Essentials of Algebra for Secondary SchoolsD.C. Heath & Company, 1904 - 367 σελίδες |
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Σελίδα iii
... complete treatment of elemen- tary Algebra , and attention is especially invited to the fol- lowing features : The introduction of easy problems at the very outset ; § 5 . The Addition and Multiplication of Positive and Nega- tive ...
... complete treatment of elemen- tary Algebra , and attention is especially invited to the fol- lowing features : The introduction of easy problems at the very outset ; § 5 . The Addition and Multiplication of Positive and Nega- tive ...
Σελίδα 176
... b ) b . If we divide the first term of this remainder by 2 a , that is , by twice the first term of the root , we obtain the second term of the root , b . Adding this to 2 a , we obtain the complete 176 ALGEBRA . Square Root of a ...
... b ) b . If we divide the first term of this remainder by 2 a , that is , by twice the first term of the root , we obtain the second term of the root , b . Adding this to 2 a , we obtain the complete 176 ALGEBRA . Square Root of a ...
Σελίδα 177
... complete divisor , 6x2 - 5 a3 . Multiplying this complete divisor by - 5 a3 , and subtracting the product from the remainder , there is no remainder . Hence , 3x2 - 5 a3 is the required square root . 2. Find the square root of 125-22x + ...
... complete divisor , 6x2 - 5 a3 . Multiplying this complete divisor by - 5 a3 , and subtracting the product from the remainder , there is no remainder . Hence , 3x2 - 5 a3 is the required square root . 2. Find the square root of 125-22x + ...
Σελίδα 178
... complete divisor , with its last term doubled . To avoid needless repetition , the last five terms of the first remainder , the last four terms of the second remainder , and the last two terms of the third remainder are omitted . Note ...
... complete divisor , with its last term doubled . To avoid needless repetition , the last five terms of the first remainder , the last four terms of the second remainder , and the last two terms of the third remainder are omitted . Note ...
Σελίδα 181
... complete divisor by the root - figure last obtained , and subtract the product from the remainder . If other periods remain , proceed as before , doubling the part of the root already found for the next trial - divisor . Note 1. It ...
... complete divisor by the root - figure last obtained , and subtract the product from the remainder . If other periods remain , proceed as before , doubling the part of the root already found for the next trial - divisor . Note 1. It ...
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9 x² a²b a²b² a³b ab² ab³ algebraic arithmetic means arithmetic progression ax² binomial Binomial Theorem cents change the sign coefficient cologarithm cube root decimal degree denominator digits Divide dividend divisor equal EXAMPLES exponent Extracting the square Find the H. C. F. Find the number Find the sum Find the value following rule formulæ geometric progression greater Hence highest common factor last term less logarithm mantissa miles an hour monomial Multiplying negative number Note number of dollars number of terms partial fractions perfect square polynomial positive integer positive number proportion quadratic equation quotient radical sign ratio Reduce remainder result second term Solve the equation Solve the following square root Subtracting Transposing trial-divisor unknown quantities Whence x²y x²y² xy²
Δημοφιλή αποσπάσματα
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...
Σελίδα 140 - If necessary, multiply the given equations by such numbers as will make the coefficients of one of the unknown quantities in the resulting equations of equal absolute value.