A Practical Treatise on Algebra: Designed for the Use of Students in High Schools and AcademiesR.S. Davis and Company, 1852 - 336 σελίδες |
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Σελίδα iii
... following Treatise is designed to present a system of theoretical and practical Algebra . It is intended to be both ... Rule ; and the pupil , who will carefully and intelligently perform them , will gain a more thorough knowledge of the ...
... following Treatise is designed to present a system of theoretical and practical Algebra . It is intended to be both ... Rule ; and the pupil , who will carefully and intelligently perform them , will gain a more thorough knowledge of the ...
Σελίδα 22
... 4 from the 7 before the operation , or add it to the remainder ; and , if added to the remainder , the expression will be thus , 6 + 4 = 10 . 68. We therefore see the propriety of the following RULE 22 ALGEBRA . SECTION III.
... 4 from the 7 before the operation , or add it to the remainder ; and , if added to the remainder , the expression will be thus , 6 + 4 = 10 . 68. We therefore see the propriety of the following RULE 22 ALGEBRA . SECTION III.
Σελίδα 23
... following RULE . Change the signs of all the quantities to be sub- tracted , and proceed as in addition ; that is , the minus quan- tities in the subtrahend must be changed to plus quantities , and the plus quantities to minus ...
... following RULE . Change the signs of all the quantities to be sub- tracted , and proceed as in addition ; that is , the minus quan- tities in the subtrahend must be changed to plus quantities , and the plus quantities to minus ...
Σελίδα 31
... following RULE . Add the exponents of the same letter to the product of the coefficients . 17. Multiply 4m4 by 3m2 . 4X3Xm1Xm2 = 12m1 + 2—12m® . 18. Multiply -5n3 by —4n3 . 19. Multiply -3a " by 3a " . Ans . 20n8 . Ans . -9a2m Ans . 8xm ...
... following RULE . Add the exponents of the same letter to the product of the coefficients . 17. Multiply 4m4 by 3m2 . 4X3Xm1Xm2 = 12m1 + 2—12m® . 18. Multiply -5n3 by —4n3 . 19. Multiply -3a " by 3a " . Ans . 20n8 . Ans . -9a2m Ans . 8xm ...
Σελίδα 37
... following RULE . Write the dividend over the divisor , in the manner of a fraction , and reduce it to its simplest form by cancelling the letters and figures , that are common to each term . Or , divide the coefficient of the dividend ...
... following RULE . Write the dividend over the divisor , in the manner of a fraction , and reduce it to its simplest form by cancelling the letters and figures , that are common to each term . Or , divide the coefficient of the dividend ...
Άλλες εκδόσεις - Προβολή όλων
PRAC TREATISE ON ALGEBRA DESIG Benjamin 1786-1864 Greenleaf Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2016 |
Συχνά εμφανιζόμενοι όροι και φράσεις
added Algebra amount arithmetical arithmetical progression binomial breadth bushels coefficients common denominator common difference common index Completing the square compound interest contains courier cube root decimal distance divide both terms dividend divisor earth Evolving EXAMPLES exponent expressed Extract the square factor Find the sum find the value following RULE formula fraction gain geometrical geometrical mean geometrical progression geometrical series given number greater Hence infinity last term less lowest terms minus quantity number be divided number of terms number or quantity obtained oxen prefixed proportionals quadratic quadratic equation quan quantity or number quotient rate per cent ratio rational quantity remainder Required the numbers Required the sum required to find second term shillings simple form simple radical form square of half square rods square root subtracted surd THEOREM third power tity Transposing transposition twice unknown quantity value of x VERIFICATION
Δημοφιλή αποσπάσματα
Σελίδα 54 - RULE.! Multiply each numerator into all the denominators except its own for a new numerator, and all the denominators together for a common denominator.
Σελίδα 39 - 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. Multiply the whole divisor by the first term of the quotient, and subtract the product from the dividend.
Σελίδα 235 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Σελίδα 61 - Now .} of f- is a compound fraction, whose value is found by multiplying the numerators together for a new numerator, and the denominators for a new denominator.
Σελίδα 263 - And if the given number be a proper vulgar fraction ; subtract the logarithm of the denominator from the logarithm of the numerator, and the remainder will be the logarithm sought ; which, being that of a decimal fraction, must always have a negative index.
Σελίδα 267 - BY LOGARITHMS. RULE. FROM the logarithm of the dividend subtract the logarithm of the divisor, and the number answering to the remainder will be the quotient required.
Σελίδα 193 - Multiply the difference of the two numbers, found by trial, by the least error, and divide the product by the difference of the errors, when they are alike, but by their sum, when they are unlike. Or say...
Σελίδα 100 - J- of the sum of the shares of the other three, the share of the second £ of the sum of the other three, and the share of the third £ of the sum of the other three ; and it was found that the share of the oldest exceeded that of the youngest by $14.
Σελίδα 284 - Then, as the difference of these results is to the difference of the two assumed numbers, so is the difference between the true result, given...
Σελίδα 119 - Multiply the index of the quantity by the index of the power to which it is to be raised, and the result will be the power required.