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6. Assign the impossible reduct modes of the five modes of the fourth figure.
7. Show that if a term particular in its premiss be universal in the conclusion, it is not possible to verify the mode by either kind of reduction.
8. If the letter p occurs in the conclusion, prove that the mode is Bramantip.
9. Find analytically the imperfect modes which are capable of reduction in three different ways. [N. B.-Reduction by means of conversion by negation is not taken into account.]
10. Prove that in reduction ad impossibile the name of a reducend mode and that of its reduct can in no case have the same initial lettersBaroko and Bokardo being excepted.
Translate the following passages into English Prose :
1. Beginning, Πέπεισμαι τοίνυν, ἦ δ' ὅς, ἐγώ, ὡς πρῶτον μέν, κ.τ.λ. Ending, ταῦτα εἶναι καὶ ξυῤῥεῖν ἀεὶ εἰς τὰ κοῖλα τῆς γῆς.
Phado, lviii. 2. Beginning, ἔτι τοίνυν πρὸς τούτοις εἰς παιδοτρίβου πέμπουσιν, κ.τ.λ. Ending, ὡς εὐθυνούσης τῆς δίκης, εὐθῦναι. Protag., xv.
3. Beginning, καὶ ἡμεῖς τῷ ὄντι ἴσως τέθναμεν· ὅπερ ἤδη του, κ. τ. λ. Ending, οὐδέν τι μᾶλλον μεταθήσει ;
4. Beginning, Δεινὸν γάρ που, ὦ Φαῖδρε, τοῦτ' ἔχει γραφή, κ. τ. λ. Ending, ἀμύνασθαι οὔτε βοηθῆσαι δυνατὸς αὑτῷ.
5. Beginning, Εξ ἀρχῆς ἄρα ἡμῖν πάλιν σκεπτέον, κ. τ. λ. Ending, οἴει εἰδέναι τό τε ὅσιον καὶ μή.
1. State the various meanings of the word Sophist, and the peculiar sense in which it is applied by Plato.
2. Who are our two main witnesses about Socrates? and how do they mutually supply each other's defects?
3. State the few particulars we know of the life of Socrates, and mention the most celebrated schools which sprang from his teaching.
4. Account for the form oxov as the second aorist of Exw.
5. What is the difference between the Accusative, the Genitive, and the Dative, in their application to relations of time?
6. State the four principal forms of the hypothetical period, and when each is used.
7. What is the rule to be observed in the use of several negatives combined?
8. What events led to the battle of Coronea?
State the principal events that occurred in Greece during the supremacy of Thebes.
10. Mention the principal events in the history of the Sicilian Greeks from the time Dionysius seized upon the supreme power to the death of Timoleon.
Translate the following passages into English:
1. Beginning, Apud te est, ut volumus. Mater tua et soror.. Ending, Mi autem abjurare certius est quam dependere.
2. Beginning, Præterea, si ulla res est quæ bonorum animos,.. Ending, se divinare non potuisse.
3. Beginning, Quid? qui volunt exclamare majus,. Ending, simili contentione animi resistendum est.
4. Beginning, Nihil erat plane quod scriberem.. Ending, Præclare convenit, aut da me lius.
Ep. ad Attic. i. 8.
Ep. ad Attic. ii. 16.
5. Beginning, At enim qua in vita est aliquid mali, . . . . Ending, tota res appellatur.
Tusc. Disp. ii. 24.
Ep. ad Attic. xvi. 14.
De Fin. v. 30.
1. Give some account of the gradual formation of the Roman plebs. 2. State the cause and result of the third plebeian secession.
3. Give some account of the war with Pyrrhus, King of Epirus. What was the speech attributed to Pyrrhus when he was leaving Italy?
4. Under what circumstances did the Romans obtain the privilege of taking part in the Isthmian games?
5. Narrate briefly the last struggle for Grecian independence.
6. Write a short military biography of Sylla.
7. Point out accurately the different uses of the Latin perfect passive participle, with the various tenses of the verb substantive, e. g., captus est, captus erat, captus fuit, captus fuerat.
8. Fidem tuam perspectam habeo. Explain accurately this use of habeo with the passive participle. With the participles of what class of verbs only is it usually found?
9. In Latin the present tense is used in several cases in which, from the analogy of our own language, we would expect the future?
10. Give the derivations of erudio, polliceor, consulo, severus, sarmentum, præsertim, sollers, succidia, debilis, supellex.
Translate the following passage into Latin Prose :
But if there were no such considerations as the good effect which selfdenial has upon the sense of other men towards us, it is of all qualities the most desirable for the agreeable disposition in which it places our own minds. I cannot tell what better to say of it, than that it is the very contrary of ambition; and that modesty allays all those passions and inquietudes to which that vice exposes us. He that is moderate in his wishes, from reason and choice, and not resigned from sourness, distaste, or disappointment, doubles all the pleasures of his life. The air, the season, a sunshiny day, or a fair prospect, are sources of happiness; and that which he enjoys in common with all the world (by his exemption from the enchantments by which all the world are bewitched) are to him uncommon benefits and new acquisitions. Health is not eaten up with care, nor pleasure interrupted by envy. He has no emulation; he is no man's rival, but every man's well-wisher; can look at a prosperous man with a pleasure in reflecting that he hopes he is as happy as himself; and has his mind and his fortune (as far as prudence will allow) open to the unhappy and to the stranger.-SPECTATOR.
These gifts in fortune's hands are found;
No rest the inconstant goddess knows,
Translate the following passage into Greek Prose :—
Beginning, Natura igitur corpus quidem hominis sic et genuit,...
Translate the following passage into Greek Trimeter Iambics :
Then fare ye well, ye citizens of Ghent !
Cic., De Fin., lib. 5.
1. Tangents to a given circle are drawn at the extremities of a chord which passes through a given point; find the locus of their point of intersection.
2. Find two lines which shall be to each other in the ratio of two regular pentagons.
3. Equiangular parallelograms are to one another in a ratio compounded of the ratios of their sides.
4. If from the extremities of the base of a triangle perpendiculars be let fall on the bisectors of the vertical angle, their rectangle equals the square of half the sum of the sides the square of half the difference of
the sides ?
5. Prove that the rectangle under the chords of the sum and difference of two arcs is equal to the difference of the squares of their chords.
6. Given base, rectangle under the sides, and the radius of the circumscribing circle; construct the triangle, and prove the corollary which you assume in the construction.
7. Give Euclid's definition of a tangent to a circle; and prove, as he has done, that the perpendicular to the radius at any point of a circle is a tangent to the circle.
8. Give Euclid's definition of the contact of two circles; and prove, as he has done, that two circles cannot have contact of either species at more than one point.
9. Find a point on a given line the sum of whose distances from three given lines shall be given.
10. Draw a line through a given point the sum of whose distances from three given points shall be given.
II. Find a point on a given circle which shall determine with two given points on the circle a triangle of maximum perimeter.
12. Draw a tangent to a given circle which shall determine with two given tangents to the circle a triangle of minimum area.
13. Prove that any two arcs of a circle have to one another the same ratio as the angles they subtend at the centre of the circle.
14. The sides of a triangle are divided each in a given ratio; what relation must subsist between the ratios of the segments, in order that lines connecting the points of section to the opposite angles may intersect at a point?
Prove that this condition is satisfied for the bisectors of the angles and the perpendiculars.
15. Given the difference of the squares of two lines, and the rectangle under them; find them.
16. Prove that the diameter of the circle which passes through the feet of the perpendiculars of a triangle is equal to the radius of the circumscribing circle.
17. Inscribe a triangle in a circle whose sides pass through given points.
18. Find the locus of a point such that the difference of the squares of the tangents drawn from it to two circles may be constant.