## 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 ... of the unknown quantity contained in any

one of their terms: as, quadratic equations,

equations, &c.

THE DocTRINE of Equations is that branch of algebra, which treats of the

methods of determining the values of ... of the unknown quantity contained in any

one of their terms: as, quadratic equations,

**cubic equations**, biquadraticequations, &c.

Side 82

A

which rises to the third power : as, a:3 ==27 ; 223–3.c-35; or a 3-ax” +bac=c. A

biguadratic equation is that in which the unknown quantity is of four dimensions,

...

A

**cubic equation**is that in which the unknown quantity is of three dimensions, orwhich rises to the third power : as, a:3 ==27 ; 223–3.c-35; or a 3-ax” +bac=c. A

biguadratic equation is that in which the unknown quantity is of four dimensions,

...

Side 123

Ans. 7 and 13 OF

unknown quantity rises to three dimensions ; and like quadratics, or those of the

higher orders, is either simple or compound. A simple

form ...

Ans. 7 and 13 OF

**CUBIC EQUATIONS**. * A**cubic equation**is that in which theunknown quantity rises to three dimensions ; and like quadratics, or those of the

higher orders, is either simple or compound. A simple

**cubic equation**is of theform ...

Side 125

Let the equation 22°–32°-i-42–5–0, be transformed into another, that shall want

its second term. OF THE SOLUTION OF

the second term of the equation when necessary, as directed in the preceding ...

Let the equation 22°–32°-i-42–5–0, be transformed into another, that shall want

its second term. OF THE SOLUTION OF

**CUBIC EQUATIONS**. RULE. Take awaythe second term of the equation when necessary, as directed in the preceding ...

Side 129

... when brought to the left hand side, -0; then if the equation, so formed, be

divided by ac-Er, according as r is positive or negative, there will arise a

quadratic equation, the roots of which will be the other two roots of the given

... when brought to the left hand side, -0; then if the equation, so formed, be

divided by ac-Er, according as r is positive or negative, there will arise a

quadratic equation, the roots of which will be the other two roots of the given

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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.