Algebra for High Schools and Colleges: Containing a Systematic Exposition and Application of the Elementary and Higher Principles of the SciencePratt, Oakley & Company, 1859 - 306 σελίδες |
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Σελίδα 8
... preceding polynomial , the first term a is understood to be + a ; for it may be regarded as 0 + a . ( 25. ) A negative quantity has an effect contrary to that of ar equal positive quantity , in the expression , or calculation , into ...
... preceding polynomial , the first term a is understood to be + a ; for it may be regarded as 0 + a . ( 25. ) A negative quantity has an effect contrary to that of ar equal positive quantity , in the expression , or calculation , into ...
Σελίδα 10
... and 2c ? 5a , -5 , and 56 ? Of a2 , bx , and 3a2 ? Of Of 3a2 , 46 , and 2c ? Of The preceding principles . and the following Rule , provide for all the cases in Algebraic Addition . RULE I. ( 31 ) For the Addition of Algebraic 10 ADDITION .
... and 2c ? 5a , -5 , and 56 ? Of a2 , bx , and 3a2 ? Of Of 3a2 , 46 , and 2c ? Of The preceding principles . and the following Rule , provide for all the cases in Algebraic Addition . RULE I. ( 31 ) For the Addition of Algebraic 10 ADDITION .
Σελίδα 13
... , ( 30 ) . What difference will be found by subtracting 2a from 3x ? By subtracting -36 from 5ax ? By subtracting ax from 106 ? By subtracting 4y from -9x 2 ? From the preceding we derive RULE II . ( 36. SUBTRACTION 13.
... , ( 30 ) . What difference will be found by subtracting 2a from 3x ? By subtracting -36 from 5ax ? By subtracting ax from 106 ? By subtracting 4y from -9x 2 ? From the preceding we derive RULE II . ( 36. SUBTRACTION 13.
Σελίδα 14
... preceding we derive RULE II . ( 36. ) For the Subtraction of Algebraic Quantities . - - to Change the sign of each term to be subtracted , + to and + , or conceive these signs to be changed , and then proceed as in Alge- braic Addition ...
... preceding we derive RULE II . ( 36. ) For the Subtraction of Algebraic Quantities . - - to Change the sign of each term to be subtracted , + to and + , or conceive these signs to be changed , and then proceed as in Alge- braic Addition ...
Σελίδα 19
... preceding principles and the two following rules , embrace the subject of Algebraic Multiplication . RULE III . ( 44. ) To Multiply a Monomial into a Polynomial . Find the product of the monomial into each term of the polynomial ...
... preceding principles and the two following rules , embrace the subject of Algebraic Multiplication . RULE III . ( 44. ) To Multiply a Monomial into a Polynomial . Find the product of the monomial into each term of the polynomial ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
acres added Algebraic approximate value Arithmetical Progression Binomial Theorem cent common denominator common difference completing the square component factors Continued Fraction corresponding cube root denotes dividend divisor Equation containing example exponent extracting the square Find a number Find the cube Find the Product Find the Quotient Find the square Find the Sum Find the value Function Geometrical Progression given Equation given fraction given number greater greatest common measure Hence imaginary improper Fraction Inequality integral irrational last term least common multiple less letters logarithm lowest terms method miles monomial multiplied negative number of terms obtained polynomial positive preceding prefixed problem proportion quadratic Quadratic Equations ratio real roots Reduce remainder required root Resolve second equation second member second term side signs changed simplest form solution square rods square root substituted subtracting Surds unknown quantity value of x whole number yards
Δημοφιλή αποσπάσματα
Σελίδα 299 - NB In the following table, in the last nine columns of each page, where the first or leading figures change from 9's to O's, points or dots are introduced instead of the...
Σελίδα 209 - A put four horses, and B as many as cost him 18 shillings a week. Afterwards B put in two additional horses, and found that he must pay 20 shillings a week. At what rate was the pasture hired ? 49.
Σελίδα 105 - Three quantities are said to be in harmonical proportion, when the first is to the third, as the difference between the first and second is to the difference between the second and third.
Σελίδα 85 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Σελίδα 177 - A set out from C towards D, and travelled 7 miles a day. After he had gone 32 miles, B set out from D towards C, and went every day J^ of the whole journey; •and after he had travelled as many days as he went miles in a day, he met A. Required the distance from C to D.
Σελίδα 206 - A hare is 50 leaps before a greyhound, and takes 4 leaps to the greyhound's 3 ; but 2 of the greyhound's leaps are equal to 3 of the hare's ; how many leaps must the greyhound take, to catch the hare?
Σελίδα 80 - What fraction is that, whose numerator being doubled, and denominator increased by 7, the value becomes §; but the denominator being doubled, and the numerator increased by 2, the value becomes f 1 Ans.
Σελίδα 79 - What fraction is that, to the numerator of which if 1 be added, the value will be •£ ; but if 1 be adde.d to the denominator, its value will be | ? Let — denote the fraction.
Σελίδα 60 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.
Σελίδα 244 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor. , M , ,• , . logi — = log