Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval School, PhiladelphiaPerkins & Purves, 1843 - 92 páginas |
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Página 11
... involve a2 to the 3d power , we are to take a three times as a factor , which is a xaxa , or a2 + 2 + 9 , or a® , ( Art . 5 , ) that is , the 3d power of a2 is a with the exponent 2 × 3 . ..... In general the nth power of am is amn ...
... involve a2 to the 3d power , we are to take a three times as a factor , which is a xaxa , or a2 + 2 + 9 , or a® , ( Art . 5 , ) that is , the 3d power of a2 is a with the exponent 2 × 3 . ..... In general the nth power of am is amn ...
Página 12
... ✓30a2bc = 5.477abc 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 , by the rules of multiplication , is + aa or 12 POWERS AND ROOTS .
... ✓30a2bc = 5.477abc 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 , by the rules of multiplication , is + aa or 12 POWERS AND ROOTS .
Página 13
... involve -a 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 is —a3 , & c . ; the even powers being positive and the ...
... involve -a 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 is —a3 , & c . ; the even powers being positive and the ...
Página 14
... Involve -b to the nth power . 5. Involve -b to the ( 2n ) th power . Ans . ( ab ) . Ans . + b ifn is even , —b " if n is uneven . Ans . +62 ( for 2n is even whatever be the value of n . ) 6. Involve -b to the ( 2n + 1 ) th power . Ans ...
... Involve -b to the nth power . 5. Involve -b to the ( 2n ) th power . Ans . ( ab ) . Ans . + b ifn is even , —b " if n is uneven . Ans . +62 ( for 2n is even whatever be the value of n . ) 6. Involve -b to the ( 2n + 1 ) th power . 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.bbr . But a log.b " b " , whence the equation 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.bbr . But a log.b " b " , whence the equation 52 LOGARITHMS .
Otras ediciones - Ver todas
Binomial Theorem and Logarithms: For the Use of the Midshipmen At the Naval ... William Chauvenet Vista previa limitada - 2024 |
Binomial Theorem and Logarithms: For the Use of the Midshipmen At the Naval ... William Chauvenet Vista previa limitada - 2024 |
Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ... William Chauvenet Sin vista previa disponible - 2017 |
Términos y frases comunes
2n³ 3n³ 3d power 3d root 4th power 4th root Algebra anti-logarithms approximate ax=b binomial theorem Briggs calculation CHAPTER common logarithms compute convenient convergent cube root decimal fraction decimal point denominator example exponential equation express the value find log find the square find the value finite number formula becomes fractional exponents given logarithm given number Hence Hutton indefinitely small infinite series integral exponents involution and evolution log.b loga m+1)th term manner method modulus multiply naperian logarithm Newton number is equal number of terms obtain places of decimals positive integer power of a+b power or root powers and roots prime numbers quantity reciprocal rithms root of a³ significant figure square root succeeding terms system of logarithms system whose base uneven unit's place unity values substituted 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.