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PLANE TKIGONOMETRY.

[Give the whole work.]

L Tan X = m. What is the cotangent of (180° — x) ? of (270° + x) ? What angle in the third quadrant has a cotangent equal to m?

2. Explain by a. figure the changes, both numerical and algebraic, through which the sine of an arc passes, as the arc increases from 0° to 360°.

3. Obtain, from fundamental formulas, all the trigonometric functions of the negative of an angle.

4. Solve the plane right triangle whose sides are 13, 12, 5.

5. Obtain, from fundamental formulas, an expression for cot (x + y), in terms of cot x and cot y.

6. Two angles of a plane oblique triangle are 13° 17' 48" and 114° 47' 9", and the included side is 0.1493. Solve the triangle.

7. Given, V = c* + d1 2cd cos B,

1 — cos x = 2 sin2 %x, s = i(b + c + d). Find an expression for sina \B.

9. In the plane oblique triangle BCD, explain in full the method of solution when the sides c, d, and the angle B are given.

ENGLISH COMPOSITION.

You are required to write a short English composition of not less than fifty lines, correct in spelling, punctuation, grammar, and expression. Make several paragraphs. Take one of these subjects : —

An account of the Trial in the Merchant of Venice.

The story of Fergus Mac Ivor, in Waverley.

Prospero's Life on the Island, and how he came there.

FRENCH.

1. Translate Into English : —

Pendant le règne du fameux Crésus, il y avait en Lydie un jeune homme bien fait, plein d'esprit, très-vertueux, de la race des anciens rois, et devenu si pauvre qu'il fut réduit à se faire berger. Se promenant un jour sur des montagnes escarpées où il rêvait sur ses malheurs en menant son troupeau, il s'assit au pied d'un arbre pour se délasser. Il aperçut auprès de lui une ouverture étroite dans un rocher. La curiosité l'engage à y entrer. Il trouve une caverne large et profonde. D'abord il n'y voit goutte; enfin ses yeux s'accoutument à l'obscurité. Il entrevoit dans une lueur sombre une urne d'or sur laquelle ces mots étaient gravés: "Ici tu trouveras l'anneau de Gygès. 0 mortel, qui que tu sois, à qui les dieux destinent un si grand bien, montre-leur que tu n'es pas ingrat, et garde-toi d'envier jamais le bonheur d'aucun autre homme." Il ouvre l'urne, trouve l'anneau, le prend, et, dans le transport de sa joie il laissa l'urne, quoiqu'il fût très-pauvre et qu'elle fût d'un grand prix. Il sort de la caverne et se hâte d'éprouver l'anneau enchanté dont il avait si souvent entendu parler depuis son enfance.— Fenelon.

2. State the tense of the italicized verbs in the above, and give it in full.

3. Give the principal tenses of venir, mourir, valoir, prendre. (Thus, Inc., etre; Pees Part., etanto' Past Part., eie; Ind. Press., je suis; Pret., je fus.)

4. Translate into French: (a) He is the best boy in the school, (b) We read1 French better than you think.1 (c) I do not doubt8 that you will come, (d) We have no more money4; have the kindness to send' us some.

1 lire. 1 croire. * douter. 4 argent, m. » bonW,/. • envoyer.

ELEMENTARY BOTANY.

1. Describe the germination of a grain of corn, a pineseed, and an acorn.

2. What are buds?

3. Describe equitant leaves

4. What are stipules?

5. What is a leaf-tendril?

6. How does it differ from a branch-tendril?

7. In how many ways may stamens be united together?

8. What is a two-lipped flower?

9. Describe the fruit of a rose, strawberry, blackberry, apple, pea, and squash.

10. Describe the leaves of this plant.

HARVARD EXAMINATION PAPERS.

JUNE, 1876.

ANCIENT HISTORY AND GEOGRAPHY.

[Answer five questions, including the first.-]

1. Draw a map of Italy, showing the position of the divisions and of the following places: Vercellae, Beneventum, Brundusium, Nola, Roma, Capua, Antium, Ostia, Asculum Apulum, Neapolis, Veii, Tibur, Tusculum, Tarentum, Pisa, Florentia, Placentia, Cannae, Cumae, Baiae.

2. The alliance of Athens and Sparta, 464 - 461 B. C, and its connection with Athenian politics.

3. The Theban supremacy.

4. Philip of Macedon.

5. The expedition of Pyrrhus to Italy.

6. State the extent of the Roman Empire at the time of Augustus. When and how were the various provinces subjected to Rome?

7. Give some account of the writers of the Augustan age.

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