## 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 62

Side 14

... and ,

as above , the result will be ( B - 6 ) XbQB - nb . For if it were ab + ab , the product

would be greater than ab , which is absurd . Also , if B be greater than b , and a ...

... and ,

**consequently**, when each of the terms of the former are multiplied by a ,as above , the result will be ( B - 6 ) XbQB - nb . For if it were ab + ab , the product

would be greater than ab , which is absurd . Also , if B be greater than b , and a ...

Side 45

It is required to find the 5th root of 243 And for the cube root , fifth root , & c . of a

negative quantity , it is plain , from the same rule , that ( -a ) X ( -a ) X ( -a ) = - 43 ;

and ( -23 ) x ( + a ) = - 45 , And

It is required to find the 5th root of 243 And for the cube root , fifth root , & c . of a

negative quantity , it is plain , from the same rule , that ( -a ) X ( -a ) X ( -a ) = - 43 ;

and ( -23 ) x ( + a ) = - 45 , And

**consequently**-235- , and -25 = -a CASE II . Side 62

... it follows , that the am expression a ' is a symbol equivalent to unity , and ,

what is above said , we may also farther observe , 1. That o added to or

subtracted ...

... it follows , that the am expression a ' is a symbol equivalent to unity , and ,

**consequently**, that it may always be replaced by 1 whenever it occurs . ( t ) ( t ) Towhat is above said , we may also farther observe , 1. That o added to or

subtracted ...

Side 63

6 For let -9 , then , if b remains the same , it is plain , the less a is , the greater will

be the quotient q ; whence , if a be indefinitely small , q will be indefinitely great :

and

6 For let -9 , then , if b remains the same , it is plain , the less a is , the greater will

be the quotient q ; whence , if a be indefinitely small , q will be indefinitely great :

and

**consequently**, when a is 0 , the quotient q will be infinite : that is , b Ö 0 ... Side 79

we shall have S = al Where it is to be observed , that if the ratio , or common

multiplier , r , in this last series , be a proper fraction , and

a decreasing one , we shall have , in that case , atar + ar + arstar ' , & c . ad

infinitum ...

we shall have S = al Where it is to be observed , that if the ratio , or common

multiplier , r , in this last series , be a proper fraction , and

**consequently**the seriesa decreasing one , we shall have , in that case , atar + ar + arstar ' , & c . ad

infinitum ...

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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.