13. Supposing the length of the lower row of seats in the upper gallery of the Theatre to be 140 feet, and each ascending row to contain 8 more seats than the one below it, except that the fifth and topmost row loses 16 spaces of 2 ft. 3 in. each between the windows, how many will the gallery hold, allowing 16 in. to each person? IV. Euclid. [N. B. Two Propositions at least from the Second Book are required.] 1. Define plane rectilineal angle, straight line, rhombus, parallel straight lines, parallelogram. 2. The angles at the base of an isosceles triangle are equal to one another; and if the equal sides be produced the angles on the other side of the base shall be equal to one another. 3. 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. 4. 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. 5. To a given straight line apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 6. 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. 7. 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. 8. 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. 9. If two triangles have two sides of the one equal to two sides of the other, each to each, and have likewise their bases equal, the angle which is contained by the two sides of the one shall be equal to the angle which is contained by the two sides, equal to them, of the other. 10. 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. 11. 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. b3 + {b (a−c)+ac}—a {b—(a−c)}+b{c—(b—a)} —ab. 3. Divide 5a2bc2, 75a2 b3 c3-15a3 b c3 by 5a2 bc2, and a-262-3c2+ab+2ac+7bc by a-b+3c. (1) 5×3+2x2-15o-6 and 7×3 — 4x2 — 21 x + 1 2; (2) 922-4 and 922 +21x+10. 11. Find the fraction which if one is added to its numerator becomes equal to, if one is added to its denominator becomes equal to . 12. My friend and I begin to play with equal sums, he gains £5 from me, and then three times his money is as much as eleven times mine; what was the sum we each had at first? ...... (V. 722–732.) Ἥβη δ ̓ ἀμφ ̓ ὀχέεσσι ἔριδος καὶ ἀϋτῆς. (ΙΙ. 146-160.) Ως φάτο Τηλέμαχος, ...... καὶ μετέειπεν. Κῆρυξ, τίπτε δέ ...... μετόπισθ' εὐεργέων. Εἷος ὁ ταῦθ' ὥρμαινε (IV. 681-695.) (ν. 365-376.) μυθήσατο θυμόν. VII. SOPHOCLES. Translate :- (Oed. Tyr. 1014-1030.) ΑΓ. Αρ' οἶσθα ...... τότ' ἐν χρόνῳ. (Hecuba 462-483.) σὺν Δηλιάσιν τε ...... "Αιδα θαλάμους. 991-1002.) ΠΟ. τί δῆτα ...... Πριαμιδῶν κατώρυχες. (Alcest. ( ...... διὰ παντός. ΑΔ. ἔμνησας ὅ μου (Bacch. 628-641.) ...... καθ ̓ ὁ Βρόμιος,... σώφρον εὐοργησίαν. ( 1125-1136.) λαβοῦσα δ ̓ ὠλέναις......σάρκα Πενθέως. (ΙΙΙ. 1. 23.) (IV. 8. 10.) Ἔτι δ ̓ ἔχομεν σώματα ἐμαυτοῦ τὰ κακά. (II. 17.) Video de istis,......publicae dependisse. Sed ne cui vestrum......genere dicendi. XI. CAESAR, De Bell. Gall. ...... Adiuvabat etiam perspici quidem posset. (III.14.) Rostro enim noceri ...... tempore eriperetur. (IV. 33.) Genus hoc est ex ...... recipere consuerint. (VI. 27.) Sunt item, ...... atque una ipsae concidunt. |