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ARITHMETIC is the art or science of computing by numbers, either whole or fractional, and is generally divided into five parts, viz. Numeration, Addition, Subtraction, Multiplication and Division.
NUMERATION Is the art of expressing numbers, characters, or figures, and teaches to read and write them by their true value. Thus, one 1, two %, three 3, four 4, five 5, six 6, seven 7, eight 8, nine 9, nought or cipher 0; and this is the reading and writing of figures.
These nine figures or digits are divided into three periods, three in each period. The first period are units, tens, and hundreds; the second period are thousands, tens of thousands, hundreds of thousands; and the third period are millions, tens of millions, hundreds of millions.
Besides the simple value of figures, each has a local value, which depends upon the place it stands in, viz. any Agure in the place of units, only represents its simple value, or so wany oires; but in the second place, it becomes so many tens, or ten times its simple value; and in the third place, it becomes an hundred times its simple value. The three periods of the nine digits are as follows, viz. Hundreds , Hundreds ?
Hundreds. of millions of thousands. S
987 6 5 4 3 2 1 The nine digits are sufficient to express most ordinary
A cipher by itself counts nothing, but placed after a figure, makes that figure ten times greater than it was before the cipher was put to it, as 1 reads one, but 1 and a 0, (cipher,) reads ten; and a cipher put to the right hand of 10, makes that ten 100, one hundred, &c. And placed after 2 makes 20, twenty, and after 20 it makes 200, two hundred, &c. But placed before a figure, will lessen the value of that figure in the same ratio as it increased the other in deci. mals; but before a whole number, it neither increases nor decreases its value, unless an integer or digit be placed on the left of the cipher, as 7 is seven, or 07 is seven, and 207 iş two hundred and seven.
To learn this table, find your multiplier in the column head, 2, 3, 4, 5, &c. and say, twice 1 is 2, twice 2 is 4, twice 3 is 6, &c. which you will see in the right-hand column.
This mode of teaching the multiplication table, is the easiest, and I presume the best, as it does not discourage the pupil to commit it to memory, as it does when in a square. It is here divided into small tasks, which appears rather a delight to the pupil, than a burden. I always adopt this plan for my pupils, and find the good effects of'it.
The teacher should cause bis pupils to have a perfect idea of the numeration and this table, before he allows them to begin figures.
Numeration or Notation.
24 Grains make
1 Pennyweight 20 Peony weights
1 Ounce. 12 Ounces
i Pound. NOTE. By these denominations are weighed gold, silver and jewels.
16 Drams make
1 Ounce, 16 Ounces
1 Pound. 28 Pounds
1 Quarter. 4 Quarters
1 Hundred weight 20 Hundred weight
1 Ton. NOTE. By this weight are weighed all coarse, heavy goods, such as iron, steel, and groceries.
20 Grains make
1 Scruple. 3 Scroples
1 Dram. 8 Drams
* Nails make
1 Quarter of a yard.
DRY MEASURE. 2 Pints make
1 Quart. 8 Duarts
1 Peçk. 4 Pecks
1 Bushel. Note. This measure is applied to grain, potatoes, apples, peaches, saling and coals, and many other articles.
LIQUID MEASURE. 4 Gills make
1 Pint. 2 Pints
i Quart. 4 Quarts
1 Gällan. 314 Gallons
1 Barrel. 42 Gallons
1 Tierce. 63 Gallons
1 Hogshead. 2 Hogsheads
1 Pipe. 2 Pipes
1 Tuo. NOTE, All liquors are measured by this measure, as also oil, vinegar, &c 231 solid inches make a gallon.
LONG MEASURE. 3 Barley Corns make
1 Inch, 12 Inches
i Foot. 3 Feet
1 Yard, 5} Yards
1 Rod. 40 Rods
1 Furlong. 8 Furlongs
1 Mile. 3 Miles
1 League. 694 Stative or 60 Geographical Miles
1 Degree on the earth. 360 Degrees the circumference of the earth. NOTE. This table is tised in measuring distances of places, or any thing else, where length is considered, without regard to breadth. A pole and perch is not always of the same length, for the statute measure of a pole or perch is 55 yards. But measuring fens and woodlands, it is customary to reckon 18 feet, and for forests 21 feet to the pole or perch. ln measuring the height of horses, 4 inches make 1 band." In measuring depths at sea, or rivers, by the fathom of 6 feet. Distances of roads, &e. is measured by a chain 4 poles long, each pole 25 links, the whole chain containing 100 links.
LAND OR SQUARE MEASURE. 144 Square Inches make 1 Square Foote 9 Square Feet
1 Square Yard. 304 Square Yards
i Square Rod. 40 Square Rols
1 Square Rood. 4 Square Foods
1 Square Acre. 640 Square Acres
1 Square Mile.
SOLID QR CUBIC MEASURE,
1 Solid Foot.
1 Cord of wood. NOTE. All solids, or things that have tength, breadth and depth, are measured by this measure. The wine gallon contains 231 solid inches, the beer gallon 282 solid or cabic inches. A bushel contains 2150,42 solid inches
60 Seconds make
1 Minute 60 Minutes
1 Hour. 24 Hours
i Day. 7 Days
February twenty-eight alone, and all the rest thirty-one.
CIRCULAR MOTION. 60 Seconds make
1 Minute. 60 Minutes
Explanation of Characters used in this book. = Two parallel lines are the marks of equality; as, 100
cents = 1 dollar, or 16 ounces = 1 pound. + Cross signifies more, or Addition; as, 4+6=10, that is,
4 added to 6 make the sum 10. Straight line signifies less, or Subtraction; as, 10—4=6,
that is, 4 taken from 10 leave or equal 6. x Denotes Multiplication; as, 4X2=8, that is, multiplied
by 2 equal 8. • A line between two points is the sign of Division; as,
10=%=5, that is, 10 divided by 2 equal 5. ) ( The reverse parenthesis also denote Division. :: Four points, set in the middle of four numbers, denote
them to be in Proportion to one another, by the Rule of Three; as, 4:6::8:12, that is, as 4 is to 6, so
is 8 to 12.
root of that number is required. a Prefixed to any number, signifies that the cube root of
that number is required. I would strongly recommend the pupil to get all the foregoing tables by heart, before he begins the several branches to which they belong By so doing, he will receive a great benefit in his progress, and save his teacher much trouble.
By praetising the numeration table in different forms, to what is here laid down, the pupil will also be enabled to read and write the following with eases