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Origin of measures of length, of surface, of capacity and

} 135

of solidity,
Origin of weights, and the balance,

136

Denominations of coin,

Division of time,

Calculations in simple and compound numbers compared,

THE FRENCH MONEY, WEIGHTS AND MEASURES,

British do.

139

New York & Connecticut do.

140

Promiscuous Examples,

RULE OF THREE by Analysis,

142

FRACTIONS,-general principles,

To reduce them to their lowest terms,

144

Prime numbers—measures to determine the measures

145

of a number,

To find common measures-a greatest com. meas.

146

To find a com. denominator,

148

Multiples--a least com. mult.,

149

To find a least com. den.,

151

Addition,

153

Multiplication,-a Fraction by a whole number,

154

A whole number by a Fraction,

156

PRACTICE,

To multiply a Fraction by a Fraction,

157

Compound Fractions,

158

FELLOWSHIP,-simple and compound, by analysis and ratio, 159–61

Subtraction,

162

Division,-a Fraction by a Fraction,

163

A whole number by a Fraction,

164

A Fraction by a whole number,

166

To reduce whole numbers to Fractions of higher denominations, 167

fractions to do.

168

fractions to do. of lower denom.

169

fractions to whole nnmbers of lower denom.

170

DECIMALS,-general principles,

To reduce Vulgar Fractions to Decimals,

174

REPETENDS, OR CIRCULATING DECIMALS,

175 & 78

To reduce whole numbers to decimals of bigher denominations, 176

Approximates,

Contraction for Sterling Money,

177

Addition,

178

Multiplication,

179

Contraction in Multiplication,

181

To reduce decimals to whole numbers, of lower denom., 182

Contraction for Sterling Money,

183

Subtraction,

Division, -

184

Contraction in Division,

186

Another mode of reducing whole numbers to decimals of

. 187

higher denom.,

Theory of circulates,

188

Arithmetical operations upon them,

193

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ERRATA.
In printing a work. on a scientific subject, entirely from manu.
script, perfect accuracy is not to be expected. Accordingly, some
errors will undoubtedly he discovered in this book; but it is believed
that the following are all, which will be likely to occasion perplexi-
ty. Page 60. Ans. ex. 10, for 328, read 378.-p. 71, in ex. 4, for 4
men read 1 man. p. 151, line 13, for 9 read 6mline 15, for multiplier,
read multiple.- p. 229, in ex. 5, insert at 5 per cent.---p. 236, ex. 2,
Ans. should be $446,985—-p. 237. Ans. by Mass. method should
be $11,370.47175.-p. 244, ex. 43, for 65, read 650. p. 249, line
6, for miles, read hours.p. 250 1. 30, for 3, read 315.-p. 284, in
Ans. to ex. 1, for ì 7 5 read ..

In a small part of the impression, p. 82. 3d line in ex. 87, for 65
“read 75.—p. 261, line 3, for products, read quotients.-p. 283, line
38, for 3 read 7, three times.

In & Lxxxix, the rule called the Massachusetts rule is erroneously
stated to have been established by law in that state. It has been
made the rule of the state of New York, by the decision of Chancel.
lor Kent. The statement was made on the authority of a number
of writers. For this correction, as well as for other important
suggestions, the author is indebted to Professor Dewey, now Prin-
cipal of the BERKSHIRE GYMNASIUM.

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How many anchors do you see here? Ans. ONE. How many ropes are there, fastened to the anchor ?

Now there is a single anchor, and a single rope ; and each of these single things, you tell me, is ONE.

Then, what is a single thing called? Hence,

A SINGLE THING OF ANY KIND IS CALLED ONE THING, OR ONE. Also A SINGLE THING OF ANY KIND IS OFTEN CALLED A UNIT, OR UNITY.

Thus, the anchor in the picture above is a unit.

If there were another anchor in the picture, how many anchors would there be ?

Ans. TWO. How many

sheaves of wheat are there here?

How many hands have you? How many thumbs? How many eyes? How many feet?

When you see one thing, and one more together, what do you

call them ? Hence, ONE UNIT AND ONE MORE ARE CALLED TWO; that is, ONE AND ONE

ARE TWO.

If there were one more sheaf in the last picture, how many sheaves would there be ?

Ans. THREE. How many pairs of snuffers are there here?

If you had another hand, how many hands would you have? If you had another eye, how many eyes would you have? When you see two things and one more together, what do you call them? Hence,

TWO UNITS AND ONE MORE ARE CALLED THREE ; that is, TWO AND

ONE ARE THREE.

If there were another pair of snuffers in the last picture, how many would there be ? Ans. FOUR.

How many hammers are there here?

TTTT

If you count your hands and feet together, how many have you?

When you see three things and one more together, what do you call them? Hence,

THREE UNITS AND ONE MORE ARE CALLED FOUR; that is, THREE

AND ONE ARE FOUR.

If there were another hammer in the last picture, how many would there be ?

Ans. FIVE.

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