## 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 |

### Inni boken

Resultat 1-5 av 34

Side 55

Let be reduced to its most simple form . 121 6 ( 8 ) The utility of reducing surds 10

their most simple forms , in order to have the answer in decimals , will be readily

parceived from considering the first

Let be reduced to its most simple form . 121 6 ( 8 ) The utility of reducing surds 10

their most simple forms , in order to have the answer in decimals , will be readily

parceived from considering the first

**question**above given , where it is , found ... Side 98

The usual method of resolving algebraical

quantities , that are to be found , by x , y , or ... having properly examined the state

of the

of the ...

The usual method of resolving algebraical

**questions**, is first to denote thequantities , that are to be found , by x , y , or ... having properly examined the state

of the

**question**, perform with these letters , and the known quantities , by meansof the ...

Side 99

to determine the expression for the others , from the nature of the

which the same method of reasoning may be followed , as above . And , in some

cases , the substituting for the sums and differences of quantities ; or availing ...

to determine the expression for the others , from the nature of the

**question**; afterwhich the same method of reasoning may be followed , as above . And , in some

cases , the substituting for the sums and differences of quantities ; or availing ...

Side 100

Let x = the first person's share , Then will 1000 - = second person's share , And 2 :

1000- * :: 7 : 9 , by the

+ 7 = 7000 , or x = = 4371. 105. = 1st share , 16 and 1000x = 1000-4371 . 10s .

Let x = the first person's share , Then will 1000 - = second person's share , And 2 :

1000- * :: 7 : 9 , by the

**question**, That is 9x = ( 1000 - X ) 7 = 7000-7x , 7000 Or 9x+ 7 = 7000 , or x = = 4371. 105. = 1st share , 16 and 1000x = 1000-4371 . 10s .

Side 101

What fraction is that , to the numerator of which if 1 1 be added , its value will be

but if i be added to the 1 denominator , its value will be 4 2 1 2 1 y + 1 4 16 Let the

fraction required be represented by ; 3 + 1 Then and by the

What fraction is that , to the numerator of which if 1 1 be added , its value will be

but if i be added to the 1 denominator , its value will be 4 2 1 2 1 y + 1 4 16 Let the

fraction required be represented by ; 3 + 1 Then and by the

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An Introduction to Algebra: With Notes and Observations : Designed for the ... John Bonnycastle Uten tilgangsbegrensning - 1818 |

### Vanlige uttrykk og setninger

according added Algebra answer arise arithmetical changed coefficient common denominator compound consequently consisting contained continued cube root denoted determined difference dividend division divisor equal equation EXAMPLES expressed extracting factors find the difference find the square find the sum find the value former four fourth fraction geometrical give Given greater greatest common measure Hence infinite integer kind known least less letters logarithms manner means method mixed quantity multiplied necessary negative Note observed operation perform person placed positive PROBLEM progression proper proportion question quotient rational reduce the fraction remainder represented Required the difference Required the sum required to divide required to find required to reduce resolved result rule second term side signifying square number square root substituted subtracted surd taken taking third tion triangle unknown quantity usual value of x Whence whole numbers

### Populære avsnitt

Side 10 - 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 20 - To reduce a mixed number to an improper fraction, Multiply the whole number by the denominator of the fraction, and to the product add the numerator; under this sum write the denominator.

Side 27 - 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 167 - Ios- y" &cFrom which it is evident, that the logarithm of the product of any number of factors is equal to the sum of the logarithms of those factors. Hence...

Side 69 - To divide the number 90 into four such parts, that if the first be increased by 2, the second diminished by 2, the third multiplied...

Side 85 - 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 85 - 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.

Side 86 - 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 30 - 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.