## 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 11

Side 4

A rational quantity , is that which can be

radical sign , or fractional index ; as a , ora , or 5a & c . An irrational quantity , or

surd , is that which has no exact root , or which can only be

...

A rational quantity , is that which can be

**expressed**in finite térms , or without anyradical sign , or fractional index ; as a , ora , or 5a & c . An irrational quantity , or

surd , is that which has no exact root , or which can only be

**expressed**by means...

Side 43

... 1 powers as the binominal theorem of Newton , may be

terms , as follows : m - 1 m2 fato ) maamfomam.167m.am - 363 , & c 2 2 3 1 1 m -

2 ( a - bm = qm - mam - 16 + m . -am - 2b2 - m . , am - 363 . & c . 2 2 3 Fam - 2b2 +

...

... 1 powers as the binominal theorem of Newton , may be

**expressed**in generalterms , as follows : m - 1 m2 fato ) maamfomam.167m.am - 363 , & c 2 2 3 1 1 m -

2 ( a - bm = qm - mam - 16 + m . -am - 2b2 - m . , am - 363 . & c . 2 2 3 Fam - 2b2 +

...

Side 50

IRRATIONAL quantities , or surds , are such as have no exact root , being usually

case , the numerator shows the power the quantity is to be raised to , and the ...

IRRATIONAL quantities , or surds , are such as have no exact root , being usually

**expressed**by means of the radi . cal sign , or by fractional indices ; in which lattercase , the numerator shows the power the quantity is to be raised to , and the ...

Side 63

Let be

index . 1 5. Let be

Let be

**expressed**with a negative index . a3 4. Let a ' be**expressed**with a positiveindex . 1 5. Let be

**expressed**with a negative index . ata 6. Let ala2 —x2 ) ' t be**expressed**with a positive index . -0 . 3 ota . a + 0 = a , and a - sa . 2. Also , if ... Side 79

... between the ratio and unity . Thus , in the series 2 , 4 , 8 , 16 , 32 , 64 , 128 ,

256 , 512 , 512 X2-2 we shall have = 1024-2 = 1022 , the sum of 2-1 the terms .

Or the same rule , without considering the last term , may be

Find ...

... between the ratio and unity . Thus , in the series 2 , 4 , 8 , 16 , 32 , 64 , 128 ,

256 , 512 , 512 X2-2 we shall have = 1024-2 = 1022 , the sum of 2-1 the terms .

Or the same rule , without considering the last term , may be

**expressed**thus :Find ...

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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.