EXAMPLE.

A houfe 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, fame breadth; alfo a femicircular window above the door, whofe height is 2 feet;-required the expence of glazing, at 1s. per fquare foot.

Which, at 1s. per fquare foot, amounts to 181. gs. 14d.

PAINTERS WORK.

PAINTERS work is measured in the fame manner as that of carpenters; and, in taking the dimenfions, 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-fhutters, &c. are reckoned double work. Deductions are to be made for chimnies, cafements,

&c.

EXAMPLE I.

The height of a room is 12 feet 9 inches, circumference 60 feet; how many fquare yards of painting?

12.75
60

9)765.00

Anf. 85 fq. yards.

9

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 inches, 5 window-fhutters, 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. old.

MISCELLANEOUS QUESTIONS.

Question 1..

What will the fide of a cube be, when the furface and foli

dity are expreffed by the fame number?

Anf. 6.

2. A ciftern 25 feet long, 15 broad, and 10 feet deep, is to be enlarged, fo as to contain four times the quantity, its depth will be 74 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 stone of 60 inches diameter; Wright and Smith paid equal fhares, 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 fhare? Wright 13.525 inches Anf. Smith 19.640 Turner=26.835

5. What is the diameter of a cylinder when the cylindric area is expreffed by the fame number with the folidity? Anf. 4. 6. My wright made me a ladder of such a length, that, by planting it on a ftreet 70 feet wide, it will reach a window on one fide 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.

Anf. {

The head diam. 25 inches.
The bottom

15

8. What ought to be the depth of a tub whofe 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 thicknefs, the length is 8 times the height;—required the thickness of the wall. Anf. 4.5 feet.

10. A tree 100 feet high, ftanding on a horizontal plane,

was

was broke by a tempeftuous wind, fo that the upper part of it ftruck the ground 30 feet from its root;-required the length of the part broke off. Anf. 54 feet.

11. A fquare within a circle contains 16 square yards ;—required the area of a square circumfcribed about the fame circle. Anf. 32 fquare yards.

12. The cubical altar at Delphos was I cubit ;-required the fide of the new altar, which was to be twice that fize, and of the fame form. Anf. 1.259921 cubits. 13. The ceiling of a room, at 6d. per fquare 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 fhillings, allowing one inch to each fhilling-required the portion of each of the daughters.

Anf.

The firft's annual income is 2509051. 125. The fecond, -1970611. 5s. 2d.

15. A gentleman had a garden furrounded 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. Anf. 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.

Anf. 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. Anf. 18 feet high.

18. The diameter of a malt bufhel is 18 inches, and its depth 8, inches; what ought to be the depth when the diameter is 10 inches ?

Anf. 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 bafe. Now C had his share next the river, B the middle divifion, and A the reft. 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 solid yard.

A pays 381. 2s 2d. Anf.B pays 151. 158.71d. Cpays 121. 2s. 2d.

20. One horse chaife, in turning round a ring, it was ob ferved 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 fquare feet. 21. The gilding of a ball, at 3d. per fquare inch, coft as much as the buying of it at 1d. 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 fections parallel to the bafe ;-required the height of each. The upper part is 27.73. Anf.The middle part The lower part

7.21.

5.06.

23. What length of a plank, that is 10 inches broad, will

make 4 fquare feet?

24. What length of a log of wood,

Anf. 5 feet 4 inches.

that is 15 inches broad

and 11 inches thick, will be equal to to cubical feet?

Anf. 8 feet 844 inches.

25. What length of a cord will strike off one-third part of a circular pond, whofe diameter is 40 yards? Anf. 38.5696 yds. 26. Two men, A and B, bought a round piece of wood, c qually thick throughout. A paid one-third'fhare, B the reft. A proposes to have a flip the whole length of the tree, for his 3 C fhare.