## 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 22

Side 11

EXAMPLES . 5xy 4aac 2xy - 2x2 2ax - 30 3x2 -2ax 3x3 + xy 2 + xy 432 -ху - 4ax

3x3 5x2 3x + 10 • Зху 4ry 6x2 + xy 8x2 ... + 2xya 2 / x -- 187 3y + 10x 2x2y +254

12xy - xy -8y + -177 3a8 — 13ty xy +3203 20 6522

EXAMPLES . 5xy 4aac 2xy - 2x2 2ax - 30 3x2 -2ax 3x3 + xy 2 + xy 432 -ху - 4ax

3x3 5x2 3x + 10 • Зху 4ry 6x2 + xy 8x2 ... + 2xya 2 / x -- 187 3y + 10x 2x2y +254

12xy - xy -8y + -177 3a8 — 13ty xy +3203 20 6522

**EXAMPLES FOR PRACTICE**. Side 12

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 John Bonnycastle.

sum ...

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 John Bonnycastle.

**EXAMPLES FOR PRACTICE**. 1. Required thesum ...

Side 13

ax - 5xya 5x2 + vr - 47 6x2 8x_x

difference of f ( a + b ) and 1 ( a - 6 ) . 2. From 3x - 2a - 6 + 7 , take 8-36 + a + 4r . 3

. From 3a + b + c - 2d , take 5 - 8c + 2d - 8 . 1. From 13x2 – 2ax + 962 take 5x27x

— 62 ...

ax - 5xya 5x2 + vr - 47 6x2 8x_x

**EXAMPLES FOR PRACTICE**. 1. Find thedifference of f ( a + b ) and 1 ( a - 6 ) . 2. From 3x - 2a - 6 + 7 , take 8-36 + a + 4r . 3

. From 3a + b + c - 2d , take 5 - 8c + 2d - 8 . 1. From 13x2 – 2ax + 962 take 5x27x

— 62 ...

Side 17

EXAMPLES 3 + y xty 5x + 4y 3x - 2y 22 : 4 - xy - ya - y m2 toxy try + ya 150 +1234

10xy - Sya 33 + * ? y - ry ? -roy- xy + y ... Y " + xy T4 + T7 9 txay + ya 32y + zya y –

xy2 - y – xy - y2 x2 * - 72 24 + 2x2y + ya X3

EXAMPLES 3 + y xty 5x + 4y 3x - 2y 22 : 4 - xy - ya - y m2 toxy try + ya 150 +1234

10xy - Sya 33 + * ? y - ry ? -roy- xy + y ... Y " + xy T4 + T7 9 txay + ya 32y + zya y –

xy2 - y – xy - y2 x2 * - 72 24 + 2x2y + ya X3

**EXAMPLES FOR PRACTICE**. 1. Side 24

3axo + 3a2 x - a3 ' be divided by 3--6 . 3. Let a3 + 5a2 x + 50x2 + x3 be divided

by a tm . 4. Let 2y3 – 19y2 + 264-17 be divided by y - 8 . 5. Let 305 +1 be divided

...

**EXAMPLES FOR PRACTICE**. 1. Let a ? 2ax + x2 be divided by a - 3 . 2. Let x3 –3axo + 3a2 x - a3 ' be divided by 3--6 . 3. Let a3 + 5a2 x + 50x2 + x3 be divided

by a tm . 4. Let 2y3 – 19y2 + 264-17 be divided by y - 8 . 5. Let 305 +1 be divided

...

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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.