6. Describe a square that shall be equal to a given rectilineal figure. 7. Draw a straight line through a given point parallel to a given straight line. 8. On the same base, and on the same side of it, there cannot be two triangles having their sides which are terminated at one extremity of the base equal to one another, and likewise those which are terminated at the other extremity. 9. If a straight line be bisected, and produced to any point, the square on the whole line thus produced, and the square on the part of it produced, are together double of the square on half the line bisected and of the square on the line made up of the half and the part produced. 10. Describe a parallelogram that shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 11. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square on the side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. 12. Prove the proposition from which any one of the following corollaries are inferred : (1) The parallelograms about the diameter of a square are likewise squares. (2) Every equiangular triangle is also equilateral. (3) All the exterior angles of any rectilinear figure are together equal to four right angles. V. Algebra. 1. If x 1,y=-2, z, what is the value of x2 + y2 + 2 − (y + z)3 ? 2. Add together 3x+4y-5%, 3Y+42−5x, 32+4x-5y; and simplify b3 — a (a2 — bc) + c3 — b (b2 — ca) + a3 — c (c2 — ab). 3. Prove that if m and n denote two positive integers, am × an = am+n; and that, if m be the greater of the two positive integers, am ÷ an = am-n. 4. Multiply 2-5y by 3x+7y, and 202 x2 xy y2 9 6 4 6 4 alo 9 5. Divide a10+a5b5+610 by a2+ab+b2. 6. Find the G. C. M. and L. C. M. of 2a2-5a+2, 2a2+3α-2, 4a2-1; and reduce to its lowest terms 10. A's age is now one-third of B's age: ten years ago A's age was one-fifth of B's age. What is A's present age? 11. The result of adding two numbers is 99: the result of dividing one number by the other is . Find the two numbers. Orford University EXAMINATION PAPERS. RESPONSIONS. MICHAELMAS TERM, 1878. Oxford AT THE CLARENDON PRESS SOLD AT THE CLARENDON PRESS DEPOSITORY 116 HIGH STREET OXFORD EXAMINATION PAPERS. RESPONSIONS. I. Latin Prose. If after so great a victory the Gauls had immediately pursued the fugitives, nothing could have hindered the entire destruction of Rome, and of all that remained in it; so astonished were the citizens at the return of those who had escaped from the battle, and so confused and panicstricken. The Gauls, however, not imagining the victory to be so great as it was, in the excess of their joy, gave way to feasting and plundering the camp; so that numbers who wished to leave the city, had leisure to escape, while they who remained, had time to recover their spirits and prepare for defence. . Accordingly, quitting the rest of the city, they retired to the Capitol, which they fortified by strong ramparts, and provided well with arms. But their first care was for their holy things: these, and the sacred fire, the Vestal Virgin took, and fled away along the side of the river. II. Grammar Paper. 1. Parse—μέμψησθε, λελῃσμένη, ἄρδην, κρυφθῆτον, παρώσας, κέκρανται, ἐδήλου, ἠνέσχετο, obsitus, cretus, experrectus, affare. 2. Decline in full—δόρυ, καθεστῶς, ἀλλήλοιν, τοιοῦτος, vaûs, senex, praeceps, par, vas (masc.), vas (neut.) 3. Give the comparative and superlative of TAμwv, πάλαιος, πρωί, ἐπιεικής, μέσος, dives, juvenis, nuper, pius, utilis. |