## An Introduction to Algebra: With Notes and Observations : Designed for the Use of Schools and Places of Public Education : to which is Added an Appendix on the Application of Algebra to Geometry |

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Side 120

... sometimes be obtained by the rules before laid down for the solution of simple

equations ; and , in this case , one of the unknown quantities being

the others may be found by substituting its value in the remaining equations .

... sometimes be obtained by the rules before laid down for the solution of simple

equations ; and , in this case , one of the unknown quantities being

**determined**,the others may be found by substituting its value in the remaining equations .

Side 134

When one of the roots of a cubic equation has been found , by the common

formula as above , or in any other way , the other two roots may be

follows : Let the known root be denoted by r , and put all the terms of the equation

...

When one of the roots of a cubic equation has been found , by the common

formula as above , or in any other way , the other two roots may be

**determined**asfollows : Let the known root be denoted by r , and put all the terms of the equation

...

Side 155

The roots of equations , of all orders , can also be

exactness , by means of the following easy rule of double position ; which ,

though it has not been generally employed for this purpose , will be found in

some ...

The roots of equations , of all orders , can also be

**determined**, to any degree ofexactness , by means of the following easy rule of double position ; which ,

though it has not been generally employed for this purpose , will be found in

some ...

Side 175

... that will apply in all the cases that may occur ; but as far as respects a particular

class of these problems relating to squares , they may generally be

by means of some of the rules derived from the following formula :PROBLEM 1 .

... that will apply in all the cases that may occur ; but as far as respects a particular

class of these problems relating to squares , they may generally be

**determined**by means of some of the rules derived from the following formula :PROBLEM 1 .

Side 184

... some value of the unknown quantity that makes the given expression a square

: in which case other values of it may be

possible , as follows : Thus , let p be a value of a so found , and make ap3 + bp +

cp ...

... some value of the unknown quantity that makes the given expression a square

: in which case other values of it may be

**determined**from this , when they arepossible , as follows : Thus , let p be a value of a so found , and make ap3 + bp +

cp ...

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An Introduction to Algebra: With Notes and Observations: Designed for the ... John Bonnycastle Uten tilgangsbegrensning - 1782 |

### Vanlige uttrykk og setninger

according added addition Algebra answer appears applied arise arithmetical assumed base become binomial changed coefficients consequently contains continued cube root decimal denominator denoted determined difference divided division divisor equal equation evident EXAMPLES expression extracting factors figure find the sum find the value former formula four fourth fraction geometrical give Given greater greatest Hence integral kind known last term latter least less logarithms manner means method multiplied natural necessary negative Note observed obtained operation positive PROBLEM proper proportion proposed quadratic question quotient rational reduced remain Required the sum required to divide required to find resolved result rule side simple solution sought square number square root substituted subtracted surd taken taking third triangle unknown quantity usual value of x Whence whole numbers

### Populære avsnitt

Side 45 - ... be the power required. Or, multiply the quantity into itself as many times, less one, as is denoted by the index of the power, and the last product will be tJie answer.

Side 43 - 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.

Side 27 - 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.

Side 87 - ... the first is to the third as the difference between the first and second is to the difference between the second and third, the quantities a, b, c, are said to be in harmonical proportion.

Side 126 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.

Side 112 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.

Side 126 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the less, is equal to 12 ? Ans.

Side 29 - If there is a remainder after the last division, write it over the divisor in the form of a fraction, and annex it with its proper sign to the part of the quotient previously obtained.

Side 224 - N .•. def. (2), x— x1 is the logarithm of that is to say, The logarithm of a fraction, or of the quotient of two numbers, is equal to the logarithm of the numerator minus the logarithm of the denominator. III. Raise both members of equation (1) to the power of n. N" =a

Side 126 - It is required to divide the number 60 into two such parts, that their product shall be to the sum of their squares in the ratio of 2 to 5.