ἀντὶ πρὸς βωμός (2) He died instead-of his friends at the altar (3) The ships have been sent away. 8. Translate into Latin and Greek-eightieth, one hundred times, threefold, twice, nineteen. 9. In what tenses is the augment used in Greek, and what are its forms? 10. State the meaning of the following words:-TOтE, ὥστε, καίπερ, ἐκεῖσε, ποῖος, usquam, coram, olim, ultro, scilicet. III. Arithmetic. 1. Multiply 125l. 158. 91d. by 45. Divide 425 tons 15 cwt. 2 qrs. 12 lbs. by 27. 2. What is a man's income if after spending of it he has 540/. left? 3. If the tax on a rent of 10l. 98. 4 d. be 1l. os. 11 d., what will be the tax on 257.? 4. Find the G. C. M. of 22176 and 23328; and the L. C. M. of 18, 32, 56, 168. 5. Find by Practice the value of 12 yds. 2 ft. 9 in. at 148. 9d. per yard. 7. Multiply 0625 by .00032, and divide 18988 by 0235; and find the vulgar fractions equivalent to 848, .027, and 2.0432. 8. Find the value of 5 of a shilling+7 of a crown+ .125 of 17. 9. Extract the square root of 39.0625, and of 438. 10. Find the cost of papering a room 15 ft. long 12 ft. wide and 10ft. high with paper 30 in. broad at 71⁄2d. per yard. 11. The yearly rent of a farm is 420l., what should be the price that a purchaser may get 3 per cent. per annum on his investment? 12. Required the compound interest on 350l. in 3 years at 5 per cent. IV. [N.B. Two Propositions at least from the Second Book are required.] 1. Define-right angle, parallel straight lines, rhombus, rectangle, circle, gnomon. 2. Draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. 3. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the two parts. 4. If from the ends of the side of a triangle there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. 5. Divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part. 6. The opposite sides and angles of a parallelogram are equal to one another, and the diameter bisects the parallelogram, that is, divides it into two equal parts. 7. If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced. 8. If the square described on one of the sides of a triangle be equal to the squares described on the other two sides of it, the angle contained by these two sides is a right angle. 9. 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. 10. Describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. V. 1. If a 1, b = −1, c = 2, find the value of = 20ab-17bc+16 ac−5 (a2 + b2 +c2). 2. From (a+1)2x— (b−1)2y take (a+1)ax−(b−1) by. 3. Multiply a2x2+abxy+b2 y2 by ax-by; and divide a2x2 + a2 b2x2 y2+b+ y2 by a2x2+abxy+b2 y2. 4. Resolve into their simple factors (1) 3a3-12a; (2) a2-a-2 ; (3) 2x2-7xy+6y2. 5. Find the G. C. M. of 20a4+a2-1 and 25a+5a3—a—I. 8. Extract the square root of (1) 16x1-32x3 +24x2 −8x+I; (2) 9a2x2-12abxy+6axz+4b2 y2 −4byz+z2. 9. Solve the equations: (1) (2) (3) (4) (x−3) + (x − 4) = } (x − 5) + § (x + 1 ) ; (5) (a-3)x = (a + b)y, } x + y = c. 10. Find a number such that one-third of it exceeds of the remainder by 10. A carriage, horse, and harness are worth together 1447.; the carriage is worth of the horse's value, and the harness of the difference between the values of the horse and carriage; what is the value of each? In what time will a cistern which holds 670 gallons be filled by two taps running simultaneously, one of which lets in 14 gallons in five minutes and the other 5 gallons in three minutes? What fraction is that which becomes = when 2 is added to its numerator, but when I is taken from its denominator? = |