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factor on A, if it happen that the other factor on B fall beyond the divifion, on either A or в, divide it by 10, or 100, &c, till the quotient found on в fall under fome divifion on the line A, and multiply this faid divifion by the fame 10, or 100, &c, for the product required.

EXAMPLE II. So when 250 is to be multiplied by 56 Having fet 1 on в to 250 on A, although 56 be found on в, it is beyond the end of A; therefore dividing it by 10, I find that oppofite to the quotient 5.6 on в, is the divifion 1400 on A; which being multiplied by 10, we obtain 14000 for the product required.

EXAMPLE III. But if 250 were to be multiplied by 1120: Having fet 1 to 250 as before, 1120 is beyond the end of B, but being divided by 100, oppofite to the quotient 11.2 on в I find 2800 on A, which being multiplied by 100, we have 280000 for the product required.

PROBLEM II.

To find the Quotient of Two Numbers.

RULE. Set I on в to the divifor on A, then against the dividend on A, is the quotient on B. EXAMPLE I. To divide 300 by 25. Having fet I on в to 25 on A, oppofite 300 on A I find 12 on B, the quotient required.

NOTE. When the dividend falls beyond the erd of the line A, let it be divided by 10, 100, or fome other power of 10 till it fall within the line, and ufe the quotient instead of it, multiplying the refult by the fame power of 10 as before.

EXAMPLE II. So if 14000 must be divided by 56. Having fet 1 to 56, the dividend cannot be found on A till it be divided by 100, the quotient being 140, oppofite to which I find 25 on B, which being

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multiplied by 100 we obtain 250 for the quotient required.

PROBLEM III.

To work the Rule-of-Three on the Sliding Rule: or baving Three Numbers given, to find a Fourth, which fhall be to the Third as the Second is to the Firft.

RULE. Set the first term on B, to either the second or third on A; then against the remaining term on B, ftands the fourth term required on A.

EXAMPLE. If 8 yards of cloth coft 24 fhillings, what will 96 yards coft at the fame rate?

Having fet 8 on в to 24 on A, opposite 96 on B, I find, on A, 288 fhillings, or 141 8s, which is the answer.

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To Extract the Square Root by the Sliding Rule.

RULE. The first 1 on c ftanding against the first on D, on the stock, oppofite the given number on c is its root on D.

EXAMPLE. To find the fide of a fquare, which fhall be equal to a triangle, or circle, &c, whofe area is 225; or, to extract the root of 225.

Here oppofite 225 on c ftands 15 on D, which is the anfwer required.

PROBLEM V.

To Extract the Cube Root by the Sliding Rule.

RULE. The line D upon the flide being fet ftraight with E; find the given number on E, and oppofite to it will be its cube root on D.

EXAMPLE. To find the fide of a cube equal to any other folid whofe content is 3375; or to find the cube root of 3375.

Here oppofite 3375 on E, ftands 15 on D, which is the anfwer required.

NOTE. It is evident that the fame lines, as are ufed in these two laft problems, will ferve to find the fquare or the cube of any given number, by taking the given number on the contrary lines.

PROBLEM VI.

To find a Mean Proportional between
Two Given Numbers.

RULE. Set one of the given numbers on c to the like or fame number on D, then against the other given number on c, is the number required on D.

EXAMPLE. To find the fide of a fquare whose area fhall be equal to that of a parallelogram whose length is 9, and its breadth 4 feet; or, to find a mean proportional between 4 and

9.

Having fet 4 on c to 4 on D, against 9 on c ftands 6 on D, which is the number fought.

PROBLEM VII.

To find a Number which shall be to a Given Number, in a given Duplicate Proportion; or baving given Three Numbers, to find a Fourth, which fall

RULE.

be to the Third, as the Square of the
Second is to the Square of the First.

Set the third number on c to the first on

D, then against the fecond on p, will be found, on c,

the fourth required,

EXAMPLE. If the area of a parallelogram, or any other figure, be 120; it is required to find the area of a fimilar figure, their like dimensions or fides being as 2 to 3.

Similar figures being as the fquares of their like dimenfions, by fetting 120 on c to 2 on D, against 3 on D, stands 270 on c, for the number fought.

PROBLEM VIII.

To find a Number which shall be to a Given Number, in a given Subduplicate Proportion; or having given Three Numbers, to find a Fourth, which shall be to the Third, as the Root of the Second is to

the Root of the First.

RULE. Set the first number on c to the third on D, then against the fecond on c, will be found the fourth on D.

EXAMPLE. The fide of a regular figure is 2, and its area 120; it is required to find the fide of a fimilar figure whofe area is 270.

The roots of the areas of fimilar figures being as their fides, we muft find a number which fhall be to 2, as the root of 270, is to the root of 120. Therefore, having fet 120 on c to 2 on D, against 270 on c, will be found 3 on D, which is the number fought.

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To find a Number in a given Triplicate Proportion to a
Number given; or, having Three Numbers given,
to find a Fourth, which shall be to the
Third, as the Cube of the Second,

is to the Cube of the First.

RULE. Set the first number on the flide D, to the

third number on E, then against the fecond on D, is the fourth required on E.

EXAMPLE. If a cafk, whofe length is 40 inches, contain 100 gallons, what will be the content of a fimilar cafk whofe length is 36 inches?.

Similar folids being as the cubes of their like fides, the content required must be to 100 gallons, as 363 is to 403. Therefore fetting 40 on D to 100 on E, against 36 on D, will be found 72°9 gallons on E, which is the content required.

PROBLEM X.

To find a Number in a given Subtriplicate Proportion to a
Given Number; or, having Three Numbers given, to
find a Fourth, which shall be to the Third, as
the Cube Root of the Second, is to
the Cube Root of the First.

RULE. Set the third number on D, to the first on
E, then against the second on E, will ftand the fourth

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EXAMPLE. What is the length of a cafk whose content is 729 gallons, fuppofing the length of a fimilar cafk to be 40 inches, and its content 100 gallons?

Since the dimenfions of fimilar folids are as the cube roots of their contents, we muft find a number which fhall be to 4b, as the cube root of 72'9 is to the cube root of 100. Therefore, having fet 40 on D to 100 on E, against 72.9 on E, will be found 36 on D, which is the length required.

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