If an iron ball 2 inches diameter weighs. 3 lb. what will a brafs ball weigh, that is 4 inches radius ?

As 2 X 2X2: 3 :: 8x8x8 :: 192 lb. of iron. ... 8 9: 192 216lb. anf.

5th. Having the lengths of the principal parts of a fhip of a given tonage, to find the lengths of the like parts of another, either greater or less.

RULE. ULE. As the tonage the cube of the length of any part any other tonage: the cube of the length of a fimilar part.

If a fhip of 300 tons have a keel 78 feet long, beam 25 feet, ftem 20 feet, ftern-poft, 24, required the length of the keel, beam, ftem, and ftern-poft of one double that burden?

To extract the biquadrate root, is to find fuch a number, which, when involved four times into itself, will produce the given number.

RULE.

UL E. First extract the fquare root of the given number, and then the fquare root, of that root, is the biquadrate root fought.

A General Rule for Extracting the Roots of all Powers.

1. Prepare the propofed number, by pointing off from the units place, as the root required directs.

2d. Find the first figure in the root by the table of powers, or otherwise by trial, which fubtract from the given number.

3d. Bring down the first figure in the next point, to the remainder, and call it the dividend.

4th. Involve the root, to the next inferior power to that required, which multiply by the propofed power, and call it the divisor.

5th. Find a quotient figure by common divifion, and annex it to the root, then involve the whole root to the propofed power, for a fubtrahend.

6th. Subtract that number, from as many points of the given power as is brought down, beginning at the loweft place, and to the remainder bring down the first figure of the next point, for a new dividend.

7th. Find a new divifor and proceed in all refpects as before directed, and thus you will obtain the root of any power propofed.

Required

Required the firft furfolid root of 293162530524? 29316250524 (124 anf.

1x5=5) 19

248832 12 X 12 X 12 X 12 X 12

IX I XIX 1 X 5 = 5, 1ft. Divisor. 12 X 12 X 12 X 12 X 5 = 103680, 2d. Divisor.

Multiplication of Mixed quantities.

Cafe ft. To multiply a whole number by a fraction,

R

ULE. Multiply by the upper number and divide by the lower, if the upper number be one divide by the lower only.

Cafe d To multiply a whole number by a mixed number.

RULE. Multiply by the friction per cafe ift. then multiply by the whole number, and and the two products as in the examples.

M

Multiply

Cafe. 3d. To multiply a fraction by a whole

number.

RULE. The fame as in cafe aft. inverting the

order as under.

Cafe 4th. To multiply a mixed number by a whole number.

RULE. Change the place of the factors and work per cale zd.

Cafe 5th. To multiply a mixed number by a mixed number

RULE

RULE. Multiply the integral part of the multiplicand by the lower number of the fractional part, and add thereto the upper number; then multiply by the mixed multiplier per cafe 2d. and divide the product by the lower number of the fractional part of the multiplicand, as in the following example.

Multiplication of Feet and Inches, called Cross Multiplication.

ULE S. Feet multiplied feet produce feet.

R Fect multiplied inches, or inches multiplied feet,

I

are inches and thereof is feet, and the remainder inches.

ΤΣ

1

Inches multiplied inches produce parts, of which

is inches &c.

ΤΖ

Cafe ft. When the feet in the factors are 12 or under, multiply first by the feet; and then by the inches, and place as the rules above direct, which add for answer.