## 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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Side 81

THE DOCTRINE OF EQUATIONS is that branch of algebra , which treats of the

methods of determining the values of ... Thus , a

which the unknown quantity is of two dimensions , or which rises to the second

power ...

THE DOCTRINE OF EQUATIONS is that branch of algebra , which treats of the

methods of determining the values of ... Thus , a

**quadratic equation**is that inwhich the unknown quantity is of two dimensions , or which rises to the second

power ...

Side 82

A cubic equation is that in which the unknown quan . tity is of three dimensions ,

or which rises to the third power : as , 23 = -27 ; 2x3 - 3x = 35 ; or x3 - ax + bx = 0 .

A biquadratic equation ... Thus , in the

A cubic equation is that in which the unknown quan . tity is of three dimensions ,

or which rises to the third power : as , 23 = -27 ; 2x3 - 3x = 35 ; or x3 - ax + bx = 0 .

A biquadratic equation ... Thus , in the

**quadratic equation**x ? + 2r = 15 , the root ... Side 108

Ans . A 1437 days , B 1741 , and c 2331

the unknown quantity , as 6 6 ax = b , or x = a A compound

...

Ans . A 1437 days , B 1741 , and c 2331

**QUADRATIC EQUATIONS**. ... A simple**quadratic equation**, is that which contains only the square , or second power , ofthe unknown quantity , as 6 6 ax = b , or x = a A compound

**quadratic equation**, is...

Side 109

Transpose all the terms that involve the unknown quantity to one side of the

equation , and the known terms to the other ; observing to arrange them so , that

the term which ... All equations , which have the index of

Transpose all the terms that involve the unknown quantity to one side of the

equation , and the known terms to the other ; observing to arrange them so , that

the term which ... All equations , which have the index of

**QUADRATIC****EQUATIONS**105. Side 110

All equations , which have the index of the unknowo quantity , in one of their

terms , just double that of the other , are ... it necessarily follows , that every

imaginary ...

All equations , which have the index of the unknowo quantity , in one of their

terms , just double that of the other , are ... it necessarily follows , that every

**quadratic equation**mur have two roots ; which are either both real , or bothimaginary ...

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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.