# An elementary course of practical mathematics, Part 2

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### Contents

 DEFINITIONS AND EXPLANATIONS 1 ADDITION 5 SUBTRACTION 9 THE VINCULUM 10 MULTIPLICATION 12 Division 15 COMMON MEASURES 18 Common MULTIPLES 22
 EvoLUTION 36 PROPORTION 39 EQUATIONS 43 SIMPLE EQUATIONS 46 Questions PRODUCING SIMPLE EQUATIONS 56 QUADRATIC EQUATIONS 63 QUESTIONS PRODUCING QUADRATIC EQUATIONS 68 ARITHMETICAL PROGRESSIONS 71

 FRACTIONS 24 INVOLUTION 35
 GEOMETRICAL PROGRESSIONS 73 UNRESOLVED EXERCISES 76

### Popular passages

Page 36 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.
Page 24 - If it is desired to reduce a whole number to a fraction, multiply the whole number by the denominator of the given fraction, and write the result over the denominator.
Page 36 - THEOREM. lf the first has to the second the same ratio which the third has to the fourth, but the third to the fourth, a greater ratio than the fifth has to the sixth ; the first shall also have to the second a greater ratio than the fifth, has to the sixth.
Page 64 - Proportion, when the ratio is the same between every two adjacent terms, viz. when the first is to the second, as the second to the third, as the third to the fourth, as the fourth to the fifth, and so on, all in the same common ratio.
Page 19 - Divide the greater number by the less, the divisor by the remainder, and thus continue to divide the last divisor by the last remainder until there is no remainder ; the last divisor will be the greatest common divisor.
Page 36 - If the product of two quantities be equal to the product of two others, two of them may be made the extremes and the other two the means of a proportion.
Page 31 - Reduce the mixed numbers to improper fractions, and compound fractions to simple ones ; after this has been done, multiply all the numerators together for the numerator of the product, and all the denominators together for its denominator. Multiply 6| by | of |. Here the mixed number 6§ _ ,p and | of J = H 6* is converted into the " " improper fraction «, and then ¥' X « = \V
Page 84 - ... To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Page 48 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, the sum, difference, product, and quotient so obtained, will be all equal to each other.
Page 36 - Multiply the divisor thus increased, by the second term of the root, and subtract the product from the remainder.