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bere given them, as printed in a Table of Contents pre-
Chap. 1. Of Contractions in the Rule of Three.
Chap. 3. Of Exchanges of Coins, Weights, and
Chap. 4. Practical Questions about Tare, Tret, Loss,
Chap. 5. Of Interest of Money, and the Construc-
Chap. 6. A Demonstration of the Rule of Three.
Chap. 7. A Demonstration of the Double Rule of
Chap. 8. A Demonstration of the Rule of Alligation :
Chap. 9. A Demonstration of the Rule of False.
Chap. 10. A Collection of choice Questions to exer-
Chap. 11. Sports and Pastimes.
The Work, thus enlarged and amended, passed through
Such was the State of this Work when it came into the
1. All the different Materials relating to any one Sub-
other in the different Parts of the Work, the Appendix,
2. Many useful Properties of Numbers, praftical Ob-
vered, will give but few Answers to Questions propounded
ġ. The Properties of Numbers considered as Roots and
Tbus altered and enlarged, the Editor conceives that
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.
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 bc 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 Division; 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 nu
merical 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
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. For 4; read, if 12 be divided by 3, the Quotient is 3
equal to 4. For 1:4:: 3: 12; read, as I is to 4, fo is 3 to 12.
TRE A TI SE
c H A P. B.
RITHMETIC teaches the properties of
thods of calculating, or computing from A certain data, the values, weights, measures,
distances, proportions, &c. of things.
2. Number is that by which every thing
is counted ; or that which answers this question, How many? (unless it be answer'd by nothing :) So if it be asked, how many days are in a week? the answer is feven, 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 fixy 7 leven, 8 eight, 9 nine, o nothing.