TUESDAY, 3RD NOVEMBER. [10 A.M. TO 1 P.M.] EUCLID. N.B.The answers to the two Sections should be given up in separate books. All intelligible abbreviations may be used. In working riders, candidates may use any propositions they consider most suitable. SECTION I. 1. Show that the sum of the angles of any rectilineal figure together with 9 four right angles is equal to twice as many right angles as the figure has sides. ABCD is a quadrilateral; the bisectors of the angles A and B meet in P, of B and C meet in Q, of C and D meet in R and of D and A meet in S; show that a circle can be described about the quadrilateral PQRS. 2. Prove that in a right angled triangle the sum of the squares on the 12 sides containing the right angle is equal to the square on the hypotenuse. ABC is a triangle right angled at 4. On AB, AC squares ABDE and ACFG are described externally to the triangle. Show that the line joining A to the middle point of BC will, when produced through A, cut EG at right angles. 3. ABC is an acute angled triangle, and AD is the perpendicular on BC. 11 Show that the square on AC together with twice the rectangle BC.BD is equal to the sum of the squares on AB and BC. P is any point within a parallelogram ABCD whose diagonals intersect in G. Show that PA2 + PB2 + PC2 + PD2 = AB2 + BC2 + 4PG2. 4. Draw a straight line touching a circle from a point without it. 5 5. If from a point outside a circle a line be drawn touching it and another 13 cutting it, prove that the rectangle contained by the whole line cutting the circle and the part of it outside the circle is equal to the square on the line that touches the circle. P is any point on the chord of contact of two tangents to a circle whose centre is O. Show that if the line through Pat right angles to PO meets the tangents in A, B, PA is equal to PB, 7. What are the nine-points implied in the term nine-points circle? 10 Show that these nine-points lie on one and the same circle. 8. Show that two triangles which have one angle of the one equal to one 14 angle of the other and the sides containing these angles proportional are similar to each other. On the sides AB, AC of a triangle two points D and E are taken so that BDCE. Show the locus of the middle point of DE is a line bisecting BC and parallel to the line bisecting the angle A. 9. Show that if four straight lines are proportionals the rectangle 10 contained by the extremes is equal to the rectangle contained by the means. If a line AB be divided internally and externally at C and D in the same ratio, and O is the middle point of AB, show that OC.OD OB3. 10. If a quadrilateral be inscribed in a circle, prove that the rectangle 10 contained by the diagonals is equal to the sum of the rectangles contained by the opposite sides. If ABCD be four points in this order on a straight line, prove that rectangle AB. CD + rectangle BC.AD = rectangle AC. BD. WEDNESDAY, 4TH NOVEMBER. GREEK HISTORY. N.B.-Please write each Section in a separate book, marking the number of the section outside. SECTION I. 1. Write what you know of the early wars of Sparta against the 11 Messenians. From what sources is the account derived and how far is it entitled to be regarded as history? 2. In what "" sense was the term Tyrant used by the Greeks ? What were the general characteristics of the rule of Tyrants? Give a brief account of the Despots of Corinth. 10 3. How did Clisthenes heal the factions of the men of the Uplands, 12 Plain and Shore? Sketch the main outlines of his constitution. SECTION II. 4. Describe the battle of Thermopyla and form some estimate of its effects on the History of Greece. 9 5. Trace very briefly the careers and form an estimate of the characters 14 of Themistocles, Pericles, Cleon and Lysander. 6. Give an account of the Athenian expedition to Sicily. SECTION III. 11 7. Sketch the career of Epaminondas and give an account of his battles 11 of Leuctra and Mantinea. 8. How was it that Philip of Macedon first failed and afterwards 11 succeeded in occupying the Pass of Thermopyla? Describe the series of events which led to this result. 9. Trace the career of Alexander the Great to his defeat of Darius at 11 the battle of Arbela. ANANDSHANKAR BAPUBUAI DHRUVA, M. A., LL.B. JEHANGIR E. DAVAR, Officier d'Académie, Univ. Gallic. In French. The Rev. S. NOTI, S.J. ... ... In Physics. In Logic. TUESDAY, 3RD NOVEMBER. ENGLISH (Text Books.) JOHNSON's-Lives of Milton, Pope, Swift and Dryden. GRAY-As in Bradshaw's Edition (Macmillan and Co.). 1. Paraphrase SECTION I. Thy form benign, O Goddess, wear, Thy philosophic train be there To soften not to wound my heart; The generous spark extinct revive, Exact my own defects to scan, What others are, to feel, and know myself a Man. 12 2. Write a very brief abstract of Gray's elegy, showing the connection 10 of thought throughout the poem, 3. Write notes on (i) (ii) Not that fair field of Enna * * nor that sweet grove of Daphne by Orontes, and the inspired Castalian spring, might with this Paradise of Eden strive. "If I must contend," said he, "Best with the best-the sender, not the sent; Or less be lost." "Thy fear," said Zephon bold, (iii) She-wolf of France, with unrelenting fangs That tear'st the bowels of thy mangled Mate, The scourge of Heaven. What Terrors round him wait! And Sorrow's faded form and Solitude behind. 4. Explain briefly the following phrases : With a vengeance; ambrosial fruit of vegetable gold; umbrageous 21 12 5. Discuss the position and importance of Gray in the history of English 20 Peetry. Or "By the general consent of critics the first praise of genius is due to the writer of an epic poem, as it requires an assemblage of all the powers which are singly sufficient for other compositions." (Johnson, Life of Milton.) Explain this, and illustrate it from Paradise Lost IV. SECTION II. 1 Discuss the justice of Johnson's criticisms in the following passages:— 25 (a) An unlearned reader, when he first opens Paradise Lost, finds himself surprised by a new language. (b) Walsh advised Pope to correctness, which the English poets had hitherto neglected. (c) The Conquest of Granada was written with a seeming determination to glut the public with dramatic wonders. (d) The flowers of the Essay on Man caught the eye, which did not see what the gay foliage concealed. (e) Surely no man could have fancied that he read Lycidas with pleasure, had he not known its author. 2. In what relation did the following stand to any one of the four 15 authors-Shadwell, Salmasius, Arbuthnot, Theobald, the Earl of Rochester. 3. What do you know of Dryden's defence, use, and final abandonment 20 of dramatic rhyme? 4. Mention the titles and the general tendencies of Swift's writings 15 occasioned by the following persons and interests :-Partridge, one Wood of Wolverhampton, Van Homrigh, Wotton and Bentley, Marlborough's campaigns. TUESDAY, 3RD NOVEMBER. [2 P.M. TO 5. P.M.] ENGLISH (Composition). The Influence of his Times upon a Poet. WEDNESDAY, 4TH NovsMBER. [2 P.M. TO 5 P.M.] SANSKRIT. Bana-Kadambarî, pp. 144-221 (Bom. Sansk, Series). Annambhatta—Tarkasangraha. 1. Translate into English : SECTION I. (a) श्रमाम्बुशिशिरीभवत् प्रसृतमन्दमन्दाकिनीमरुत्तरलितालकाकुलललाट चन्द्रद्युति अकुङ्कुमकलङ्कितोज्ज्वलकपोलमुत्प्रेक्ष्यते निराभरणमुन्दरश्रवणपाशसौम्यं मुखम् . (४) पाप्मभ्यश्च पुनातु वर्धयतु च श्रेयांसि सेयं कथा मङ्गल्या च मनोहरा च जगतो मातेव गङ्गेव च ; तामेतां परिभावयन्त्वभिनयैर्विन्यस्तरूपां बुधाः शब्दब्रह्मविदः कवेः परिणतप्रज्ञस्य वाणीमिमाम् • 2. Explain fully, with reference to the context : (a) अस्येतद्, आर्यपुत्र अस्त्येतद् । ( 6 ) कथं नामशेषामित्याह । (c) गुरुजनोपरोधात् क्षणं क्षभ्यतामतिक्रमो रामस्य । (d) अहो संविधानकम् | (e) अयं पुनरविरुद्धः प्रकार इति वृद्धेभ्यः श्रूयते । (f) तं हि धर्मं धर्मसूत्रकाराः समामनन्ति । 3 Make a few remarks on the language, ideas and sentiments of the Uttara Ramacharita, 50 |