## First Lessons in Algebra, Embracing the Elements of the Science ... |

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Side 35

To finish with what has reference to algebraic multiplication, we will make

a few results of frequent use in Algebra. Let it be required to form the square or

second power of the binomial (a+b). We have, from

To finish with what has reference to algebraic multiplication, we will make

**known**a few results of frequent use in Algebra. Let it be required to form the square or

second power of the binomial (a+b). We have, from

**known**principles, (a+b)”= ... Side 64

To express algebraically the relation between the

. 2nd. To find a value for the unknown quantity, in terms of those which are

. This latter part is called the solution of the equation. The given or

To express algebraically the relation between the

**known**and unknown quantities. 2nd. To find a value for the unknown quantity, in terms of those which are

**known**. This latter part is called the solution of the equation. The given or

**known**parts ... Side 72

It is first necessary to perform the multiplications indicated, in order to reduce the

two members to two polynomials, and thus be able to disengage the unknown

quantity r, from the

It is first necessary to perform the multiplications indicated, in order to reduce the

two members to two polynomials, and thus be able to disengage the unknown

quantity r, from the

**known**quantities. Having done that, the equation becomes,” ... Side 174

If we represent the coefficient of a by 2p, and the

2px=q, an equation containing but three terms ; and we see, from the above

examples, that every complete equation of the second degree may be reduced to

this ...

If we represent the coefficient of a by 2p, and the

**known**term by q, we have a”--2px=q, an equation containing but three terms ; and we see, from the above

examples, that every complete equation of the second degree may be reduced to

this ...

Side 177

I. Reduce the equation to one of the

the second term, square it, and add the result to both members of the equation. III.

Then extract the square root of both members of the equation ; after which, ...

I. Reduce the equation to one of the

**known**forms. II. Take half the coefficient ofthe second term, square it, and add the result to both members of the equation. III.

Then extract the square root of both members of the equation ; after which, ...

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First Lessons in Algebra: Embracing the Elements of the Science Charles Davies Uten tilgangsbegrensning - 1840 |

First Lessons in Algebra: Embracing the Elements of the Science Charles Davies Uten tilgangsbegrensning - 1839 |

First Lessons in Algebra: Embracing the Elements of the Science Charles Davies Uten tilgangsbegrensning - 1841 |

### Vanlige uttrykk og setninger

added addition affected algebraic antecedent apply arithmetical becomes binomial called cents changing coefficient common difference completing composed consequent considered contain cube denominator denotes difference Divide dividend division divisor dollars double elimination entire equal equation example exponent expression extracting the square extremes factors figure Find the square Find the values following RULE four fourth fraction gives greater half Hence indicated interest involving known last term less letter manner means method monomial Multiply negative number of terms obtain operations ounces perfect square periods person polynomial positive progression proportion question quotient radical ratio received Reduce remainder represent result rule second degree second term similar simplest form square root Substituting subtract taken tens third tion transposing twice units unknown quantity Verification whence write yards

### Populære avsnitt

Side 230 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A ; B ; : C : D; and read, A is to B as C to D.

Side 231 - Quantities are said to be in proportion by composition, when the sum of the antecedent and consequent is compared either with antecedent or consequent.

Side 155 - Obtain the exponent of each literal factor in the quotient by subtracting the exponent of each letter in the divisor from the exponent of the same letter in the dividend; Determine the sign of the result by the rule that like signs give plus, and unlike signs give minus.

Side 233 - AC and by clearing the equation of fractions we have BO=AD; that is, Of four proportional quantities, the product of the two extremes is equal to the product of the two means.

Side 175 - Since the square of a binomial is equal to the square of the first term, plus twice the product of the first term by the second, plus the square of the second...

Side 138 - Multiply the divisor, thus augmented, by the last figure of the root, and subtract the product from the dividend, and to the remainder bring down the next period for a new dividend But if any of the products should be greater than the dividend, diminish the last figure of the root.

Side 214 - A merchant bought cloth for which he paid £33 15s., which he sold again at £2 8s. per piece, and gained by the bargain as much as one piece cost him : how many pieces did he buy ? Ans.

Side 35 - The square of the sum of two quantities is equal to the square of the first, plus twice the product of the first and second, plus the square of the second.

Side 214 - To find a number such that if you subtract it from 10, and multiply the remainder by the number itself, the product shall be 21. Ans. 7 or 3.

Side 230 - Of four proportional quantities, the first and third are called the antecedents, and the second and fourth the consequents ; and the last is said to be a fourth proportional to the other three taken in order...