## 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 5

Side 175

We are, also, farther satisfied of the reasonableness of this doctrine, by finding, in

fact, that a finite quantity is frequently convertible into an infinite series, as

appears in the case of circulating

is ...

We are, also, farther satisfied of the reasonableness of this doctrine, by finding, in

fact, that a finite quantity is frequently convertible into an infinite series, as

appears in the case of circulating

**decimals**. Thus two-thirds expressed decimallyis ...

Side 204

It is also evident, that the logarithms of 1, 10, 100, 1000, &c. being 0, 1, 2, 3, &c.

respectively, the logarithm of any number, falling between 0 and 1, will be 0 and

some

...

It is also evident, that the logarithms of 1, 10, 100, 1000, &c. being 0, 1, 2, 3, &c.

respectively, the logarithm of any number, falling between 0 and 1, will be 0 and

some

**decimal**parts ; that of a number between 10 and 100, 1 and some**decimal**...

Side 205

Where the sign — is put over the index, instead of before it, when that part of the

logarithm is negative, in order to distinguish it from the

always to be considered as +, or affirmative. Also, agreeably to what has been

before ...

Where the sign — is put over the index, instead of before it, when that part of the

logarithm is negative, in order to distinguish it from the

**decimal**part, which isalways to be considered as +, or affirmative. Also, agreeably to what has been

before ...

Side 206

Thus, for instance, if i be made to denote the index, or integral part of the

logarithm of any number N, and d its

10m x N-(i+m)+ d ; log. H= (i-m) + d , where it is plain that the

Frn ...

Thus, for instance, if i be made to denote the index, or integral part of the

logarithm of any number N, and d its

**decimal**part, we shall have log N= i+d; iog.10m x N-(i+m)+ d ; log. H= (i-m) + d , where it is plain that the

**decimal**part of theFrn ...

Side 214

from the

be added to the indices, or integral parts, after the manner of positive and

negative quantities in algebra. - Which method will be found much more

convenient, ...

from the

**decimal**part of the logarithms is always affirmative, and must, therefore,be added to the indices, or integral parts, after the manner of positive and

negative quantities in algebra. - Which method will be found much more

convenient, ...

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

### Vanlige uttrykk og setninger

a-Ha acº Algebra arise arithmetical mean arithmetical series bers binomial coefficient consequently cube root cubic equation decimal denoted dividend division divisor equal ExAMPLES FOR PRACTICE expressed find the difference find the square find the sum find the value find two numbers geometrical geometrical progression geometrical series give given equation given number greater number greatest common measure Hence improper frac improper fraction infinite series last term letters loga logarithms mixed quantity multiplied natural number negative nth root number of terms number required perpendicular plane triangle PROBLEM proportion quadratic equation question quotient rational reduce the fraction remainder required the numbers Required the sum required to convert required to divide required to find required to reduce result rithm rule second term simple form square number square root substituted subtracted surd tion transposition unknown quantity value of ac Whence whole numbers

### Populære avsnitt

Side 16 - 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 26 - 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 33 - 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 187 - 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 91 - 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 39 - ... and the quotient will be the next term of the root. Involve the whole of the root, thus found, to its proper power, which subtract from the given quantity, and divide the first term of the remainder by the same divisor as before ; and proceed in this manner till the whole is finished*.

Side 107 - 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 107 - 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 108 - 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 36 - 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.