V. 1. A shilling weighs 3 dwts. 15 grs., of which 3 parts out of 40 are alloy, and the rest pure silver. How much is there of alloy, and what is the weight of pure silver? per cent. 2. Add together the greatest and least of the fractions 2, 3, 11, 18; and subtract this sum from the sum of the other two fractions. 3 19 3. What must be the rate of interest per cent. per annum, in order that the interest on fifty dollars may be one cent. per diem ? 4. The cost of carpeting a room, whose length is 18 feet, at 3s. 6d. a square yard, is £5 12s.; and the cost of painting the walls, at 4s. 6d. a square yard, is £17. Find the height and breadth. 5. Solve the following equations: 6. Two vessels contain each a mixture of wine and water. In the first vessel the quantity of wine: the quantity of water :: 1: 3, and in the second :: 3:5. What quantity must be taken from each in order to form a third mixture, which shall contain 5 gallons of wine and 9 of water? 7. If be a fraction in its lowest terms, shew that it can be b reduced to a finite decimal only when bis of the form 2'5; and that in this case the number of decimal places is r or s according as r or s is the greater. 8. Find the number of permutations and combinations of n things taken r and r together. 9. Assuming the Binomial Theorem when the index is a positive integer, prove it when the index is a positive fraction; and apply it to extract the square root of 24 to six places of decimals. 10. Sum the following series: (1) 2 − 1 + 1⁄2 − 1 + &c. to infinity. (2) 1a + 22 + 32 + &c. to n terms. 11. Explain what is meant by the circular measureof an angle; and find to six places of decimals the circular measure of the angle containing 30 minutes. 12. What are the signs of the sine, cosine, and tangent in each of the four quadrants? and between what limits do they lie? Is the equation cos 20 = (a + b) * possible equation ? 13. Give a geometrical proof of the equation cos (AB) = cos A cos B + sin A sin B, when A is < 180° and A-B> 90°. 14. State the principle on which we may find any trigonometrical function of an angle not exactly contained in the tables. Prove this principle in the case of the logarithmic sine, and shew that it fails when the angle is nearly 0° or 90°. 15. Explain the ambiguous case in the solution of obliqueangled triangles. If A = 30°, AB = 5, BC = 3, solve the triangle; having given log 12 = 1.0791812; L sin 56°.26′ = 9·9207717; difference for 1' = 838. 16. If a and ẞ be the roots of the equation x2 - px + q = 0, Ρ shew that tan ̄1a + tan1ß = tan^1. 1 Չ 17. Prove the equation = tantan30+ tan30 - &c., and deduce Machin's series for the determination of 7. 18. Describe the principle of the Vernier, and explain its use. SCHOLARSHIP EXAMINATION. SIDNEY SUSSEX COLLEGE. October, 1861. I. Translate, adding a short note wherever a word, a construction, or an allusion seems to require it: 1. From Καὶ μὴν Σίσυφον εἰσεῖδον. to Hoм., Od., XI. 592-626. Quote any examples from ancient or modern poets where the sound is made an echo to the sense. Write a short account of the various opinions which have been held with respect to the authorship of the Homeric poems. 2. From "Ιωνες δὲ καὶ Αἰολέες.... to .... δεησομένους "Ιωσι τιμωρέειν, HERODOTUS, I. 141, Describe briefly the Grecian colonies on the coast of Asia Minor. Do the names afford any clue to the relative dates of the respective settlements? 3. From Πάτερ, πιθοῖ μοι, κεί νέα .... to παθόντα δ ̓ οὐκ ἐπίστασθαι τίνειν. SOPH., Ed. Col., 1181-1203. What middle tenses are ever used passively, and vice versá? 4. From Διὸ δὴ καὶ ἐμήκυνα.... to ... ἢ τοῦ δέους ἀπηλλάγησαν. THUC., I1. 42. Write a summary of the leading events in the Peloponnesian war so far as it has been chronicled by Thucydides. 5. From Ορώ, Προμηθεῦ.... to ...ζημία προστρίβεται. Escн., Prom., 307–329. What is meant by the terms 'protasis' and 'apodosis'? Give the different classes of conditional propositions which can be formed with l in the protasis. 6. From Ἡ δὲ ὀψιμαθία φιλοπονία.... to .... αὐτὸς αὑτῷ τερετίζων.—THEOPHR. Char. What were the chief liturgies at Athens ? II. Translate into Greek Iambics: Who now persists in calling Fortune false? Nor in the furrows of my hand; who dares COLERIDGE'S Wallenstein. Translate into Greek Prose: The peace of Constance presented a noble opportunity of establishing a permanent union. But dark, long-cherished hatred, and that implacable vindictiveness which, at least in former ages, distinguished the private manners of Italy, deformed her natural character, which can only be the aggregate of individual passions. For revenge she threw away the pearl of great price, and sacrificed even the recollection of that liberty which had stalked like a majestic spirit among the ruins of Milan. The victim by turns of selfish and sanguinary factions, of petty tyrants, and of foreign invaders, Italy has fallen like a star from its place in heaven; she has seen her harvests trodden down by the horses of the stranger, and the blood of her children wasted in quarrels not their own. Conquering or conquered, still alike a slave; a long retribution for the tyranny of Rome. HALLAM. III. Translate, adding a short note wherever a word, a construction, or an allusion seems to require it: 1. From Ipsis doctoribus hoc esse curæ.... Translate the following extracts, naming the Author, and explaining the allusions: 1. ....... . Cujus prudentia monstrat Summos posse viros et magna exempla daturos 2. Romæ nutriri mihi contigit, atque doceri 3. "Veritatem laborare nimis sæpe, aiunt, extingui nunquam. Gloriam qui spreverit, veram habebit. Sine, timidum pro cauto, tardum pro considerato, imbellem pro perito belli vocent: malo te sapiens hostis metuat, quam stulti cives laudent. Nec ego, ut nihil agatur, moneo; sed ut agentem te ratio ducat, non fortuna: tuæ potestatis semper, tuaque omnia sint. Armatus intentusque sis, neque occasioni tuæ desis, neque suam occasionem hosti des. Omnia non properanti clara certaque erunt: festinatio improvida est et cœca." 4. Quis tulerit Gracchos de seditione querentes, 5. Tu vero felix, non vitæ tantum claritate, sed etiam opportunitate mortis (ut perhibent, qui interfuerunt novissimis sermonibus tuis) constans et libens fatum excepisti; tanquam pro virili portione innocentiam Principi donares. Sed mihi filiæque, præter acerbitatem parentis erepti, auget mæstitiam, quod adsidere valetudini, fovere deficientem, satiari vultu, complexu, non contigit. Excepissemus certe mandata vocesque, quas penitus animo figeremus. 6. Atque utinam his potius nugis tota illa dedisset 7. Huic ab adolescentia bella intestina, cædes, rapinæ, discordia civilis, grata fuere; ibique juventutem suam exercuit. Corpus patiens inediæ, vigiliæ, algoris, supra quam cuiquam credibile est; animus audax, subdolus, varius, cujus rei libet |