9. If 12 horses are required to plough 16 acres in 4 days working 9 hours a day, in how many days will 20 horses plough 20 acres working 8 hours a day? 10. A broker calls in 6400l. invested on mortgage at 4 per cent. and invests three-fourths of the amount in railway shares paying 6 per cent. at 130; the rest he invests in foreign securities paying 5 per cent. at 96. Find the difference of annual income. 11. At what rate per cent. will the simple interest on 6000l. amount to 9457. in 4 years? 12. A farmer purchased 120 lambs at 30s. a head in the autumn. During the winter 12 died, but he sold the rest in May at 458. each. What was his gain per cent. ? 13. Find the present worth of 2000l. due 3 years hence at 5 per cent. IV. 1. Define-plane superficies, right angle, circle, gnomon, figure, parallel straight lines. 2. Draw a straight line perpendicular to a given straight line of unlimited length, from a given point without it. 3. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line. 4. At a given point in a given straight line, make a rectilineal angle equal to a given rectilineal angle. 5. Parallelograms upon equal bases, and between the same parallels, are equal to one another. 6. Describe a parallelogram equal to a given rectilineal figure, and having an angle equal to a given rectilineal angle. 7. In any right-angled triangle, the square which is described on the side subtending the right angle, is equal to the squares described upon the sides which contain the right angle. 8. 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 of half the line bisected, is equal to the square of the straight line which is made up of the half and the part produced. 9. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double of the square of half the line bisected, and of the square of the line made up of the half and the part produced. 10. Divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 11. Describe a square that shall be equal to a given rectilineal figure. 2. (1) Square d-e-f, and subtract 9ab (b-3a) from (3a-b)3; (2) Divide a5—a1+a3—a2+a-1 by a3-1. 3. Find the L. C. M. of (1) 12 (α—b)2, 2a2 -262, 15(a3 —b3); (2) x2-5x+6, x2-6x+8, x2 −3x+2; and the G. C. M. of 8a3+12 a2b+6ab2+b3 and 2a2-ab-b2. 4. Reduce to their lowest terms the fractions 6. Shew that the square of the sum of any two numbers is greater than the square of their difference by four times their product. 7. Find the square root of (1) 25a2+120a +144+30ab +726+962; (2) 9a2 8 ab 1662 25 15 81 8. Solve the equations: 9. At what times are the hands of a watch at right angles between the hours of seven and eight? A tourist starts at noon from the foot of a mountain and walks to the top at the rate of two miles and a half per hour. After resting for three-quarters of an hour, he descends at the rate of four miles per hour, and reaches his starting-point at 4 p. m. What was the length of his walk? A man's income is diminished by £450, but as the income tax is raised from four-pence in the pound to six-pence, he finds he has to pay the same amount as before. State his two incomes. Translate :(ΙΙΙ. 369-382.) (V. 720-732.) (XVIII. 369-379.) (XXI. 251–264.) Translate : (I. 328-335.) (ΙΙ. 420-426.) (ΙΙΙ. 430-439.) (IV. 450-458.) (V. 400-407.) VI. HOMER, I. I-V. Η καὶ ἐπαΐξας......... εὐώδεϊ κηώεντι. Ηφαίστου δ' .........κόπτε δὲ δεσμούς. VII. Τοῦ δ'..... ...... κεδνὴ ἑκάτερθε παρέστη. Τοῖσιν δ'.... .....ἐϋστρέπτοισι βοεῦσιν. Ως ἔφαθ', οἱ δ ̓.........καὶ δῖος Ἐχέφρων. Ενδιος δ' δ.........δένδρεον ὑψιπέτηλον. ̓Αλλ ̓ ὅτε τόσσον...........μεγαλήτορα θυμόν. (VI. 262–269.) Αὐτὰρ ἐπὴν ἀποξύουσιν ἐρετμά. (VII. 159–166.) ‘Αλκίνο, οὐ μέν...........ἔνδον ἐόντων. (VIII. 372-380.) Οἱ δ ̓ ἐπεὶ οὖν............ὑπὸ κόμπος ὀρώρει. (ΙΧ. 382-390.) Οἱ μὲν μοχλόν............δέ οἱ πυρὶ ῥίζαι. Εἶσεν δ ̓ εἰσαγαγοῦσα.........αἰὲν ἔδουσιν. (Χ. 233-243.) (Agam. 1257-1265.) Τί δήτ' ἐγώ.........συμβάλω τόδε. (Prom. Vinct. 484-491.) Τὰ λοιπά..... ἐξαμύνονται νόσους. 597-608.) ΙΩ. Πυρί με......βίαν γυμνάζεται. 941-948.) Τοῖον παλαιστὴν........δουλεύειν δίχα. (451-460.) (877-887.) (1200-1210.) EURIPIDES, Bacch. ΠΕ. Μέθεσθε..... ......ὅστις εἶ γένος. |