A and B's horses together are supposed to do

of the

work, A and C's, B and C's 18; they are to be paid proportionally; what is each one's share of the money?

Proof,

$26'45.

*ી.) 23. 2.)

134. A person, who was possessed of 2 of a vessel, sold of his share for 375£.; what was the vessel worth? Ans. 1500£.

135. A gay fellow soon got the better of of his fortune; he then gave 1500£. for a commission, and his profusion continued till he had but 450£. left, which he found to be just of his money, after he had purchased his commission; what was his fortune at first? Ans. 3780£. 136. A younger brother received 1560 £., which was just of his elder brother's fortune, and 5g times the elder brother's fortune was as much again as the father was worth, pray, what was the value of his estate? Ans. 19165£. 14 s. 34 d.

137. A gentleman left his son a fortune, of which he spent in three months; of of the remainder lasted him nine months longer, when he had only 537£. left; what was the sum bequeathed him by his father?

Ans. 2082£. 18 s. 2 d.

138. A cannon ball, at the first discharge, flies about a mile in eight seconds; at this rate, how long would a ball be in passing from the earth to the sun, it being 95173000 miles distant?

Ans. 24 years, 46 days, 7 hours, 33 minutes, 20 seconds. 139. A general, disposing his army into a square battalion, found he had 231 over and above, but, increasing each side with one soldier, he wanted 44 to fill up the square; of how many men did his army consist?

Ans. 19000.

140. A and B cleared, by an adventure at sea, 45 guineas, which was 35£. per cent. upon the money advanced, and with which they agreed to purchase a genteel horse and carriage, whereof they were to have the use in proportion to the sums adventured, which was found to be 11 to A, as often as 8 to B; what money did each adventure?

Ans. A 104. 4 s. 218 d., B 75£. 15 s. 9 d. 141. Tubes may be made of gold, weighing not more than at the rate of 25 of a grain per foot? what would be the weight of such a tube, which would extend across the

Atlantic from Boston to London, estimating the distance at 3000 miles? Ans. 1 lb. 8 oz. 6 pwts. 3 grs. 142. A military officer drew up his soldiers in rank and file, having the number in rank and file equal; on being reinforced with three times his first number of inen, he placed them all in the same form, and then the number in rank and file was just double what it was at first; he was again reinforced with three times his whole number of men, and, after placing them all in the same form as at first, his number in rank and file was 40 men each; how many men had he at first? Ans. 100 men.

143. Supposing a man to stand 80 feet from a steeple, and that a line reaching from the belfry to the man is just 100 feet in length; the top of the spire is 3 times as high above the ground as the steeple is; what is the height of the spire? and the length of a line reaching from the top of the spire to the man? See ¶ 109.

Ans. to last, 197 feet, nearly. 144. Two ships sail from the same port; one sails directly east, at the rate of 10 miles an hour, and the other directly south, at the rate of 74 miles an hour; how many miles apart will they be at the end of 1 hour?

2 hours? 24 hours? 3 days? Ans. to last, 900 miles. 145. There is a square field, each side of which is 50 rods; what is the distance between opposite corners ?

Ans. 7071+ rods. 146. What is the area of a square field, of which the opposite corners are 70'71 rods apart? and what is the length of each side? Ans. to last, 50 rods, nearly. 147. There is an oblong field, 20 rods wide, and the distance of the opposite corners is 33 rods; what is the length of the field? its area?

Ans. Length, 26 rods; area, 3 acres, 1 rood, 13 rods. 148. There is a room 18 feet square; how many yards of carpeting, 1 yard wide, will be required to cover the floor of it? 182324 ft. 36 yards, Ans. 149. If the floor of a square room contain 36 square yards, how many feet does it measure on each side?

Ans. 18 feet. When one side of a square is given, how do you find its area, or superficial contents ?

When the area, or superficial contents, of a square is given, now do you find one side?

150. If an oblong piece of ground be 80 rods long and 20 rods wide, what is its area ?

D

E A

C

Note. A Parallelogram, or Oblong, has its opposite sides equal and parallel, but the adjacent sides unequal. Thus A B C D is a parallelogram, and also E F C D, and it is easy to see, that the contents of both are equal. Ans. 1600 rods, 10 acres. 151. What is the length of an oblong, or parallelogram, whose area is 10 acres, and whose breadth is 20 rods?

Ans. 80 rods.

152. If the area be 10 acres, and the length 80 rods, what is the other side?

When the length and breadth are given, how do you find the area of an oblong, or parallelogram?

When the area and one side are given, how do you find the other side?

153. If a board be 18 inches wide at one end, and 10 inches wide at the other, what is the mean or average width of the board? Ans. 14 inches. When the greatest and least width are given, how do you find the mean width?

154. How many square feet in a board 16 feet long, 1'8 feet wide at one end, and 1'3 at the other?

Mean width,

feet, Ans.

18+ 1'3

2

= 1'55; and 1'55 X 16 = 24'8

155. What is the number of square feet in a board 20 feet long, 2 feet wide at one end, and running to a point at the other? Ans. 20 feet. How do you find the contents of a straight edged board, when one end is wider than the other?

If the length be in feet, and the breadth in feet, in what denomination will the product be?

If the length be feet, and the breadth inches, what parts of a foot will be the product?

156. There is an oblong field, 40 rods long and 20 rods wide; if a straight line be drawn from one corner to the opposite corner, it will be divided into two equal right-angled triangles hat is the area of each? 2 acres, 2 roods.

Ans. 400 square rods

157. What is the area of a triangle, of which the base is 30 rods, and the perpendicular 10 rods? Ans. 150 rods. 158. If the area be 150 rods, and the base 30 rods, what is the perpendicular? Ans. 10 rods. 159. If the perpendicular be 10 rods, and the area 150 rods, what is the base? Ans. 30 rods. When the legs (the base and perpendicular) of a rightangled triangle are given, how do you find its area?

When the area and one of the legs are given, how do you find the other leg?

Note. Any triangle may be divided into two right-angled triangles, by drawing a perpendicular from one corner to the opposite side, as may be seen by the annexed figure.

Here A B C is a triangle, divided into two right-angled triangles, A d C, and d B C; therefore the whole base, A B, multiplied by one half the perpendicular d C, will give the area of the whole. If A B 60 feet, and C16 feet, what is the area? Ans. 480 feet 160. There is a triangle, each side of which is 10 feet what is the length of a perpendicular from one angle to its opposite side? and what is the area of the triangle?

Note. It is plain, the perpendicular will divide the opposite side into two equal parts. See T 109.

Ans. Perpendicular, 8'66 + feet; area, 43'3 +feet. 161. What is the solid contents of a cube measuring 6 feet on each side? Ans. 216 feet. When one side of a cube is given, how do you find its solid contents?

When the solid contents of a cube are given, how do you find one side of it?

in 10 bricks?

162. How many cubic inches in a brick which is 8 inches long, 4 inches wide, and 2 inches thick? in 2 bricks? Ans. to last, 640 cubic inches. 163. How many bricks in a cubic foot? in 40 cubic 'eet? Ans. to last, 27000. 164. How many bricks will it take to build a wall 40 feet m length, 12 feet high, and 2 feet thick?

in 1000 cubic feet?

Ans. 25920

165. If a wall be 150 bricks, 100 feet, in length, an 4 bricks, 16 inches, in thickness, how many bricks wi lay one course?

2 courses?

Y

10 courses? If the

wall be 48 courses, 8 feet, high, how many bricks will build it? 150 X 4600, and 600 X 48 = 28800, Ans. 166. The river Po is 1000 feet broad, and 10 feet deep, and it runs at the rate of 4 miles an hour; in what time will it discharge a cubic mile of water (reckoning 5000 feet to the mile) into the sea? Ans. 26 days, 1 hour.

167. If the country, which supplies the river Po with water, be 380 miles long, and 120 broad, and the whole land upon the surface of the earth be 62,700,000 square miles, and if the quantity of water discharged by the rivers into the sea be every where proportional to the extent of land by which the rivers are supplied; how many times greater than the Po will the whole amount of the rivers be? Ans. 1375 times.

168. Upon the same supposition, what quantity of water, altogether, will be discharged by all the rivers into the sea in a year or 365 days? Ans. 19272 cubic miles.

169. If the proportion of the sea on the surface of the earth to that of land be as 10 to 5, and the mean depth of the sea be a quarter of a mile; how many years would it take, if the ocean were empty, to fill it by the rivers running at the present rate ? Ans. 1708 years, 17 days, 12 hours.

170. If a cubic foot of water weigh 1000 oz. avoirdupois, and the weight of mercury be 13 times greater than of water, and the height of the mercury in the barometer (the weight of which is equal to the weight of a column of air on the same base, extending to the top of the atmosphere) be 30 inches; what will be the weight of the air upon a square foot? a square mile? and what will be the whole weight of the atmosphere, supposing the size of the earth as in questions 166 and 168?

Ans. 2109'375 lbs. weight on a square foot.

mile.

of the whole atmosphere.

171. If a circle be 14 feet in diameter, what is its circumference?

Note. It is found by calculation, that the circumference of a circle measures about 34 times as much as its diameter, or, more accurately, in decimals, 3'14159 times. Ans. 44 feet. 172. If a wheel measure 4 feet across from side to side, how many feet around it ? Ans. 124 feet. 173. If the diameter of a circular pond be 147 feet, what is its circumference ? Ans. 462 feet