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Value of an Annuity for ever, at Compound Interest.

Value of an Annuity in Reversion, at Compound Interest
Single Position

Double do.

Permutation, Combination and Composition of Quantities
Miscellaneous Questions

LOGARITHMS

LOGARITHMS.

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EXPLANATION OF CHARACTERS.

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SIGN

IGNIFIES equality as 20 shillings I pound, signifies, that 20 shillings are equal to one pound.

Signifies plus, or addition : as, 4+2 = 6.

Signifies minus, or subtraction: as, 6—2—4.

X Into, signifies multiplication: as, 3 X 2 = 6.

By, or ) ( signifies division: as, 623, or 2)6(3.

Division may alfo be denoted by placing the dividend. over a line, and the divisor under it: thus6+2=3.

::

Signifies arithmetical proportion: thus 24:: 68; here the meaning is, that 4-2=8—6—2.

: Signifies geometrical proportion thus 2:4::3:6, which is to be read, as 2 to 4, so is 3 to 6.

Signifies arithmetical progression.

Signifies continual geometrical proportion, or geometrical progression.

.. Signifies therefore.

- Signifies the second power, or square.

3Signifies the third power, or cube.

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Signifies any rest of any power.

NOTE. The number, or letter, belonging to the above signs of powers and roots, is called the index, or exponent.

A line, or vinculum, drawn over several numbers, signifies, that the numbers under it are to be considered jointly thus, 20—7+8=5; but without the vincu lum, 20-7+8=21.

aba Xb the product of a and b.

ARITHMETIC.

ARITHMETIC is the art of computing by numbers,

and has five principal or fundamental rules for its operations; viz. Notation, Addition, Subtraction, Multiplication, and Division.

ΝΟΤΑΤΙΟΝ. *

Notation teacheth how to express any proposed number, either by words or characters.

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* As it is absolutely necessary to have a perfect knowledge of our excellent method of notation, in order to understand the reasoning made use of in the following notes, I shall endeavour to explain it in as clear and concise a manner as possible.

First, then, it may be observed, that the characters, by which all numbers are expressed, are these ten; 0, 1, 2, 3, 4, 5, 6, 7, 8,9; o is called a cypher, and the rest, or rather all of them, are called figures or digits. The names and signification of these characters, and the origin or generation of the numbers they stand for, are as follow: o nothing; I one, or a single thing called an unit; 1+1=2 two; 2+1=3 three; 3+1=4 four; 4+1=5 five; 5+16 six; 6+1=7 feven; 7+18 eight; 8+1=9 Dine ; and 9+1ten; which has no single character; and thus by the continual addition of one, all numbers are generated.

2. Beside

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