## A Treatise on Algebra: Containing the Latest Improvements. Adapted to the Use of Schools and Colleges |

### Inni boken

Resultat 1-5 av 5

Side 16

The multiplicand , being to be

the multiplier , must be

multiplier separately , and the separate results added together . 21 . When there

are ...

The multiplicand , being to be

**taken**as many times additively as is denoted bythe multiplier , must be

**taken**as many times as is denoted by each term of themultiplier separately , and the separate results added together . 21 . When there

are ...

Side 246

Thus , if we take the quantities a , b , c ; then abc , acb , bac , bea , cab , cba are

the permutations of these three quantities

cb are the permutations of these quantities

Thus , if we take the quantities a , b , c ; then abc , acb , bac , bea , cab , cba are

the permutations of these three quantities

**taken**all together ; ab , ac , ba , be , ca ,cb are the permutations of these quantities

**taken**two and two ... Side 247

Reasoning in the same manner for b , we shall have ( n - 1 ) permutations of the n

quantities

quantities in succession ; hence the whole number of permutations will be n ( n ...

Reasoning in the same manner for b , we shall have ( n - 1 ) permutations of the n

quantities

**taken**two and two , in which b stands firsi , and so on for each of the nquantities in succession ; hence the whole number of permutations will be n ( n ...

Side 248

( 1 ) Hence it appears that , if the above law of formation hold good for any one

class of permutations , it must hold good for the class next superior ; but it has

been proved to hold good when p = 2 , or for the permutations of n quantities

( 1 ) Hence it appears that , if the above law of formation hold good for any one

class of permutations , it must hold good for the class next superior ; but it has

been proved to hold good when p = 2 , or for the permutations of n quantities

**taken**two ... Side 250

Therefore the latter , namely , the whole number of permutations , or n ( 1 - 1 ) ( n

- 2 ) . . . . ( n - p + 1 ) , divided by the number of permutations of each combination

, or 1 . 2 . 3 . . . p , will give the number of combinations of n quantities ,

Therefore the latter , namely , the whole number of permutations , or n ( 1 - 1 ) ( n

- 2 ) . . . . ( n - p + 1 ) , divided by the number of permutations of each combination

, or 1 . 2 . 3 . . . p , will give the number of combinations of n quantities ,

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### Andre utgaver - Vis alle

A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ... Charles William Hackley Uten tilgangsbegrensning - 1846 |

A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ... Charles William Hackley Uten tilgangsbegrensning - 1847 |

A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ... Charles William Hackley Uten tilgangsbegrensning - 1849 |

### Vanlige uttrykk og setninger

according adding affected algebraic amount apply arrangement becomes binomial calculations called changed coefficients column common consequently considered contain corresponding cube denominator derived determine difference distance divide dividend division divisor elimination entire equal equation evident EXAMPLE exponent expression extract factors figures formula four fourth fraction functions give Given greater greatest Hence imaginary increased inequation infinite interest known least less letter limit logarithm manner means measure method modulus multiplied necessary negative obtain operation original permutations polynomial positive preceding present problem progression proportion proposed equation quotient radical ratio reduce remainder represent result rule satisfy second term simple solution square root substituting subtract successive suppose taken tens third tion transformed true unknown quantity variations Whence whole number write zero

### Populære avsnitt

Side 129 - ... two triangles are to each other as the products of their bases by their altitudes.

Side 172 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.

Side 107 - There will be as many figures in the root as there are periods in the given number.

Side 237 - B set out from two towns, which were distant 247 miles, and travelled the direct road till they met. A went 9 miles a day ; and the number of days, at the end of which they met, was greater by 3 than the number of miles which B went in a day. How many miles did each go ? 17.

Side 23 - 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 261 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Side 184 - It is required to divide the number 99 into five such parts, that the first may exceed the second by 3, be less than the third by 10, greater than the fourth by 9, and less than the fifth by 16.

Side 128 - When four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second, and so on, quadruplicate, &c.

Side 48 - Multiply all the numerators together for a new numerator, and all the denominators together for a new denominator.

Side 237 - There are two square buildings, that are paved with stones, a foot square each. The side of one building exceeds that of the other by 12 feet, and both their pavements taken together contain 2120 stones. What are the lengths of them separately ? Ans.