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(a) They thought they would wait till they saw whether he intended to follow them or not.
(b) Who told us how we ought to set about the work? (c) If they were not to deprive the enemy of these ships, they would repent of it.
(d) O that he had not answered at all, as it was in his power to hold his peace!
(e) They affirmed that if they had not revolted froı Athens, she would soon have enslaved them.
Translate into Greek:
In the camp before Numantia the wisdom and courage of Tiberius were all the more conspicuous (deaìáμñw) because of the unfitness (approria) of the Roman commander. The besieged Numantines had even ventured to come out and engage the besiegers before the walls of the town. And in the battle that ensued, if not victorious, they so disheartened (xatanyoow) the Roman general that he determined to raise the siege (draviaTapa). Orders were sent round (ñɛpearɣélλw) to the soldiers to hold themselves in readiness (παρασκευάζω) to evacuate the camp during the night. He hoped in this way to withdraw unobserved by the inhabitants of the place. But the enemy were on the watch (77pέw)
and made a spirited attack (προθύμως ἐπιτίθεμαι) upon the retreating army which they quickly surrounded (ἐγκυκλόω) and forced into an unfavourable position (συνωθέω εἰς χαλεπὸν τόπον) from which there was no escape Despairing of (ἀπογιγνώσκω) safety, the general sent a herald to the Numantines to ask for a truce. They replied that they had no confidence in (πιστεύω) any of the Romans except Tiberius. If the general wanted peace, he must send him to them. Accordingly Tiberius was sent to the enemy's camp and partly by persuasion, partly by concession (συγχωρέω) he obtained peace for his countrymen and saved an army of twenty thousand men.
Translate at sight:
τὸ δ ̓ ἐκ τοῦ ἰσθμοῦ τεῖχος εὐθὺς οἱ Ἀθηναῖοι ἀποτειχίσ αντες ἐφρούρουν τὸ δ' ἐς τὴν Παλλήνην ἀτείχιστον ἦν· οὐ γὰρ ἱκανοὶ ἐνόμιζον εἶναι ἔν τε τῷ ἰσθμῷ φρουρεῖν καὶ ἐς την Παλλήνην διαβάντες τειχίζειν, δεδιότες μὴ σφίσιν οἱ Ποτιδαιᾶται καὶ οἱ ξύμμαχοι γιγνομένοις δίχα ἐπιθῶνται. καὶ πυνθανόμενοι οἱ ἐν τῇ πόλει Αθηναῖοι τὴν Παλλήνην ἀτείχιστον οὖσαν, χρόνῳ ὕστερον πέμπουσιν εξακοσίους καὶ χιλίους οπλίτας ἑαυτῶν καὶ Φορμίωνα τὸν ̓Ασωπίου στρατ ηγόν. ὃς ἀφικόμενος ἐς τὴν Παλλήνην καὶ ἐξ ̓Αφύτιος ορμώμενος προσήγαγε τῇ Ποτιδαίᾳ τὸν στρατὸν κατὰ βραχύ προϊὼν καὶ κείρων ἅμα τὴν γῆν. ὡς δὲ οὐδεὶς ἐπεξῄει ἐς μάχην, ἀπετείχισε τὸ ἐκ τῆς Παλλήνης τεῖχος· καὶ οὕτως ἤδη κατὰ κράτος ἡ Ποτίδαια ἀμφοτέρωθεν ἐπολιορκεῖτο καὶ ἐκ θαλάσσης ναυσὶν ἅμα ἐφορμούσαις.
Thucydides, B. I., 64.
State in language the theorem here given by symbols, and prove it.
2. Prove that if Ax" + Bän−1 + Sa+T be divided by x-1 the remainder will be A+B+...S+ T. Show that 10+3x7 -2x-2 is divisible by x-1.
5. Two ropes are in length as 4: 5 ; 6
by 1 2
feet are cut
from each and their lengths are then as 3: 4. What was their original lengths?
In an isosceles triangle the base is b, the side & and 5 times the area is bs /5. Find the ratio of the side to the base.
6. Extract the square root of 8-215; and show by examples how you would
i. reduce an entire surd to a mixed surd.
ii. free a fraction from a binomial surd denominator.