Socius mercatoris: or The merchant's companion: in three parts. The first, being a plain and easie introduction to arithmetick, vulgur and decimal, the extraction of the square and cube roots, with a table of 200 square roots, and their use in the resolution of square equations. The second, a treatise of simple and compound interest and rebate, with two tables for the calculation of the value of leases or annuities, payable quarterly, the one for simple, the other compound interest, at 6 per cent. per annum, with rules for making the like for any other rate. The third, a new and exact way of measuring solids in the form of a prismoid and cylindroid, with the frustums of pyramids and of a cone: whereunto is added, some practical rules and examples for cask-gauging. By John Mayne, philo-accomptant.

REDUCTION.

TO reduce a vulgar Fraction into a decimal Fraction, your Rule is: Divide your Nu∣merator by your Denominator, and the Quotient will be a decimal Fraction of the same value with the vulgar Fraction. So ¼, if reduced into a decimal Fraction, will be .25.

Example.

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Here note, That only the even parts of an Integer will be exactly reduced into a decimal Fraction, as ½, 2/8, 2/16, &c. In all Surds, there will be some Remainder, but if you carry your decimal Fraction to four or five places, making the last one more than it is, if the sixth Figure be above 5, or else leave them out, and your Calculation will come near the truth; but if any desire to be more exact, he may take as many as he please.

Examples.

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To reduce any decimal Fraction out of a greater denomination into a lesser, multiply the Fraction by those parts of the Integer into which you would have it reduced; as .65 being the parts of a Pound, you would know how many Shillings are contained in the Fraction, multiply it by 20: If you desire the Pence therein contained, multiply it by 240; or if Farthings, multiply by 960, the number of Farthings in a Pound or 20 Shillings.

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The decimal parts of a Foot are reduced, by multiplying them by 12; if parts of a Foot Square, by 144; and the decimal parts of a Foot Solid, by 1728, the Cubick Inches in a Foot of Solid. The decimal parts of a Pound, are re∣duced by 16, the Ounces in a Pound Aver∣dupois; and 12, the Ounces in a Pound Troy. The decimal parts of a Beer Barrel by 36, and by 32 reduceth the parts of an Ale Barrel, into Gallons; and Gallons into Pints, by 8; Gallon•• into Cubick Inches, by 282; and for Win•• Gallons, by 231, the number of Cubick In∣ches in such a Gallon, &c.

As greater denominations are reduced to lesser, by a multiplication of the several part•• of the Integer; so lesser denominations ar••

reduced to greater, by division. Any number of Shillings are reduced into Pounds, and the decimal parts of a Pound, if you divide them by 20; and Pence, if divided by 240.

Example.

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Hours are reduced into the decimal parts of a Day, if you divide them by 24, the Hours in a Day Natural; and Minutes into the parts of an Hour, if divided by 60.

Perches are reduced into the decimal parts of an Acre, if you divide them by 160, the number of Square Poles or Perches in an Acre; and any number of Feet into Poles, and the decimal parts of a Pole, if you divide them by 16.5 the Feet in a Pole, or by 158.25 the number of Square Feet in a Square Pole; but if Wood-land Measure by 18, or if a Square Pole by 324, the Square Feet in a Pole or Perch of such Measure.

Any number of Inches are reduced into the parts of a Beer Barrel, if divided by 10152; and into Ale Barrels and parts, by 9024; &c.

For the ease of the Reader here is made a Table of English Coin reduced into the decimal parts of a Pound sterling.

A Table of Reduction of English Coin, the Integer being one Pound.

Shil∣lings.	Deci∣mals.		Pence.	Decimals of a Pound.
19	.95		11	.0458333
18	.9		10	.0416667>
17	.85		9	.0375
16	.8		8	.0333333<
15	.75		7	.0291667>
14	.7		6	.025
13	.65		5	.0208333
12	.6		4	.0166667>
11	.55		3	.0125
10	.5		2	.0083333<
9	.45		1	.0441667>
8	.4
7	.35
6	.3
5	.25		Far∣things.	Decimals of a Pound.
4	.2
3	.15		3	.003125
2	.1		2	.0020833
1	.05		1	.0010417>

The Vse of the Table.

Having any Quest. wherein Pounds, Shillings & Pence, are required to be under one denomi∣nation, viz. Pounds, and the parts of a Pound: First seek in the Column of Shillings for your Shillings, and set down the Fraction that stands against it; then in the Column of Pence, seek your Pence; in the Farthings, your Farthings; add all these together, and the Sum is the decimal Fraction desired.

Example.

What is the decimal Fraction for 17 s. 9 d. ¾?

First as the decimal parts of a Pound seek for 17 s. and the Fraction against it in the other Column is .85;

Which set down thus

.85

Then against 9 d. I find

.0375

And against 3 Farthings

.003125

Their Sum is

.890625

Which is the Number required, and is the decimal Fraction for 17 s. 9 d. ¾, as parts of a Pound.

Again, having a decimal Fraction in the parts of a Pound, and its desired to know the value thereof in lesser denominations: Let it be the Fraction before found, viz. .890625: I seek in the Table of Fractions for the neerest to it,

and find .85, and against it 17 s. I then set .85 down, and subduct it from the other, and there remains .040625; I look over the Table again, and find the next neerest is .0375, against it 9 d. I subduct that; and find the Remainder .003125, stand against 3 Farthings.

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So finding the value of any other decimal Fraction: If any thing remain after the last subduction, being less than a Farthing, I cast it away as of small regard.