algebraic quantities arithmetic means arithmetic series arithmetical progression ciphers common denominator common difference decimal fractions decimal places digits Divide dividend divisor equal Extract the square figures Find the g. c. m. Find the greatest Find the simple Find the sum Find the value following equations four quantities geometric series geometrical progression greatest common measure guinea H. J. S. SMITH HEAVISIDE hence infinity integer ISAAC TODHUNTER least common multiple lowest terms miles Multiply number of terms numerator and denominator obtained odd number places of decimals pound present value prime number Prof proportion quotient rate per cent recurring decimal Reduce remainder Show simple interest Simplify the expressions Solve the equations Solve the following square root subtract unity unknown quantities vulgar fraction Wednesday whole number yards
Page xliii - Permutando, or alternando, by permutation or alternately; when there are four proportionals, and it is inferred that the first is to the third, as the second is to the fourth.
Page lxiii - When any number of quantities are proportionals, as one antecedent is to its consequent, so is the sum of all the antecedents to the sum of all the consequents.
Page xlvii - Article, — j— = — -=- ; oa bd also - =" — j ac , , a—bb c—dd a—b c- d therefore - x - = — -- x - or = j bade ac or a — b : a :: c — d : c, and inversely, a '. a — b :: c : c — d. This operation is called convertendo. 396. When four quantities are proportionals, the sum of the first and second is to their difference as the sum of the third and fourth is to their difference.
Page xlii - If the numerator and denominator of a fraction be multiplied by the same number, the value of the fraction is not altered.
Page 76 - A ship sails with a supply of biscuit for 60 days, at a daily allowance of a pound a head ; after being at sea 20 days she encounters a storm in which 5 men are washed overboard, and damage sustained that will cause a delay of 24 days, and it is found that each man's daily allowance must be reduced to fivesevenths of a pound.
Page 24 - ... product of all the divisors and numbers in the last line will be the least common multiple required.
Page 80 - Prove, from a property of the circle, that if four quantities are proportionals, the sum of the greatest and least is greater than the sum of the other two.
Page 26 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.