitus, the past participle passive of cognosco, a verb of the third conjugation cognosco, cognovi, cognitum, cognoscere. Oblitus, nominative, singular, masculine of oblitus, the past participle, passive of the verb oblino. Oblino, oblevi, oblitum, oblinere.

4. The future infinitive passive is in Latin, expressed by the supine in -um with iri, the infinitive passive of eo. Amatam iri is literally "to be gone to be loved," equivalent to "to be about to be loved."

7. Quisquis signifies whatever. It is used when among a number of specimens of a class none is excepted. Quisquiss consileo fecit, with whatever design he did it.

Quivis signifies "any you please," "all alike." Cujusvis est hoc facere; "any man (i.e., all indiscriminately) can do this.”

8, The locative case is the case which express es the place at which something happens. In Latin, the locative case is identical in form with the genitive in singular nouns of the first and second declensions, and with the ablative in plural nouns, and in nouns of the third declension.

The ethic dative is a dative (especially in the case of the personal pronouns), used to signify that the matter spoken of is regarded with interest by some person; as quid mihi, Celsus agit, how does my friend Celsus.

Intransitive verbs frequently take a noun in the accusative case of kindred meaning; as Duram servit servitutem. He serves a hard slavery. This is called the cognate accusative.

The objective genitive denotes that which is the object of the feeling or action spoken of. It is usually used with nouns, adjectives, or participles, that signify skill, care, desire, or whatever is contrary to these, as

Tempus edax rerum, Time, the consumer of things.

9.

(a) Accusative with infinitive,

We perceive that fire is hot.
Caius says that it pleases him.

(b) Ut with subjunctive,

Many men praise others that they may be praised by them.

(c) Quo with subjunctive,

I think that something should be given to the physician that he may be the more attentive.

(d) Quin with subjunctive,

It cannot be denied that it is more disgraceful to deceive than to be deceived. (e) Quominus with subjunctive,

It was owing to Caius that it was not done.

(f) Ne with subjunctive,

I fear that he will come.

10.

(a) Urbs Veii ab Romà haud longe abest.

(b) Imperator sestertios denos civibus dedit. (c) Mancinus nuncium pacem ab Iberibus petitum misit.

(d) Ne loquere quasi quæ conjuras ignoremus. (e) Innocentium miseremur, sed nihil obstabit quin sontes puniamus.

(ƒ) Homicida, tonitrum audiens, ne in se directus sit, metuit.

Translation from Caesar, Book 1.

XXXIX. While he lingered a few days at Vesontio for corn and provisions, in consequence of our delay, and the reports of the Gauls and traders who proclaimed the Germans to be of immense size of body and of surpassing valour and discipline in arms, so that not even their looks and keen expression of eye could be withstoodon a sudden so great a fear seized the whole army that the minds and feelings of all were not a little shaken. This was originated by the tribunes of the soldiers, who, following Cæsar from the city through friendship, had no great experience in military affairs, one of whom having alleged one reason, another, another, why they thought it necessary for them to set out, they besought his permission to depart; some, influenced by shame, remained, that they might not incur the suspicion of cowardice. These could neither command their countenances, nor sometimes restrain their tears; hidden in tents, they either bewailed their fate, or with their friends moaned over the common danger. Wills were being drawn up on all sides in the whole camp. By the reports and cowardice of these, by degrees even those were disturbed who had great experience of campssoldiers and centurions, and those who commanded the cavalry, who, not wishing to be ranked with those more cowardly, said that they did not fear the enemy, but dreaded the defiles of the route and the denseness of the woods, which lay between them and Ariovistus, or that provisons would not be obtained with sufficient ease. Some even announced to Cæsar when he commanded the camp to be moved and the standards to be advanced, that the soldiers would not heed his command nor advance the standards through fear.

XL. When he perceived these things, having called a council, and the centurions of all ranks being summoned to it, he upbraided them in strong terms, "in the first place because they had presumed to complain or think about either in what direction, or with what design they were being led forth. Ariovistus, during his own consulship had most eagerly sought the friendship of the Roman People. Why should anyone

imagine that he was so rash as to swerve from his allegiance? He himself was persuaded that, having learnt his demands, and perceived the

moderation of the conditions, he would neither spurn his own friendship, nor that of the Roman People. But if, spurred on by rage and madness, he should declare war, what, pray, had they to fear? Or why should they distrust either their own bravery or his own watchfulness? A trial of the enemy had been made within the memory of our fathers, when, the Cimbri and Teutons being defeated by Caius Marius, the army itself seemed deserving of no less praise than its general. A trial had been made likewise in the late rising of the slaves, when they were assisted by that science and discipline which they had learnt from us. From that occasion they could judge how much firmness could effect; because that those

whom, unarmed, they had at first dreaded, afterwards they had vanquished when armed and victorious. In brief, they were those same Germans whom the Helvetii had so often fought, not only in their own country but in Germany, and whom they had for the most part defeated, though they themselves, nevertheless, could not cope with

These

our army. If the defeat and rout of the Gauls affected any, these would find, on inquiry, that the Gauls being weakened by the protracted war, Ariovistus, when for many months he had confined himself to his camp and morasses, and declined battle, had conquered them more by system and policy than by bravery. Which plan might have availed against barbarous and inexperienced men, but he could not even hope that our army could be overcome by it. As to those who cloaked their cowardice under a pretended distrust of the supply of provisions and of the passes of the journey, they appeared to him to act presumptuously in either distrusting the leadership of the general or dictating to him. things concerned him; the Sequani, Leuci, and Lingonae were to supply him with provisions; even now the corn was ripe in the fields; of the journey they would shortly judge for themselves. As to the soldiers not obeying him, or advancing the standards, that report in no way disturbed him; for he knew that whoever an army had refused to obey had either failed through some unlucky action, or some crime had been discovered against him coupled with avarice. His innocence was proved by his whole life, and his good fortune by his war with the Helvetii. Therefore he was resolved, what he otherwise would have postponed a little longer, to move the camp in the fourth watch of the next night, so that he might know as soon as possible whether a sense of shame and duty, or a sense of fear, would prevail with them. But, if none would follow him, he would yet march with the tenth legion alone, whose valour he did not doubt, and

they would be his prætorian guard." Cæsar chiefly favoured this legion, and he had the greatest confidence in their bravery.

XLI. Having delivered this speech, the feelings of all were changed in a wonderful degree, both the greatest alacrity and desire to carry on the war was discovered, and the commander of the tenth legion returned thanks to him through the tribune of the soldiers, because he had formed the highest opinion of them, and they assured him that they were most ready to prosecute the war. Then the remaining legions through the tribunes of the soldiers and the centurions of the first rank

endeavoured to appease Cæsar ; "that they had never either hesitated or feared, nor did they deem it their duty, but that of the general to deliberate as to the management of the war. Their explanation being accepted, and the road being explored by Divitiacus, because in him of all the others he had the greatest confidence, and (it being found) that by a circuit of fifty miles he could lead the army through open places, about the fourth watch as has been said, he set out. On the seventh day, not having ceased his march, he was informed by scouts that the forces of Ariovistus were five-and-twenty miles from us.

1. Define an angle, a right angle, a triangle, a rectangle, an equilateral triangle.

How many parts of one triangle must in general be given equal to the corresponding parts of another, in order that the triangles may be equal in all respects? What cases does Euclid discuss? Enunciate the propositions in which he proves these cases.

2. Show how to draw a straight line perpendicular to a given straight line from a given point upon it.

Show that this is a particular case of the problem of bisecting a given rectilineal angle.

3. A straight line is drawn so as to meet two parallel straight lines. Show that it makes the alternate angles between the parallel lines equal.

State the other relations between the angles which the line drawn across makes with the two parallel straight lines.

4. Prove that, if one side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles, and that the

three angles of every triangle are together equal to two right angles.

The angles ABC, ACB of a triangle are bisected by two straight lines meeting in 0. With centre B and radius BO, a circle is described cutting CO again in D. Prove that the angles DBO and B A C are equal.

5. Prove that the square on that side of an obtuse-angled triangle which subtends the obtuse angle, is greater than the sum of the squares on the two sides which contain the obtuse angle, by twice a certain rectangle.

If the base of a triangle be bisected, the sum of the squares on the other sides of the triangle is double of the sum of the square on half the base and the square on the line joining the middle point of the base with the opposite angle.

6. Show that if PQ be any chord of a circle, and a line be drawn perpendicular to P Q through its middle point, the centre of the circle must lie in this line.

Hence show how to describe a circle of which a portion only is given.

7. Prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc.

Deduce that the angle in a segment greater than a semicircle is less than a right angle, and the angle in a semicircle is a right angle.

8. Prove that, if a straight line touch a circle and from the point of contact another straight line be drawn to cut the circle, the angles which this line makes with the former are respectively equal to the angles in the alternate segments.

If two circles touch one another, show that any straight line drawn through the point of contact will cut off from them similar segments.

9. Show how to inscribe a circle in a given triangle.

Show that the three straight lines which bisect the angles of a triangle all meet in a point, and that the two lines which bisect two exterior angles of a triangle meet in a point on the line which bisects the third angle internally.

10. Describe an isosceles triangle having each angle at the base double of the vertical angle.

Show that if the two points of intersection of the two circles in the figure be joined with each other, and with the centre of the larger circle, a second triangle of the kind required will be formed, equal in all respects to the first.

A rectangle is a quadrilateral whose angles are right angles, but whose sides are not all equal.

An equilateral triangle is that which has its three sides equal.

To prove that two triangles are in all respects equal there must be given three independent parts of the one respectively equal to the corresponding parts of the other.

NOTE.-The angles of a triangle are not three independent parts, since any two determine the third. (See Article Trigonometry, p. 53.)

Euclid discusses the cases in which there are given.

(1.) Two sides and the included angle in the one equal to the corresponding sides and angle in the other. (Euclid I. 4.)

(2.) The three sides of the one respectively equal to the three sides of the other. (Euclid I. 8.)

AD2+BD'=2AE+2ED. (Euclid II. 9.) Adding to each 2CD AD+CD2+CD2+BD2=2AE+2(ED2+CD2) That is, AC+ BC2 = 2AE2 + 2CE (Euclid I. 47.)