7. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other, the base of that which has the greater angle shall be greater than the base of the other. 8. Describe a square that shall be equal to a given rectilineal figure. 9. If a straight line falling on two other straight lines make the exterior angle equal to the interior and opposite angle on the same side of the line, or make the interior angles on the same side together equal to two right angles, the two straight lines shall be parallel to one another. 10. If a straight line be divided into any two parts, the squares on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square on the other part. 11. If two angles of a triangle be equal to one another, the sides also which subtend, or are opposite to, the equal angles, shall be equal to one another. V. 1. If a = 1, b = 3, c = 5, d = o, find the value of {a2_b3/ (b+c−d) } 2 — {( 3 c — 2 b)2 — (3 d+a−2c)2}. and from the sum subtract -3ax+ 4by- 2cz, x3-4x2-19x-14 and 2x3-9x2 — 38x+21. 5. Find the L. C. M. of x2-15x+56 and 2-192x+84. 6. Find the square root of 81a1-108a3b+54a2b2 — 12 ab3 +b*. 8. Solve the equations : (1) 4x-3(4-5x) = 7—3 (17—x); 9. The seventh part of a man's property is equal to his whole property diminished by £1614; what is the whole amount? 10. A and B could finish a piece of work in 15 days; after working together 6 days, A alone finished the remainder in 30 days; in what time could either alone do it all? (I. 5. 5.) (III. 4. 21.) (IV. 5. 24.) (V. 7. 6.) :- ἐσθλὸν ἕρπει. Φωνῆς δ ̓ ἄπωθεν......κάτω φθοράν. Ὁ μὲν ἦν......στόνος ἀμφοῖν. VIII. EURIPIDES. Ω πατρὶς, ...... οὔποτ ̓ ἔσται. Ἤρξω μὲν ......... ἀλλ ̓ ἀπώλεσα, ...... ......... Καὶ πρῶτα Ἴτω δίκα ......... IX. XENOPHON, Anabasis. Ἐν τούτοις ἔσταζον ῥοαί. τιμᾶν θεούς. Ἐπεὶ δὲ ......... ἐπιπαρῇσαν οὗτοι. |