EXAMPLE. A house with 3 rows of windows, 5 in a row, the dimenfions of the first row is 6 feet 4 inches by 4 feet 2 inches; of the fecond row, 5 feet 9 by the fame breadth; of the third, 5 feet 3 inches, same breadth; also a semicircular window above the door, whose height is 2 feet;-required the expence of glazing, at 1s. per square foot. Which, at 1s. per square foot, amounts to 181. 9s. Id. PAINTERS WORK. PAINTERS work is measured in the fame manner as that of carpenters; and, in taking the dimensions, the line must be bent into all the hollows, and over all the projections, in order to to afcertain the furface which has been touched with the brush. The painting of the bars of windows is reckoned whole work, it being troublesome; and railing a whole furface painted on both fides. Doors, window-shutters, &c. are reckoned double work. Deductions are be made for chimnies, casements, &c. EXAMPLE I. The height of a room is 12 feet 9 inches, circumference 60 feet; how many square yards of painting ? 12.75 9)765.00 Anf. 85 fq. yards. Ex. 2. The height of a room is 11 feet 7 inches, circumference 74 feet 10 inches, the door 7 feet 6 inches by 3 feet 9 inches, 5 window-shutters, each 6 feet 8 inches by 3 feet 4 inches, the breaks in the windows 14 inches deep and 8 feet high, the chimney 6 feet 9 inches by 5 feet; a closet, the height of the room, 3 feet deep and 4 feet 9 inches in front, with shelving, at 22 feet 6 inches by 10 inches, painted on both fides, what will the whole amount to, at 6d. per square yard ? Anf. 31. 14s. od. What will the fide of a cube be, when the furface and folidity are expreffed by the fame number? Ans. 6. 1 2. A cistern 25 feet long, 15 broad, and 10 feet deep, is to be enlarged, so as to contain four times the quantity, its depth will be 7+ feet, and the fides in the proportion of 3 to 5 ;-required the fides. Anf. 34.641013, and 57.735026 feet. 3. Required the diameter of a globe equal to a cube, whose Anf. 7.43. fide is 6. 4. Three men, Wright, Smith, and Turner, bought a grinding ftone of 60 inches diameter; Wright and Smith paid equal shares, and Turner one-half share; each partner is to grind the stone in his turn, first Wright, then Smith, and Turner last. How much of the diameter ought each to grind down for his share? Wright=13.525 inches Ans. Smith =19.640 Turner=26.835 5. What is the diameter of a cylinder when the cylindric area is expressed by the fame number with the folidity? Ans. 4. 6. My wright made me a ladder of such a length, that, by planting it on a street 70 feet wide, it will reach a window on one side 40 feet high; by turning it over, without moving the foot, it will do the fame by a window 30 feet;-required the length of the ladder. Anf. 50 feet. 7. My coppersmith agreed to make me a flat-bottomed kettle, that should contain 13 ale gallons: The depth of the kettle is 12 inches, the top and bottom diameters are in the proportion of 5 to 3 ;-required the diameters. Ans. The head diam. 25 inches. 15 8. What ought to be the depth of a tub whose base and head diameters are 20 and 10, to contain 9163 folid inches ? Anf. 50 inches. 9. There is a wall containing 18225 folid feet, the height is 5 times the thickness, the length is 8 times the height ;-required the thickness of the wall. Ans. 4.5 feet. 10. A tree 100 feet high, standing on a horizontal plane, was was broke by a tempestuous wind, so that the upper part of it struck the ground 30 feet from its root;-required the length of the part broke off. Ans. 54 feet. 11. A fquare within a circle contains 16 square yards;-required the area of a square circumscribed about the same cirAnf. 32 square yards. cle. 12. The cubical ?ltar at Delphos was I cubit ;-required the fide of the new altar, which was to be twice that size, and of the fame form. Anf. 1.259921 cubits. 13. The ceiling of a room, at 6d. per square yard, amounted to 21. 10s.; the breadth is 22 feet;-required the length. Anf. 40 feet. 14. A man left two daughters; ordered by his will that the eldest should have annually the rent of a square field, and the younger the rent of a circular one; the rent of each field, at 20s. per acre, would exactly furround it in shillings, allowing one inch to each shilling; required the portion of each of the daughters. { Ans. SThe first's annual income is 2509051. 125. The fecond, -1970611. 5s. 2d. 15. A gentleman had a garden surrounded by a terrace walk; the length of the garden is 500 yards, and the breadth 400 yards; the walk was equal to of the garden ;-required the breadth of the walk. Ans. 13.6809 yards. 16. A gentleman has a garden 100 feet long and 80 broad, but intends to make a walk half round it that shall take up half the ground;-required the breadth of the walk. Ans. 25.96876. 17. The length of a room is 40 feet, and breadth 30 feet; the expence of painting the walls, at 6d. per square yard, is 71. -required the height of the room. Ans. 18 feet high. 18. The diameter of a malt bushel is 18 inches, and its depth 8,5 inches; what ought to be the depth when the diameter is 20 inches? Ans. 6.8448 inches. 19. Three 19. Three farmers, A, B, and C, had each an equal share of a triangular field, whose base, being a river, measured half an English mile, its content being 120 acres: the marches were drawn parallel to the base. Now C had his share next the river, B the middle division, and A the rest. They agreed with an undertaker to dig a ditch from the top of A's divifion perpendicular to the river fide. The breadth of the ditch at a medium is 6 feet, and depth 44 feet. Required the undertaker's charge against each of the three farmers, at 4d. per folid yard. 20. One horse chaise, in turning round a ring, it was ob served that the outer wheel made three turns for every two of the inner wheel. The height of the wheels being 4+ feet, and distance 5 feet, required the area of the space or ring included betwixt the tracts of the wheels. Anf. 392.7 square feet. 21. The gilding of a ball, at 3d. per square inch, cost as much as the buying of it at Id. per cubical inch: It is required to find its diameter. Anf. 18 inches. 22. A cone, whose height is 40 inches, is to be divided into three equal parts, by sections parallel to the base;-required the height of each. The upper part is 27.73. Ans. The middle part 7.21. 5.06. Ans. 5 feet 4 inches. 23. What length of a plank, that is to inches broad, will make 4+ square feet? 24. What length of a log of wood, that is 15 inches broad and II inches thick, will be equal to to cubical feet? Anf. 8 feet 8 inches. 25. What length of a cord will strike off one-third part of a circular pond, whose diameter is 40 yards? Anf. 38.5696 yds. 26. Two men, A and B, bought a round piece of wood, e qually thick throughout. A paid one-third share, B the reft. A proposes to have a flip the whole length of the tree, for his share. 3 C |