A Mathematical Course for the Matriculation Examination of the University of London, Part 1

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1877
 

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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 8 - R for which the following conditions are satisfied: (i) ( + b) + c — a + (b + c) and (a . b) . c — a . (b . c) for all a, b, c, e R (associative).
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.
Page 29 - Divide the common denominator by the denominator of each fraction, and multiply the quotient by the numerator, and the product will be the numerator of the fraction required.

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