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In some places, double measure is allowed for hips, rallics, gutters, &c. and no deduction for chimneys.


A Nate roof is 30 feet long and 26 feet over,-how many squares are in it?

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Ex. 2. How many squares tiling in a roof 351 feet deep, and whose length is 48 ?

An. 16 squares 92 feet. Ex. 3. How much Nating in a pavilion roof, with a platform 50 feet long and 30 broad at the eaves, and 30 feet long by to at the platform ; 14. feet from the platform to the eaves, taken the shortest way, and 17 along the hips?

Anf. 5 roods 31 yards.


Glaziers take their dimensions in feet, inches, and parts. All circular, triangular, &c. windows, are 'measured as if they were squares; and the greatest lengths and breadths are taken on account of the trouble and waste of glass attending the cutting


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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 second row, 5 feet 9 by the same 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.

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369 4 Which, at 1s. per square foot, amounts to 181. gs. 1 d.


PAINTERS work is measured in the same 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 ascertain the surface 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 sides. Doors, window-fhutters, &c. are reckoned double work. Deductions are w be made for chimnies, casements, &c.


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



Anf. 85 sq. 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 inche's 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 ro inches, painted on both fides-what will the whole amount to, at 6d. per square yard ?

Anf. 31. 145. 0 d.



Question 1.

What will the side of a cube be, when the surface and folidity are expressed by the same number?

Anf. 6.

Anf. 4.

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 sides in the proportion of 3 to 5 ;-required the sides. Anf. 34.641013, and 57-735020 feet.

3. Required the diameter of a globe equal to a cube, whose fide is 6.

Ans. 7.43. 4. Three men, Wright, Smith, and Turner, bought a grinding stone 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 same number with the solidity ?

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 same by a window 30 feet ;-required the length of the ladder,

Ans. 50 feet. 7. My coppersmith agreed to make me a flat-bottomed kettle, that should contain 137} 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.

head The bottom

15 8. What ought to be the depth of a tub whose base and head diameters are 20 and 10, to contain 9163 solid 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.

Anf. 4.5 feet. . ļo. A tree 100 feet high, standing on a horizontal plane,


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.

Anf. 54 feet. 11. A square within a circle contains 16 square yards ;-required the area of a square circumscribed about the same circle.

Anf: 32 square yards. 12. The cubical altar at Delphos was i cubit ;-required the fide of the new altar, which was to be twice that size, and of the same form.

Ans: 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 205. per acre, would exactly surround it in shillings, allowing one inch to each shilling ;-required the portion of each of the daughters.

The first's annual income is 250905l. 125.
The second,

-197061l. 55. 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.

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 7!. -required the height of the room. Anf. 18 feet high.

13. 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 19 inches ?

Anj. 6.8448 inches.

19. Three

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