3. Nazarites who might drink no wine were also forbidden to "All is not lost; the unconquerable will Section 4. Parse the words printed in italics. Section 5. 1. What evidence is there of an eastern origin of the languages of Central Europe? 2. What is the classification of the European languages? 3. What are the elements of modern English, and what is its history? Section 6. 1. Give examples of six of the elementary sounds of the English language. 2. Distinguish between the sharp and flat mute consonants. 3. Under what circumstances does a combination of sharp and flat mute consonants in the same syllable become pronounceable? Give examples of this. Section 7. Transpose the following passage :— "To preside in the public assembly of his countrymen, Gideon, the renowned champion of Israel, quitted the threshing-floor; and to lead the Roman armies to battle, Cincinnatus, the conqueror of the Volci, left his plough, and to return to his native fields, afterwards declined the rewards gained by his victories." GEOMETRY, TRIGONOMETRY, AND (One question only to be answered in each section.) 1. Straight lines which are parallel to the same straight line are parallel to one another. 2. If two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of the one greater than the angle contained by the two sides equal to them of the other; the base of that which has the greater angle shall be greater than the base of the other. 3. In every triangle the square of the side subtending either of the acute angles is less than the square of the sides, containing it by twice the rectangle contained by either of these sides, and the straight line intercepted between the acute angle and the perpendicular let fall upon it from the opposite angle. (The first case only of this proposition need be demonstrated.) Section 2. 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. 2. If one angle of a triangle be equal to the sum of the other two, the greatest side is double of the distance of its middle point from the opposite angle. 3. If from the point of intersection of the straight lines which beset two angles of an equilateral triangle straight lines be drawn parallel to the sides of the triangle they will trisect the sides. Section 3. 1. Find the value of sin (2 n + 3) π 2. Show that sin a = sin (60° + a)· sin (60° a) 3. Show that sin (n + 2) a. sin na = sin2 (n + 1) a sin2 a. Section 4. 1. Find the value of sin 60°. 2. Expand cos (a + b) 3. Having given two sides of a triangle, and the included angle investigate a method adapted to logarithmic calculation for determining another angle without first determining the third side. Section 5. 1. From the top of a tower 100 feet in height, the angular depression of a distant object is observed to be 11 deg. 13 sec. What is the distance of the object? 2. To determine the distance from one another of two inaccessible objects C and D, by observations from stations A and B in the same plane, whose distance A B is known. Example to be worked by construction A B 600, C A D =37°, D A B = 58° 20′, C B A 3. The distance of three inaccessible objects, A, B, C (in the same plane) from one another are, respectively, 840, 760, and 1000 yards. These are observed at a distant point P, and the angle A P B is found to be 22 deg. 11 sec., the angle AP C 17 deg. 13 sec. Determine the position of P by construction, and its distance from the points A B C; or show how these may be determined by calculation. Section 6. 1. Define the logarithm of a number N to the base a: and show that 2. Expand ax. 10 3. Investigate an expression for determining the logarithm of a number to any given base in a converging series. Section 7. 1. Investigate an expression for the area of a quadrilateral figure inscribed in a circle. 2. Expand sin ma in terms of sin x. 3. Determine either angle of a spherical triangle in terms of its sides. Section 8. 1. Investigate a rule for determining the area of a trapezoid. 2. What is the area of a circular plot of ground whose diameter is 27 chains. 3. The side of an octagon is 10 feet, what is its area? 4. A ring is generated by the revolution of an equilateral triangle whose side is three inches, about an axis parallel to one of its sides, and distant 6 inches from it. What is the solidity of the ring and its surface. Section 9. 1. One side of a rectangular field is double the other; the field measures 20A. OR. 19P., what are its sides ? 2. Given the several offsets, 15, 25, 40, 10, 60, 30, 25, 8, 18, 9, 8, 4, 6, 0. taken at one chain's length. Required the area. 3. Required the plan and content of a four-sided field contained by straight lines according to the following field-book :— (One question only is to be answered in each section.) 1. Involve (√ 2—3√3) to the third power. √ 4 ax b 1. At what price per head must a farmer purchase a flock of 100 sheep, that, expending £10 in feeding them, and losing 9, he may be able to sell the remainder at £2 each and gain £20? 2. I turn over the pages of a book by fours, and find three odd ones. I then turn them over by fives, and find two odd ones. The last time I do not turn them over so often by twenty times as I did the first. How many pages were there? 3. A passenger train and a luggage train, the one travelling at 10 miles per hour less speed than the other, set out at the same time, the one from London and the other from Carlisle, 210 miles apart, and pass one another at a certain station on the road. The passenger train sets out from Carlisle to return, two hours after the luggage train sets out to return from London; and it is observed that they pass one another at the same station. At what rate do they travel, and how far from London is the station? Section 7. 7, the 1. The first term of an arithmetical progression is number of terms 8, and the sum 28. What is the common difference? |