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INTH DJCT ON,-a brief survey of the science of Mathematics,

13

Different methods of proving Subtraction,

Subtracting numbers expressed by the Roman Notation,

GENERAL RULE for Multiplication,

Different methods of proving Multiplication,

Contractions in Multiplication, six methods,

44

44

47

SECTION IV.

Method of finding the prime numbers in any series,

89

93

Table of prime numbers from 1 to 3413.

Numbers changed from the decimal to other scales of Notation,

94

95

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Division of Fractions, common method,

Division of Fractions by Cancelation,

Contractions in Division of Fractions, three methods,

Complex Fractions reduced to Simple ones,

133

136

138

139

SECTION VIII.

COMPOUND NUMBERS,

144

Tables of Compound Numbers,

144

The Standard for Gold and Silver Coin of the United States,

The Standard UNIT of Weight of the United States,

145

147

Origin of Weights and Measures,

147

The Avoirdupois Pound of the United States and Great Britain,

The Standard UNIT of Length of the United States,

148

150

66

of New York and Great Britain,

The Standard UNIT of Liquid Measure of the United States,
of Dry Measure of the United States,
Method of determining whether a given year is Leap Year,
French Money, Weights and Measures,

Foreign Weights and Measures, compared with United States,
GENERAL RULE for Reduction,

Cubic Measure reduced to Dry, or Liquid Measure, &c.,

Compound Numbers reduced to Fractions,

To find the cost of articles bought and sold by the 100 or 1000,

238

Commission deducted in advance, and the balance invested,

247

INTEREST,

249

General method for computing Interest,

252

Second method, multiplying the Prin. by the Int. of $1 for the time,

255

To compute Interest by half the number of months,

257

To compute Interest by the number of days,

258

Applications of Interest, remarks on Promissory Notes, &c.,

258

To find what sum must be discounted to produce a given amount,

Insurance, four Cases,

277

278

The sum to be insured to recover the premium and the property,

282

To find what sum must be assessed to raise a given net amount,

295

INTRODUCTION.

ART. 1. Anything which can be multiplied, divided, or measured, is called QUANTITY. Thus, lines, weight, time, number, &c., are quantities.

OBS. 1. A line is a quantity, because it can be measured in feet and inches; weight can be measured in pounds and ounces; time, in hours and minutes; numbers can be multiplied, divided, &c.

2. Color, and the operations of the mind, as love, hatred, desire, choice, &c., cannot be multiplied, divided, or measured, and therefore cannot properly be called quantities.

2. MATHEMATICS is the science of Quantity.

3. The fundamental branches of Mathematics are, Arithmetic, Algebra, and Geometry.

4. Arithmetic is the science of Numbers.

5. Algebra is a general method of solving problems, and of investigating the relations of quantities by means of letters and signs.

Oвs. Fluxions, or the Differential and Integral Calculus, may be considered as belonging to the higher branches of Algebra.

6. Geometry is that branch of Mathematics which treats of Magnitude.

7. The term magnitude signifies that which is extended, or which has one or more of the three dimensions, length, breadth, and thickness, Thus, lines, surfaces, and solids are magnitudes.

QUEST.-1. What is Quantity? Give some examples of quantity. O. Why is a line a quantity? Weight? Time? Numbers ? Are color and the operations of the mind quantities? Why not? 2. What is Mathematics? 3. What are the fundamental branches of mathematics? 4. What is Arithmetic? 5. Algebra ? 6. Geometry 1 1. What is meant by magnitude?