Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval School, Philadelphia |
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Página 11
Thus , to involve a2 to the 3d power , we are to take a three times as a factor , which is a3 × a3 × a3 , or a2 + 2 + 2 , or ao , ( Art . 5 , ) that is , the 3d power of a3 is a with the exponent 2 × 3 . In general the nth power of am ...
Thus , to involve a2 to the 3d power , we are to take a three times as a factor , which is a3 × a3 × a3 , or a2 + 2 + 2 , or ao , ( Art . 5 , ) that is , the 3d power of a3 is a with the exponent 2 × 3 . In general the nth power of am ...
Página 12
Thus , ✓30abc = 5.477a / bc 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 ) × ( -a ) , which , -a by the rules of multiplication , is + aa 12 POWERS AND ...
Thus , ✓30abc = 5.477a / bc 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 ) × ( -a ) , which , -a by the rules of multiplication , is + aa 12 POWERS AND ...
Página 13
-a by the rules of multiplication , is + aa or + a2 ; but if we involve to the 3d power , we have ( —a ) × ( —a ) × ( —a ) , which , by the same rules , is -aaa or — a3 . It is evident that the 4th power of a is + a * ; the 5th power of ...
-a by the rules of multiplication , is + aa or + a2 ; but if we involve to the 3d power , we have ( —a ) × ( —a ) × ( —a ) , which , by the same rules , is -aaa or — a3 . It is evident that the 4th power of a is + a * ; the 5th power of ...
Página 14
Involve -b to the nth power . - 5. Involve -b to the ( 2n ) th power . Ans . + ben ( for 2n is even whatever be the value of n . ) EXAMPLES . Ans . xm + n + rym + n + ezm + nte or ( xyz ) m + n + r . Ans . ( xm ― nyn - z — m ) P . Ans ...
Involve -b to the nth power . - 5. Involve -b to the ( 2n ) th power . Ans . + ben ( for 2n is even whatever be the value of n . ) EXAMPLES . Ans . xm + n + rym + n + ezm + nte or ( xyz ) m + n + r . Ans . ( xm ― nyn - z — m ) P . Ans ...
Página 52
Involve this equation to any power , as the nth . The first member is involved by multiplying the exponent log . b by n , according to Art . 8 , and we have an log.b = b " . 1 * 1 a log.b " = b " , a log.bn But 52 LOGARITHMS .
Involve this equation to any power , as the nth . The first member is involved by multiplying the exponent log . b by n , according to Art . 8 , and we have an log.b = b " . 1 * 1 a log.b " = b " , a log.bn But 52 LOGARITHMS .
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Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ... William Chauvenet Sin vista previa disponible - 2017 |
Términos y frases comunes
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 a² rule shown significant figure simply square root substitute subtracting succeeding terms third true 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.
Información bibliográfica
| Título | Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval School, Philadelphia |
| Autor | William Chauvenet |
| Editor | Perkins & Purves, 1843 |
| Procedencia del original | Universidad de Harvard |
| Digitalizado | 1 Mar 2007 |
| Largo | 92 páginas |
| Exportar cita | BiBTeX EndNote RefMan |