Subftract the Content of the lefler Cone from the Content of the greater; and the Remainder shall be the Content of the Frus ftrum

PROBLEM XVII.

The Fruftrum BCDE

BCDE given to find AD the Gde of the Cone belonging to it.

Multiply DE by BD, and divide the product by DEBC, the Quotient is AD

. fought,

Example
Multiply DE = 6

by BD = 12

which divide 72
by DE - BC = 3

-
the Quotient is AD = 24-

PROBLFM XVIII

To find the Superficial Content of die Segment of a Sphere.

RULE.

Multiply the Heighth by the Circumference of the Sphere, to which product add the Area of its Circular Bafe, and that Sum is the Area fought.

Prob. 19. To Measure a Cube.

RULE

Cube the Side: That is, multiply the fide of the Cube by it felf, and that product again by the fide of the Cube, which Cube number is the Solid Content thereof.

Example.

Fig. 81. Let ABCDEFG reprefent a Cube; whofe Side let be 30 Inches; I de anand the Content.

By the Line of Numbers.

Extend the Compaffes, from 1, to 30, the fame extent will reach from 30 to 900, and from thence to 27000, the Content.

Prob. 20. To Measure a Parallelopipedon

RULE.

which

Multiply the Length by the Breadth and the product by the Depth ; gives you the Solid Content,

Example.

Fig. 82. Let ABCDEFG, represent a Parallelopipedon; whofe length AB is 40 Inches, the breadth BC= 30 Inches, and Depth CD = 15; what's the Content Length 40 Breadth = 30

1200

Depth 15

6000

18000 Content.

Brob..21%

Prob. 21. To Measure a Globe or Sphere.

To find the Solid Content, there are feveral ways. As firft multiply the Cube of the Diameter by 11, and divide the product by 21, the Quotient is the Solid Content,

2. Or multiply the Diameter, by part of the Globes Superficies, the product is the Solid Content: Or one fixth part of the Diameter multiplyed by the Spheres Superficies gives the fame..

3. Otherways, Multiply the Area of the Circle, whofe Diameter is equal to the Globes Diameter by of the Diameter, the product is the Solid Content: Or, Multiply the Diameter by of the Circles Area, produces the fame.

Prob. 22. To find the Solid Content of a Cone

RULE.

By 9 Prob. foregoing, find out the Area of its Bafe, and multiply that by of its heighth, and that product is the Solid Content of the Cone required.

Example.

There is a Cone, the Circumference of whofe Bafe is 22.5; and its heighth is 16.

Is to

I demand the Solid content of such a Cone. As 22.

7. So is 22. 5 thé Circumference of the Base. To 7.16 the Diameter of the Base:

Then multiply 22. 5, which is 11. 25, by 7.16 2which is 3.58, and it produceth 40.286, which is the Superficial Content of the Basé. Again, multiply 4. 286, by so 333, which is of the Heighth of the Cone, and it produceth 214. 84657.1 the Solid Content.

But here you are to observe that the Naneing. side of the Code is not to be taken for its true height, but a Perpendicular let fall from its Vertex, to its Base is its true heighth; and the fame is to be observ'd in the Pyramid.

Prob. 23. To find the Solid Content of a

Pyramid. Between the Cone and Pyramid, this is the Difference. As the Cone hath a Circular Base, the Pyramid hath a right-lined Figure for its Base, so that its Base and Superficies are Angular, its. Vertex terminating in a Point.