Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval School, PhiladelphiaPerkins & Purves, 1843 - 92 páginas |
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Página 38
... decimals only , this term , as well as all the succeeding terms , may be neglected . Therefore we have $ 28 = 3 ( 1+ ; = 3 × 1.0122 = 3.0366 nearly . We divided 28 into two such parts that one of them was an ex- act power of the third ...
... decimals only , this term , as well as all the succeeding terms , may be neglected . Therefore we have $ 28 = 3 ( 1+ ; = 3 × 1.0122 = 3.0366 nearly . We divided 28 into two such parts that one of them was an ex- act power of the third ...
Página 40
... decimals . This term will be 2.828428 X 1 ( 4951184 ) X ; 2x22 ( 2828428 ) * which may be expressed approximately thus , 3 ( 5,000,000 ) * X- 3 × ( 5 × 106 ) 75 1 10 ^ ( 8,000,000,000,000 ) 3 ̄10 × ( 8 × 1012 ) 2 ̄64 × 10131012 ° 51 ...
... decimals . This term will be 2.828428 X 1 ( 4951184 ) X ; 2x22 ( 2828428 ) * which may be expressed approximately thus , 3 ( 5,000,000 ) * X- 3 × ( 5 × 106 ) 75 1 10 ^ ( 8,000,000,000,000 ) 3 ̄10 × ( 8 × 1012 ) 2 ̄64 × 10131012 ° 51 ...
Página 42
... decimals ; and let x be the correction to be added to a , or the difference between a and the true root ; then the first significant figure of x must be in the ( n + 1 ) th place , and a + x represents the true root of N ; that is , N ...
... decimals ; and let x be the correction to be added to a , or the difference between a and the true root ; then the first significant figure of x must be in the ( n + 1 ) th place , and a + x represents the true root of N ; that is , N ...
Página 46
... decimal form 2.7 102.7-500 . and we may write 55. As another example take the equation 8x = 20 , in which x is evidently between 1 and 2 . 1 Let x = 1 + then we have x ' 1 81+ 20 5 = = 20 , or 8 - l or 2 ' To ( 5 ) -8 , = in which x is ...
... decimal form 2.7 102.7-500 . and we may write 55. As another example take the equation 8x = 20 , in which x is evidently between 1 and 2 . 1 Let x = 1 + then we have x ' 1 81+ 20 5 = = 20 , or 8 - l or 2 ' To ( 5 ) -8 , = in which x is ...
Página 47
... decimals . Taking the decimals to two places , it is approximately ( 1.19 ) ' = 1.28 in which " " is found to be between ... decimal form of the exponent 1.44 , we may remark that 44 it is equal to 1 or 144 and may EXPONENTIAL EQUATIONS . 47.
... decimals . Taking the decimals to two places , it is approximately ( 1.19 ) ' = 1.28 in which " " is found to be between ... decimal form of the exponent 1.44 , we may remark that 44 it is equal to 1 or 144 and may EXPONENTIAL EQUATIONS . 47.
Outras edições - Ver tudo
Binomial Theorem and Logarithms: For the Use of the Midshipmen At the Naval ... William Chauvenet Pré-visualização limitada - 2024 |
Binomial Theorem and Logarithms: For the Use of the Midshipmen At the Naval ... William Chauvenet Pré-visualização limitada - 2024 |
Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval ... William Chauvenet Pré-visualização indisponível - 2017 |
Palavras e frases frequentes
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
Passagens conhecidas
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.