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6. Triangles and parallelograms of the same altitude are to one another as their bases,
7. In equal circles, angles, whether at the centres or circumferences, have the same ratio which the arches, on which they stand, have to one another.
ARITHMETIC.-(ABERDEEN.) 1. Find by practice the cost of 8 cwt. 2 qr. 20 lb. at £6 178. 4d. per cwt.
2. Paid £46 178. for 5 lb. 15 dwt., how much must be paid for 9 lb. 15 grains ?
3. If 19 men can build 47 yards of wall in 12 days, how many men will build 96 yards 2 feet 7 inches in 21 days?
4. Find the interest of £749 for 2 years 70 days at 34 per cent. per 5. Add 7 , of 11, $ of 23} and .
6. Reduce these to decimal fractions: 1a, 21, 866, ris, and ašo, then add the decimal fractions,
7. Find the fourth proportional to 4 18 : 74 :: 4 acres 3 roods and ? poles ; either by common or decimal fractions.
8. Reduce 3 Ib. 12 oz. to the decimal fraction of a hundred-weight, 9. What is the square root of 649,75312 ? and of 19; ? 10. Multiply duodecimally 37 feet 9 inches 6 pts. by 8 feet 10 inches 4 pts.
ARITHMETIC.-(INVERNESS.) 1. If a clerk has a salary of £72. 188. a year, commencing on the 1st of January, how much has he to receive on leaving his situation on the 251h of September?
2. If a man can travel 360 miles in 12 days, of 8 hours each, how many miles, at the same rate of walking, will he travel in 60 days, of 6 hours each?
3. Add 3 of 4, 1 of 6 of 4+ together. 4. Divide 2 of 41 by i of g.
5. A gentleman who possessed the j of a copper-mine, sells y of his share for £453. What was the whole mine worth?
6. Find the greatest common measure of 620 and 2108.
9. A bill of £1000 became due on June 17th, of which £250 were paid Aug. Ist ; £300 on Oct. lith; £150 on Novenber 17th; and the balance on Dec. 31st. How much interest was there due at 43 per cent. ?
10. What is the solidity of a rectangular block of marble, whose length is 10ft. 4in. 3", breadth 7st. 2in. 6", and thickness 4ft. 6'?
11. Required the square root of 27• 225.
12. The first term of a decreasing equidifferent series is 59, the common difference 2, and the number of terms 24. Required the last term.
13. Find the amount of £325. 128. 6d. for 17 years, at 4 per cent. compound interest.
14. A person purchased a perpetual annuity of £320 for £10,000. What rate of interest had he for his money?
y 4. A gentleman left £210 to three servants, to be divided in continued proportion, so that the first shall have £90 more than the last. 5. Solve the equations
x + xy + y2 = 52;
xy - x2 = 8. 6. Find the roots of the equation
23 - 6x2 + 11x – 6 = 0.
TRIGONOMETRY.-(EDINBURGH. 1. Show that Sec A = NI + Tan 2A
• Sin A Tan A =
and NI-Sin 2A
1 Cosec A =
N 2 Versin A - Versin 'A 2. In a right-angled triangle if two parts be given besides the right angle, show that the other parts may be found, and give the solutions. ; 3. Solve the triangle in which AC = 176, BC = 133, and C=730.
4. A line was measured on the side of a lake 500 yards, and the angles at its extremities contained by it and lines drawn to a castle on the opposite side of the lake were 79° 23' and 54° 22. What is the distance of the castle from the extremities of the base ?
5. The diameter of the earth is 7912 miles. What is the height of a mountain which is visible at the distance of 180 miles ?
PRACTICAL MATHEMATICS.—(EDINBURGH.) 1. What is the area of a triangle whose sides are 50 and 42 feet 6 inches, and the contained angle 45° ?
2. Find the area of a ring, the diameters of the containing circles being 30 and 40 feet.
3. Find the area of a four-sided field, the diagonal being 1245 links and the perpendiculars on it from the opposite angles 675 and 450 links.
4. What is the area of a triangular field whose sides are 2569, 5025, and 4900 links?
5. B'is 3.5 feet below A, C 4•7 above B, D 2.9 below C, and E 11:4 above D. What is the difference of level of A and E?
MECHANICS.-(Glasgow.) 1. How many tons of coals will an engine of 3 horse-power raise per hour, from a pit whose depth is 120 fathoms?
2. A train of 80 tons moves at the uniform speed of 20 miles per hour, on a level rail whose friction is 6 lbs. per ton : required the horse-power due to friction.
3. How many cubic feet of water will an engine of 8 horse-power raise per
hour, from a pit whose depth is 160 fathoms, supposing the modulus of the pump to be ?
4. The area of one portion of a steam-engine is 500 square in., the mean effective pressure of the steam upon each inch of the piston 30 lbs., the length of the stroke 8 feet, and the number of strokes performed per minute 20; required the horse-power.
5. The handle of a windlass is 2 feet, what must be the radius of the axle, so that a man meeting a pressure of 60 lbs. upon the handle may raise a tub of coals weighing 4 cwts ?
6. In a compound screw, the length of the lever is 3 feet, the distance between the threads of the large screw } in., and that of the small one ; if 60 lbs be applied to the extremity of the level, what will be the pressure produced on the press-board ?
7. If a body be projected upwards with a velocity of 96} feet, to what height will it attain in 2 seconds?
8. In the handle of a common pump, the piston rod is placed at 3 in. from the fulcrum, a power of 60 lbs. is applied at the distance of 30 inches from the fulcrum, what will be the force lifting the piston ?
ASTRONOMY.-(EDINBURGH.) 1. Name and describe briefly the principal systems of astronomy. 2. Name the primary planets, and give a brief account of three of them.
3. Give the distance of the sun from the earth, his diameter, and his magnitude, as compared with the earth.
4. Give a representation of your idea of the comparative dimensions of the planets.
5. Account for the heat of summer and the cold of winter. 6. What occasions an eclipse of the sun? of the moon ?
7. Give the astronomical meaning of the term parallax. Distinguish diurnal and annual parallax.
8. How may the distances of the fixed stars be inferred from the long absence and return of comets ?
9. State the three laws of Kepler.
Hos agmine venientes T. Herminius legatus conspicatus, interque eos insignem veste armisque Mamilium noscitans, tantò vi majore, quàm paulò antè Magister equitum, cum duce prælium iniit, ut et uno ictu transfixum per latus occiderit Mamilium, et ipse, inter spoliandum corpus hostis, veruto percussus, quum victor in castra esset relatus, inter primam curationem exspiraverit. Tum ad equites dictator advolat, obtestans, ut, fesso jam pedite, descendant ex equis, et pugnam capessant. Dicto paruere: desiliunt ex equis, provolant in primum, et pro antesignanis parmas objiciunt. Recipit extemplo animum pedestris acies, postquam juventutis proceres, æquato genere pugnæ, secum partem periculi sustinentes vidit. Tum demum impulsi Latini, perculsaque inclinavit acies. Equiti admoti equi, ut persequi hostem posset. Secuta et pedestris acies. Ibi, nihil nec divinæ nec humanæ opis dictator prætermittens, ædem Castori vovisse fertur : ac pronunciâsse militi præmia, qui primus, qui secundus, castra hostium intrâsset. Tantusque ardor fuit, ut eodem impetu, quo fuderant hostem, Romani castra caperent. Hoc modo ad lacum Regillum pugnatum est. Dictator et magister equitum triumphantes in urbem rediêre.
Livy, Book ii. Chap. 20. 1. Distinguish agmen, exercitus, and acies.
2. Conjugate and distinguish venio and veneo-give a compound verb from the laiter, both in its contracted and uncontracted form.
3. Parse and construe veste-whence derived ? Give its principal modern derivatives with their meanings.
4. Equitum—how many cavalry were usually joined to each legion? What were they called, and how divided ?
3. Occiderit-parse and conjugate. Distinguish occido and occido-give the derivation of each. Which of the compounds of the former want the supine ?
6. Veruto-give the literal meaning of this word. Name and describe the offensive and defensive arms of ihe Roman Legionaries, and the organization of a Legion. Wherein did it differ from the Macedonian Phalanx ?
7. Dictator —descr:be the office of Dictator. Who was the first Dictator, and on what occasion was he created ?
8. Descendant—when does ut take the subjunctive and when the indicative?
9. Capessant — conjugate — whence derived ? Give any verb similarly formed.
10. Antesignani—who were these ? 11. Distinguish parma, scutum, clypeus, and pella. 12. Proceres-give its derivation, and distinguish Proceres and Oplimates.
Quis Parthum paveat ? quis gelidum Scythen ?
Bellum curet Iberiæ ?
Te mensis adhibet deum :
Et magni memor Herculis.
Quum Sol oceano subest.
Horace, Odes, Book iv., 5, 25, 40, 1. Conjugate parturio, parco, misceo, and præsto. 2. Distinguish incolumis and integer. 3. Distinguish condere and condire. 4. Translate
Sæpe ego longos Cantando puerum memini me condere soles. 5. Alteris mensis : explain this fully. 6. Laribus: whence is this derived, and what is its meaning ? 7. Distinguish between Lares præstites and Lares compitales. 8. What constituted the Sacra Privata among the Romans ?
9. Ferius-give its derivation-mention what you know regarding these days and distinguish
1. Feriæ Stativæ,
Indictæ, 10. Distinguish mane and diluculo. 11. Uvidimgive a contracted form of this word—whence is it derived ?
GREEK.-(GLASGOW.) TranslateΚυρος δε, συγκαλέσας τους στρατηγούς είπεν. «'Απολελοίπασιν ημάς Ξενίας και Πασίων" αλλ' εύ γε μέντοι επιστάσθωσαν,ότι ούτε αποδεδράκασιν, (οίδα γαρ ώπη οΐχονται,) ούτε αποπεφεύγασιν, έχω γάρ τριήρεις ώστε ελεϊν το εκείνων πλοίον. 'Αλλά, μα τους θεούς, ουκ έγωγε αυτούς διώξω ουδ' έρει ουδείς, ως εγώ, έως μεν άν παρή τις, χρώμαι, επειδάν δε απιέναι βούληται, συλλαβών και αυτούς κακώς ποιώ και τα χρήματα αποσυλώ. 'Αλλά ιόντων, ειδότες ότι κακίους εισί περί ημάς ή ημείς περί εκείνους. Καίτοι έχω γε αυτών και τέκνα και γυναίκας εν Τράλλεσι φρουρούμενα. αλλ' ουδε τούτων στερήσονται, αλλ' απολήψονται της πρόσθεν ένεκα περί έμε αρετής.”
Xenoph. Anab. Book i. Chap. 4. 1. στρατηγούς.-Whence derived? Give the word for a soldier, α camp, to encamp, an army, and to command an army.
2. απολελοίπασιν.-Parse and conjugate. Give the 1st Aor. Pas. and 2nd Aor. Act. With what case is the middle voice construed ?
3. επιστά σθωσαν.-Parse and conjugate. What is the meaning of επιστήμη? give two adjectives connected with it signifying scientific.
4. Distinguish όπη, όπου, όποι, and oπή.
8. épei.-Parse and conjugate. In what tenses is the verb deficient, and whence are they supplied ?
9. dao ovdW.-Whence derived ? ils uncontracted form ? and literal meaning ?
12. φρουρούμενα.-Whence derived? Give the words for a garrison and its commander.
Και καθίσας ο Ιησούς κατενάντι του γαζοφυλακίου έθεώρει πως ο όχλος βάλλει χαλκών εις το γαζοφυλάκιον" και πολλοί πλούσιοι έβαλλαν πολλά. Και ελθούσα μία χήρα πτωχή έβαλε λεπτά δύο, ό έστι κουράντης.
Και προσκαλεσάμενος τους μαθητάς αυτού, λέγει αυτούς. Αμήν λέγω υμίν, ότι η χήρα αύτη ή πτωχή πλείον πάντων βέβληκε των βαλλόντων εις το γαζοφυλάκιον.
Πάντες γάρ έκτου περρισσεύοντος αυτούς έβαλον" αύτη δε εκ της υστερήσεως αυτής πάντα όσα είχεν έβαλεν, όλον τον βίον αυτής.
St. Mark, Chap. xii., ver. 41-44. 1. γαζοφυλακίου-Give its component parts and the word for a treasurer. 2. πολλοί-Compare and give the singular throughout all its cases, 3. State any peculiarity in the intlexion of liquid verbs.
4. κοδράντης-What was the value of this coin Is the word properly Greek ?
5. προσκαλεσάμενος-Parse and conjugate the simple verb. 6. For what is αυτού contracted? Distinguish between αυτού and αυτού.
7. Conjugate θεώρεω, βάλλω, έρχομαι, and έχω, 8. πλείον πάντων-Why in the genitive ? 9. Distinguish between βίος and βιός. 10. περισσεύοντος-parse, conjugate, and give its component parts. 11, nepi-How many cases does it govern? Give its peculiar meaning with each of them.