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

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Side 128

It is evident that the exponent of the leading letter in the first term will be the same

as the exponent of the power; and that this exponent will diminish by unity in

each term to the right, until we reach the

It is evident that the exponent of the leading letter in the first term will be the same

as the exponent of the power; and that this exponent will diminish by unity in

each term to the right, until we reach the

**last term**, which does not contain the ... Side 219

Hence, for finding the

common difference by one less than the number of terms. II. To the product add

the first term: the sum will be the

serves to ...

Hence, for finding the

**last term**, we have the following RULE. I. Multiply thecommon difference by one less than the number of terms. II. To the product add

the first term: the sum will be the

**last term**. EXAMPLES. The sormula l-a+(n-1)rserves to ...

Side 221

The first term of a decreasing progression is 60, the number of terms 20, and the

common difference 3: what is true

–57–3. 2. The first term is 90, the common difference 4, and the number of terms ...

The first term of a decreasing progression is 60, the number of terms 20, and the

common difference 3: what is true

**last term**2 l=a—(n—1)r gives lité0–(20–1)3–60–57–3. 2. The first term is 90, the common difference 4, and the number of terms ...

Side 225

The

common difference 2 The formula 7"> l—a n—l - 16–4 gives 7 ====3. 2. The

difference 2 ...

The

**last term**is 16, the first term 4, and the number of terms 5: what is thecommon difference 2 The formula 7"> l—a n—l - 16–4 gives 7 ====3. 2. The

**last****term**is 22, the first term 4, and the number of terms 10: what is the commondifference 2 ...

Side 243

Let l be this term ; we then have the formula l=aq"-1, by means of which we can

obtain any term without being obliged to find all the terms which precede it.

Hence, to find the

Raise the ...

Let l be this term ; we then have the formula l=aq"-1, by means of which we can

obtain any term without being obliged to find all the terms which precede it.

Hence, to find the

**last term**of a progression, we have the following RULE. I.Raise the ...

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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...