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according Adding algebraic arithmetic arranged called cents coefficient common factor complete containing corresponding cube root decimal denominator derive difference digits Divide dividend division divisor dollars equal EXAMPLES Expand exponent expression Extracting the square factor figures Find Find the number Find the value following rule formula fourth fraction geometric given gives greater Hence increased indicated laws less letter logarithm lowest means method miles an hour Multiplying negative Note obtained perfect piece polynomial positive positive integer problem progression proportion prove quadratic quotient ratio receive Reduce remainder represent respectively result satisfied second term Simplify solution Solve the equation square root Substituting Subtracting term third Transposing travels twice units unknown quantities varies Whence write written
Σελίδα 280 - In any proportion,, the terms are in proportion by Composition ; that is, the sum of the first two terms is to the first term as the sum of the last two terms is to the third term.
Σελίδα 132 - At what time between 3 and 4 o'clock are the hands of a watch opposite to each other ? Let x = the number of minute-spaces passed over by the minutehand from 3 o'clock to the required time. Then, since the hour-hand is 15 minute-spaces in advance of the minute-hand at 3 o'clock, x — 15 — 30, or x — 45, will represent the number of minute-spaces passed over by the hour-hand.
Σελίδα 41 - Divide the first term of the dividend by the first term of the divisor, and write the result as the first term of the quotient.
Σελίδα 132 - How far can he ride in a coach which travels 41 miles an hour, so as to return in time, walking back at the rate of 3| miles an hour ? 44.
Σελίδα 22 - From §§36 and 37, we have the following rule: To subtract one number from another, change the sign of the subtrahend, and add the result to the minuend.
Σελίδα 281 - In a series of equal ratios, any antecedent is to its consequent, as the sum of all the antecedents is to the sum of all the consequents. Let a: 6 = c: d = e :/. Then, by Art.
Σελίδα 59 - ... the square of the second. In the second case, we have (a — &)2 = a2 — 2 ab + b2. (2) That is, the square of the difference of two quantities is equal to the square of the first, minus twice the product of the two, plus the square of the second.
Σελίδα 280 - In any proportion the terms are in proportion by Alternation ; that is, the first term is to the third as the second term is to the fourth.
Σελίδα 161 - A certain sum of money at simple interest amounts in m years to a dollars, and in n years to b dollars. Required the sum and the rate of interest. 47. A...