### Contents

 PART 1 DIVISION 37 THE GREATEST COMMON MEASURE 51 FRACTIONS 67 ADDITION OF FRACTIONS 73 INVOLUTION 81 The Binomial theorem 101
 EQUATIONS 104 SIMULTANEOUS EQUATIONS 151 RATIO 203 PROPORTIONAL EQUATIONS 213 PROGRESSION 227 To find the lesser extreme 239

### Popular passages

Page 31 - The square of the sum of two quantities is equal to the square nf the first, plus twice the product of the first by the second, plus the square of the second.
Page 210 - If four magnitudes are in proportion, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page 32 - ... the product of the two, plus the square of the second. In the third case, we have (a + b) (a — 6) = a2 — b2. (3) That is, the product of the sum and difference of two quantities is equal to the difference of their squares.
Page 208 - COMPOSITION ; that is, the sum of the first and second, will be to the second, as the sum of the third and fourth, is to the fourth.
Page 32 - The square of the difference of two quantities is equal to the square of the first, minus twice the product of the first and second, plus the square of the second.
Page 76 - We have therefore the following rule for the multiplication of fractions : Multiply the numerators together for the numerator of the product, and the denominators for its denominator.
Page 255 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Page 209 - If four magnitudes constitute a proportion, the first will be to the sum of the first and second as the third is to the sum of the third and fourth.
Page 138 - We shall now show that every equation with one unknown quantity has as many roots as there are units in the highest power of the unknown quantity, and no more.
Page 228 - ... progression, is equal to the sum of the first and last terms multiplied by half the number of terms; therefore, the sum of the moments about R, is 5,000 X 5!L±.§!