Subtraction of Repeating Decimals Multiplication of Repeating Decimals..................................... HEATH'S TREATISE ON ARITHMETIC. BOOK I. PRELIMINARY IDEAS-DEFINITIONS AND FORMATION OF NUMBERS- NUMERATION, ADDITION, SUBTRACTION, MULTIPLICATION, AND DIVISION OF WHOLE NUMBERS. SECTION I. Preliminary Ideas, Definitions, and Formation of Numbers. 1. A limited portion of any natural object; as of time, space, weight, heat, &c., or of any substance, fluid, solid, or æriform, is called quantity. 2. The object of all mathematical science is to measure quantity. 3. Quantity can only be measured by comparing it with some known quantity of the same kind acknowledged as a standard. 4. Standard Measures, to prevent error or variableness, are generally derived from nature. For example, measures of time, from the time of the revolution of the earth about its axis of space, from the length of a barley-corn, taken from the middle of a full-grown ear; also, from the circumference of the earth: of weight, from the weight of a grain of wheat, taken as above; also, from the weight of a definite quantity of distilled water: of heat, from the temperature of boiling water, &c. 5. Quantity, mathematically considered, is only susceptible of increase and diminution; these are, therefore, called the attributes of quantity. 6. A quantity may be increased in two ways: either by 11 |