here given them, as printed in a Table of Contents pre-
fixed thereto.

Chap. 1. Of Contractions in the Rule of Three.
Chap. 2. Of Rules of Practice by Aliquot Parts.
Chap. 3. Of Exchanges of Coins, Weights, and

Measures.

Chap. 4. Practical Questions about Tare, Tret, Lofs,

Gain, Barter, Factorship, and measuring of Tapestry.

Chap. 5. Of Interest of Money, and the Conftruc-

tion of Tables to value Annuities, &c.

Chap. 6. A Demonstration of the Rule of Three.

Chap. 7. A Demonftration of the Double Rule of

Fellowship.

Chap. 8. A Demonstration of the Rule of Alligation :

Where alfo of the Compofition of Medicines.

Chap. 9. A Demonstration of the Rule of False.

Chap. 10. A Collection of choice Questions to exer-

cise all the Parts of Vulgar Arithmetic; to which are

added various Practical Questions, about the Menfura-

tion of Superficial Figures and Solids, with the Gauging

of Veffels.

Chap. 11. Sports and Pastimes.

The Work, thus enlarged and amended, passed througb

divers Editions, till about the Year 1700, when Mr.

George Shelley, Writing-Master of Chrift's-Hospital,

wrote a Supplement to it, containing divers practical,

compendious, and easy Methods for the Performance of

particular Cafes in most of the Rules of Arithmetic; to-

gether with Decimal Tables useful in the Computation of

Interest and Exchanges, and some useful Rules and Ob-

fervations relating to Practical Measuring.

Such was the State of this Work when it came into the

present Editor's Hands, under whose Care it has met with

the following Alterations and Additions :

1. All the different Materials relating to any one Sub-

ject, which in the former Editions lay separated from each

other

other in the different Parts of the Work, the Appendix,

and the Supplement, are here collected together into their

proper Places; so far as the same could be done confiftent-

ly with the keeping the Doctrine of whole Numbers sepa-

rate from that of Fractions, before-mentioned by Mr.

Kersey.

2. Many useful Properties of Numbers, practical Ob-

Jervations, and Compendiums in Operations (not men-

tioned in the former Editions) are bere inserted in their

proper Places.

3. The Demonstrations given by Mr. Kerfey, which

were founded on Geometrical and Algebraical Principles,

are fupplied by others purely Arithmetical.

4. The Properties of Numbers confidered as Prime and

Composite are delivered, as a necessary Help to the Ma-

nagement of Fractions.

5. The Operations of Vulgar Fractions are rendred

much easier, by an Artifice in the Management and Ab-

breviation of them.

6. The Doctrine of Repeating or Circulating Decimals

is introduced, and the Management of them, in a more

general and easy Manner than hitherto taught, is scien-

tifically explained.

7. An universal Rule of Proportion, which answers

the Purpose of the several Rules of Three, single, double,

direct or inverse, in whole Numbers or Fractions, is de-

livered and illustrated by many Examples; in which the

great Usefulness of the above-mentioned Method of manag-

ing and abbreviating Vulgar Fractions, will abundantly

appear.

8. The Rule of Alligation Alternate, as hitherto deli-

vered, will give but few Answers to Questions propounded
therein, most of which are capable of many, and some of
innumerable Answers: To remedy this Defect, a Method
is laid down to find more Answers than the common Rules
will give, in those Cases which admit of more; and as
many Answers as the Computer pleases, in those Cafes
where the Number of Answers is unlimited.

9. The Properties of Numbers confidered as Roots and

Powers, and the Nature and Properties of Logarithms

are compendiously explained.

10. A more practical Method of extracting the Cube-

Root is inferted, instead of that delivered by Mr. Kersey;

to which is annexed a Table of the Square and Cube-

Roots of all Integers less than 145.

11. The Properties of Numbers in Arithmetical Pro-

portion continued, are more fully explained and illustrated.

12. The Properties of Numbers in Geometrical Pro-

gression are also more particularly bandled, with a View to

the Application of fuch Numbers, to the Computations

relating to Compound Interest.

13. Mr. Shelley's Tables of Simple Interest are brought

into a narrower Compass, and adapted to those Rates

which are now commonly wanted.

14. The Tables for Compound Interest and Annuities,

are enlarged from 30 to 60 Years, and computed to the

Same Rates as those of Simple Interest, the manner of

making and using them is more particularly shewn; easy

Methods are given to find Numbers beyond the Extent of

the Tables; and some new Tables are added, relating to

Half-yearly and Quarterly Payments.

15. A great Variety of Examples, with their Answers,

are inserted; which will not only be a good Exercise for

Learners, but will also serve to ease Teachers of the Bur-

then of writing out Questions.

16. A copious Index is annexed, to which the Reader

may turn for more particular Information of the Contents

of the whole.

Thus altered and enlarged, the Editor conceives that
this Work contains, methodically, all that is necessary to be
known, or performed in Common Arithmetic; and by con-
Sequence, that the Purchasers hereof need not be at the
Trouble, or Charge of looking into any other of the, almost,
numberless Writers on that Subject.

If the above Improvement in the Operations of the Rule of Alligation Alternate, should prove of Service in real Bufiness; the Knowledge thereof may induce the Editor to publish some farther Thoughts upon that Subject.

Bell-Dock, Wapping,
April 4th, 1751.

The Explanation of certain Marks and Characters, which, for the Sake of Brevity and Perfpicuity, are frequently used in the ensuing Work.

+ is the Mark of Addition; and, when it stands between two Numbers, denotes that they are to be added together. is the Mark of Subtraction; and, when it stands between two Numbers, denotes that the latter is to be taken from the former.

X is the Mark of Multiplication; and, when it stands between two Numbers, it denotes that they are to be multiplied together.

is the Mark of Divifion; and, when two Numbers are placed in the same manner as the two Points are here, it denotes that the Number above is to be divided by that below.

= is the Mark of Equality; which, being set between two numerical Expressions, denotes that they are equal between themselves.

:::: are the Marks of Proportionality; and denote that the Numbers, between which they are placed, are proportional Numbers.

EXAMPLES.

For 4+3=7; read, the sum of 4 and 3 is equal to 7.
For 4-3=1; read, when three is taken from 4, the Re-

mainder is equal to 1.

For 4X3=12; read, the Product of 4 and 3 is equal to 12.

= 4; read, if 12 be divided by 3, the Quotient is

equal to 4.

For 1:4::3: 12; read, as I is to 4, so is 3 to 12.

A

TREATISE

OF

Common Arithmetic.

I.

CHAP. I.

Concerning NOTATION of Numbers.

A

RITHMETIC teaches the properties of Numbers; and by them deduces the methods of calculating, or computing from certain data, the values, weights, measures, diftances, proportions, &c. of things.

2. Number is that by which every thing is counted; or that which anfwers this question, How many? (unless it be answer'd by nothing :) So if it be afked, how many days are in a week? the answer is seven, which is therefore called the Number of days in a week.

3. The Notes or Characters, by which Number is ordinarily expressed, are these, I one, 2 two, 3 three, 4 four, 5 five, 6 fix, 7 seven, 8 eight, 9 nine, o nothing.