2. Translate Aeneas, miratus enim motusque tumultu, 66 Dic," ait, "o virgo, quid vult concursus ad Quidve petunt animae ? vel quo discrimine ripas Haec omnis, quam cernis, inops inhumataque Portitor ille Charon; hi, quos vehit unda, sepulti. Transportare prius, quam sedibus ossa quierunt. Tum demum admissi stagna exoptata revisunt." Multa putans, sortemque animo miseratus iniquam. 3. (a) In the first sentence of question 1, section B, explain the grammatical construction of every case. (b) In question 2, section B, remark on the constructions and explain the allusions in the following:-olli, di cuius iurare timent et fallere numen-portitor ille Charon-centum errant annos- -Anchisa satus-sortem miseratus iniquam. 4. Decline throughout Classe, coniunx, iecur, opibus, remigibus, tabe. ALGEBRA. The Board of Examiners. Every result must be reduced to its simplest form. The whole of the working of a question must be sent in as part of the answer. 2{(x + y)(x + z) + (y + z) (y + x)+(x+x) (x + y)} = 2{(y + z)2 + (≈ + x)2 + (x + y)2} (yz)2 - (x − x)2 - (x − y)2. (ii) (iii) (x — 3a)2 + (x − 3b)2 + (x − 3c)2 7. Diophantus passed in infancy the sixth part of his life, in adolescence a twelfth, then he married, and in this state he passed a seventh of his life and five years more, then he had a son, whom he survived four years, and who only reached the half of his father's age. How old was Diophantus when he died? 8. A takes x times as long to do a piece of work as B and C together, B takes y times as long as C and A together, and C takes z times as long as A and B together; prove that GEOMETRY. The Board of Examiners. The symbol must not be used; and the only abbreviation admitted for "the square described on the straight line AB" is "sq. on AB," and for "the rectangle contained by the straight lines AB, CD" is 66 rect. AB, CD." 1. ABC is a triangle having AB equal to AC. AB, AC are produced to D and E respectively. Prove that the angle DBC is equal to the angle ECB. 2. The sides of a rectilineal figure are produced successively in the same direction. Prove that the sum of the angles so formed is four right angles. 3. To describe a rectangle which shall be equal to a given rectilineal figure. 4. The difference of the squares on two unequal straight lines is equal to the rectangle contained by their sum and their difference. 5. If a straight line be bisected and produced to any point the squares on the whole line produced and on the part produced are together double of the squares on half the straight line and on the straight line made up of the half and the part produced. 6. On the straight line AB describe the square ABDC. Bisect AC in E. Join EB. Produce CA to F, making EF equal to EB. On AF describe the square AFHG. Produce HG to meet CD in K. Prove that the square FG is equal to the rectangle GD. 7. Every point in a chord of a circle is either on or within the circle. 8. If two circles touch externally, the straight line joining their centres passes through the point of contact. 9. On a given straight line to describe a segment of a circle containing an angle equal to the third part of two right angles. ENGLISH. The Board of Examiners. NOTE.-Pay particular attention to the spelling and punctuation of what you write; the writing must be neat and legible. The Essay must be attempted. 1. (a) Parse fully each word which is printed in italics in the following passage: Time hovers o'er, impatient to destroy, And shuts up all the passages of joy: In vain their gifts the bounteous seasons pour. The fruit autumnal, and the vernal flow'r; With listless eyes the dotard views the store: He views and wonders that they please no more. Now pall the tasteless meats and joyless wines, And Luxury with sighs her slave resigns. (b) What part in the construction of the principal sentence in which it occurs does the expression they please occupy ? 2. Make a full analysis of the following passage:— Deign on the passing world to turn thine eyes, And pause a while from learning, to be wise; There mark what ills the scholar's life assail. |