Translate the following passage into Greek Tragic Iambics : Tut. In thee, my child, the nobleness of manners, Creu. Follow; be heedful where thou set thy steps. EURIP., Ion. MR. ABBOTT. Translate into Latin Hexameters : We all stand up against the spirit of Cæsar, And after seem to chide them. This shall make Translate into Greek Prose: The reader of history may be compared to a traveller, who leaves his own country, to visit others which are far off, and very different from that in which he has been living. The manners and customs of the nations which he is going to see are either wholly new to him, or he is already in some measure acquainted with them by the information and researches of others. So it is with the reader of history. He is either beginning a study to which he was altogether a stranger, and meets, for the first time, with facts and circumstances of which he had never heard before, or he is partly retracing his own steps, and filling up the details of a plan which had been previously exhibited to him in outline. It is, perhaps, difficult to say in which of the two cases his gratification and amusement will be greatest; and the minds of different readers will be differently affected, according to the degree of knowledge already possessed upon the subject which they are reading. ENGLISH LANGUAGE AND COMPOSITION. MR. BARLOW. 1. Give some account of the principal sources from which the English language has enriched its vocabulary; the periods at which it has made its chief additions; and the character of the additions which at different periods it has made. 2. Illustrate the following assertion:-"There are aspects in which the English is among the least imaginative of all languages, even while it has been employed in some of the greatest works of imagination which the world has ever seen." 3. Point out the changes of meaning which the following words have undergone :-Attorney, curate, disease, duke, enormous, feature, idiot, imp, nursery, offal, poacher, puny, raisin, room, silly, spice, staple, tuition. 4. Explain the following idioms "by-the-bye." "Many a man," "by-and-by," 5. Construct sentences to illustrate the distinctions between the following words :-To puzzle, to perplex, to embarrass; to distinguish, to discriminate; calm, tranquil, quiet; fear, fright, terror, alarm; misfortune, calamity, disaster. 6. Re-write the following passage in good English Prose: In many a field, by civil fury stain'd, No sooner dawn'd the fair-disclosing calm The miserable coast. Before them stalk'd, Rapine, and murder, all with blood besmear'd, Without or ear, or eye, or feeling heart; While close behind them march'd the sallow power Of desolating famine, who delights In grass-grown cities, and in desert fields; And purple-spotted pestilence, by whom Even friendship scared, in sickening horror sinks Each social sense and tenderness of life. 7. Describe, as vividly as you can, a railway accident, or a shipwreck. 8. Write a short essay on the following saying:-"Whosoever is delighted in solitude is either a wild beast or a god." MR. ABBOTT. 1. Write a brief account of the life of Alcibiades, Themistocles, or Conon. 2. Mention the circumstances which led to the establishment of the Athenian supremacy. 3. Write a history of the relations of Greece and Persia after the Peloponnesian War. 4. Give some account of the Solonian Constitution, and of the changes which it had undergone in the time of Pericles. 5. Describe the Grecian system of colonization, distinguishing the different classes of colonies. 6. Draw an outline of the coast from Attica to the Hellespont, marking places historically important. 7. Describe a route which might be taken by a traveller from Persia to Corinth, stating the rivers and mountains, if any, to be passed, the cities which might be visited, and for what each was remarkable. 1. Distinguish the significations of diá, vτó, τapá, according to the several cases with which they are used. 2. What are the significations of kará, πapá, diá in composition? 3. Explain the use and construction of καταγιγνώσκειν, καταδικάζειν : also the construction of verbs and adjectives expressing difference. 4. State the principal rules for the arrangement of words in a sentence in Greek. 5. How are the relations of time expressed by the cases and prepositions? HISTORY, GEOGRAPHY, AND GRAMMAR. MR. DICKSON. 1. Write an account of any two of the following events, giving the date of each : a. The battle of the Alia. b. The battle of Sentinum. c. The death of Sertorius. d. The recall of Cicero from exile. 2. What are the dates and provisions of the following enactments : a. Lex Decemviralis. b. The Licinian Rogations. c. Lex Julia et Papia Poppaa. 3. Notice any remarkable actions performed by P. C. Scipio Nasica, L. Papirius Cursor, and M'. Acilius Glabrio. 4. Distinguish between Municipium, colonia, præfectura. 5. Write articles for a Classical Dictionary under the titles Massilia, Illiberis, Aqua Sextiæ, Orontes, Cyzicus, Seriphus. 6. Write down the Latin names of Cologne, Coblenz, Turin, Perugia, Aosta, Saragossa. 7. Set out the march of Hannibal from the Trebia to Canna. 8. Conjugate and give the English of lambo, scăbo, mico, crepo, pango, spondeo. 9. Form adjectives from doceo, verto, rubeo, cedrus, scurra, tribus; and mark the quantity of each word. 10. What cases follow fungor, potior, memini, misereor. 11. Enumerate the prepositions which are constructed d. With the accusative. b. With the ablative. c. With both the accusative and the ablative. 12. By what case is at a place expressed, when the noun is of the first, second, or third declension? Illustrate the rules by examples. Mathematical Sizarship. GEOMETRY. MR. TOWNSEND. 1. If A, B, C, D, E, &c., be the several vertices of a polygon of any form taken in consecutive order, and O any arbitrary point, a. Explain in what sense it is true that the sum of the triangular areas AOB, BOC, COD, &c., is constant, whatever be the position of 0. b. Hence, give a general definition of the area of a polygon which shall include the case of figures, any two or more of whose sides intersect each other internally. 2. Given the four sides of a quadrilateral, and the order of their succession, a. Construct the figure so as to have any given area, and show from the construction that the case of maximum area is that in which the four vertices lie in a circle. b. Hence, prove by elementary geometry that the plane figure of maximum area bounded by a line of given length is a circle. 3. If A, B, C be the three vertices of any triangle circumscribed round a circle, and AP, BQ, CR the three perpendiculars from them upon any tangent to the circle, prove the relation BC. AP+CA. BP+AB. CP = 2 area of triangle. 4. If A and A', B and B', C and C' be the six vertices in opposite pairs of any tetragram circumscribed round a circle; AP and A'P', BQ and B'Q', CR and C'R', the six perpendiculars from them upon any tangent to the circle; and O the centre of the circle: prove the relation AP. A'P': BQ. B'Q': CR. C'R' : : OA. OA': OB. OB': OC.OC'. 5. If A, B, C, D, E, &c., be any system of points, and O their mean centre for any system of multiples a, b, c, d, e, &c., prove the general relation (a). Σ (a. OA2) = Σ (ab. AB2), and show how it becomes modified in the particular case when Σ (a) = 0. 6. Prove either of the following reciprocal theorems : a. The six centres of perspective of any three chords of a circle, taken two and two, lie three and three on four lines. b. The six chords of intersection of any three angles circumscribed round a circle, taken two and two, pass three and three through fou r 7. Prove either of the following cases of homographic division :— a. If the vertices of a system of similar triangles lie on fixed lines, all homologous points lie on fixed lines, and determine homographic systems of points on their several lines. b. If the sides of a system of similar triangles pass through fixed points, all homologous lines pass through fixed points, and determine homographic systems of rays through their several points. 8. Prove either of the following cases of involution :— a. If A, B, C be any three points on a common axis or rays through a common vertex, and A', B', C' the three harmonic conjugates of any fourth point or ray P with respect to B and C, C and A, A and B respectively; the three systems of six points or rays B and B', C and C', A and P C and C', A and A', B and P; A and A', B and B', C and P; are each in involution. b. In the same case, if A', B', C' be any three points or rays in involution with A, B, C; and A", B", C" the three harmonic conjugates of A, B, C' with respect to B and C, C and A, A and B respectively; the several systems of three points or rays A', B", C"; A", B′, C"; A" B′′ C′ are each in involution with A, B, C. 9. Apply the method of homographic division to the solution of either of the following problems : : a. Given four points on a common axis or rays through a common vertex A, B, C, D, find two others, X and Y, so that the systems ABXY and CDXY shall have each a given anharmonic ratio. b. Given three points on a common axis or rays through a common vertex A, B, C, to find three others, X, Y, Z, so that the three systems BCYZ, CAZX, ABXY shall have each a given anharmonic ratio. 10. Apply the method of inversion to the solution of either of the following problems ; a. Describe a circle cutting three given circles at three given angles. b. Describe a circle cutting four given circles at equal (or supplemental) angles. 11. The three centres of similitude of any three similar and similarly (or oppositely) placed figures, taken two and two, lie in a right line; what does this property become by reciprocation from any arbitrary centre? |