## Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval School, Philadelphia |

### Dentro del libro

Página 11

The product of a ' and bs is abs ; the a ? quotient of a divided by 63 is Sometimes quantities to be multiplied or divided contain powers of the same quantity ; these may be multiplied or divided by the above

The product of a ' and bs is abs ; the a ? quotient of a divided by 63 is Sometimes quantities to be multiplied or divided contain powers of the same quantity ; these may be multiplied or divided by the above

**rules**, and the operation ... Página 12

Thus , V30abc = 5.477a7bc nearly . 14. Thus far we have said nothing of the signs of powers and roots . If we involve -a to the 2d power , we have ( -a ) x ( -a ) , which , 1 -a . by the

Thus , V30abc = 5.477a7bc nearly . 14. Thus far we have said nothing of the signs of powers and roots . If we involve -a to the 2d power , we have ( -a ) x ( -a ) , which , 1 -a . by the

**rules**of multiplication , is + 12 POWERS AND ROOTS . Página 13

-a . by the

-a . by the

**rules**of multiplication , is + aa or + a ” ; but if we involve --a to the 3d power , we have ( -a ) x ( -a ) x ... and the 5th root of -as will be Hence the**rule**, the even root of a positive quantity is either positive or ... Página 15

In the preceding chapter we have applied the

In the preceding chapter we have applied the

**rules**for the multiplication , division , & c . of powers only to those ... We have seen that this would be var , but algebraists have agreed to apply to such cases the general**rule**for the ... Página 16

We apply the

We apply the

**rules**given in the preceding chapter also to fractional and negative exponents . Thus , to multiply at by at we add the exponents ( Art . 5 ... Applying the**rule**for division of powers , ( Art . 6 , ) we have a } = a2 .### Comentarios de la gente - Escribir un comentario

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Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ... William Chauvenet Sin vista previa disponible - 2017 |

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3d root 4th power 4th root according adding apply approximate assumed base becomes binomial theorem Briggs calculation called CHAPTER characteristic coefficients common compute construction contain convenient convergent correct corresponding cube root decimal demonstration denominator derive determined difference divided division effected employed equal equation evident evolution example expand exponential equation exponents express extract factor find the value formula fraction fractional exponents given gives greater Hence indefinitely integral involution involve known less loga manner method modulus multiply naperian logarithm nearly negative neglected Newton number of terms obtain operation places places of decimals positive preceding principle quantity quotient reciprocal reduced remainder rendered repeated represent result rithms rule shown significant figure simply square root substitute subtracting succeeding terms successively third true uneven unity whence

### Pasajes populares

Página 50 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Página 49 - The logarithm of the product of two or more numbers is equal to the sum of the logarithms of those numbers.

Página 61 - The fourth term is found by multiplying the second and third terms together and dividing by the first § 14O.

Página 50 - The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor.

Página 19 - Cxz+, etc.=A'+B'x+C'z2 + , etc., must be satisfied for each and every value given to x, then the coefficients of the like powers of x in the two members are equal each to each.

Página 74 - The logarithm of a number in any system is equal to the Naperian logarithm of that number multiplied by the modulus of the system.

Página 49 - Corollary. When the base is less than unity, it follows, from art. 3, that the logarithms of all numbers greater than unity are negative, while those of all numbers less than unity are positive. But when, as is almost always...

Página 55 - ... place, the characteristic being positive when this figure is to the left of the units' place, negative when it is to the right of the units' place, and zero when it is in the units

Página 27 - I have no doubt that he made the difcovery himfelf, without any light from Briggs, and that he thought it was new for all powers in general, as it was indeed for roots and quantities with fractional and irrational exponents.

Página 50 - Bee that to divide one number by another, we subtract the log. of the divisor from the log. of the dividend, and the remainder is the log.