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

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Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ... William Chauvenet No preview available - 2017 |

### Common terms and phrases

3d root 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 denominator determined difference divided division effected employed equal equation evident evolution example expand exponential equation exponents express extract factor find log find the value formula fraction 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 represent result rithms root of aČ rule shown significant figure simply square root substitute subtracting succeeding terms third true unity whence

### Popular passages

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

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

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

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

Page 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.

Page 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.

Page 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...

Page 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

Page 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.

Page 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.