Binomial Theorem and Logarithms: For the Use of the Midshipmen at the Naval School, PhiladelphiaPerkins & Purves, 1843 - 92 páginas |
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Página 15
... represent- ing a fraction in the same form with whole numbers . In the same way we shall find 1 1 ; - 1 We see then that the negative exponent indicates the reciprocal EXPONENTS IN GENERAL . 15 CHAPTER II EXPONENTS IN GENERAL,
... represent- ing a fraction in the same form with whole numbers . In the same way we shall find 1 1 ; - 1 We see then that the negative exponent indicates the reciprocal EXPONENTS IN GENERAL . 15 CHAPTER II EXPONENTS IN GENERAL,
Página 16
... reciprocal of a power ; that is , a- is the reciprocal of a ; a is the recipro- cal of a1 ; a ― m is the reciprocal of am , & c . 21. We apply the rules given in the preceding chapter also to fractional and negative exponents . Thus ...
... reciprocal of a power ; that is , a- is the reciprocal of a ; a is the recipro- cal of a1 ; a ― m is the reciprocal of am , & c . 21. We apply the rules given in the preceding chapter also to fractional and negative exponents . Thus ...
Página 17
... reciprocals of each other ; thus , a1 is the reciprocal of a1 , a3 of a - 2 , & c . , and am of a - m . The term ao is found ( as the other terms are found ) by subtract- ing 1 from the exponent of the preceding term , 3 EXPONENTS IN ...
... reciprocals of each other ; thus , a1 is the reciprocal of a1 , a3 of a - 2 , & c . , and am of a - m . The term ao is found ( as the other terms are found ) by subtract- ing 1 from the exponent of the preceding term , 3 EXPONENTS IN ...
Página 53
... log . 1 = 0 . This follows also from Art . 60 ; for log . bx1 = log . b + log . 1 , and bx1 is b ; so that this equation is simply log.blog.blog . 1 , or 0 = log . 1 . 65. The logarithm of the reciprocal of a number is LOGARITHMS . 53.
... log . 1 = 0 . This follows also from Art . 60 ; for log . bx1 = log . b + log . 1 , and bx1 is b ; so that this equation is simply log.blog.blog . 1 , or 0 = log . 1 . 65. The logarithm of the reciprocal of a number is LOGARITHMS . 53.
Página 54
... reciprocal of a number is the loga- rithm of that number taken negatively . For b being any number , we have whence we have a log . bb , 1 1 a log . b b ' or by Art . 20 that is , a - log b 1 log . b - = 1 b ' log . b . This also ...
... reciprocal of a number is the loga- rithm of that number taken negatively . For b being any number , we have whence we have a log . bb , 1 1 a log . b b ' or by Art . 20 that is , a - log b 1 log . b - = 1 b ' log . b . This also ...
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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.