## 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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Resultat 1-5 av 28

Side 4

Incommensurable quantities , are such as have no mon measure , or

except unity . Thus , 15 and 16 , 2 and 3 , and a + b and a2 +62 , are

incommensurable quantities . A multiple of any quantity , is that which is some

exact number of ...

Incommensurable quantities , are such as have no mon measure , or

**divisor**,except unity . Thus , 15 and 16 , 2 and 3 , and a + b and a2 +62 , are

incommensurable quantities . A multiple of any quantity , is that which is some

exact number of ...

Side 14

Which method is often preferable to that of executing the entire process ,

particularly when the product of two or more factors is to be divided by some

other quantity , because , in this case , any quantity that is common to both the

Which method is often preferable to that of executing the entire process ,

particularly when the product of two or more factors is to be divided by some

other quantity , because , in this case , any quantity that is common to both the

**divisor**and ... Side 18

... which like signs give + in the quotient , and unlike signs - , as in findin . their

products ( e ) . It it libre also to be observed , that powers and roots of the same

quantity , are divided by subtracting the index of the

dividend .

... which like signs give + in the quotient , and unlike signs - , as in findin . their

products ( e ) . It it libre also to be observed , that powers and roots of the same

quantity , are divided by subtracting the index of the

**divisor**from that of thedividend .

Side 19

CASE I. When the

the dividend over the

simplest form , by cancelling the letters and figures that are common to each term

.

CASE I. When the

**divisor**and dividend are both simple quantities . RULE . Setthe dividend over the

**divisor**, in the manner of a fraction , and reduce it to itssimplest form , by cancelling the letters and figures that are common to each term

.

Side 20

When the

down in the same inanner as in division of numbers , ranging the terms of each of

them so , that the higher powers of one of the letters may stand before the lower ...

When the

**divisor**and dividend are both compound quantities . RULE . Set themdown in the same inanner as in division of numbers , ranging the terms of each of

them so , that the higher powers of one of the letters may stand before the lower ...

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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.