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
... evolution is the inverse of involution . In general the nth root mn of amn is an or am . 10. The involution and evolution of the product or quotient of powers are effected in the same manner . The 4th power of a2b3 is asb12 ; the 5th ...
... evolution is the inverse of involution . In general the nth root mn of amn is an or am . 10. The involution and evolution of the product or quotient of powers are effected in the same manner . The 4th power of a2b3 is asb12 ; the 5th ...
Página 12
... evolution may always be performed upon these , and the result prefixed to the literal part . Thus , the 3d root of 8a 32a10b is 2ỷa ; the square root of 16a3b is 4a√✓ab ; the 5th root of is 2a2 5 b - C Sometimes it is convenient to ...
... evolution may always be performed upon these , and the result prefixed to the literal part . Thus , the 3d root of 8a 32a10b is 2ỷa ; the square root of 16a3b is 4a√✓ab ; the 5th root of is 2a2 5 b - C Sometimes it is convenient to ...
Página 15
... evolution of powers given in Art . 9. To extract the 3d root of a2 , according to this rule , we divide the exponent by 3 , which gives a3 ; therefore , a3 and a are equivalent expressions , both signifying " the 3d root of a squared ...
... evolution of powers given in Art . 9. To extract the 3d root of a2 , according to this rule , we divide the exponent by 3 , which gives a3 ; therefore , a3 and a are equivalent expressions , both signifying " the 3d root of a squared ...
Página 16
... involution of powers , ( Art . 8 , ) we have 3 ( af ) 3 = a * × 3 = a§ . m m Хр mp ( an ) = an = an ( a ― m ) n — a — mn . ( am ) —n — a — mn . ( am ) —namn . 24. Applying the rule for evolution of powers , ( 16 EXPONENTS IN GENERAL .
... involution of powers , ( Art . 8 , ) we have 3 ( af ) 3 = a * × 3 = a§ . m m Хр mp ( an ) = an = an ( a ― m ) n — a — mn . ( am ) —n — a — mn . ( am ) —namn . 24. Applying the rule for evolution of powers , ( 16 EXPONENTS IN GENERAL .
Página 17
... evolution of powers , ( Art . 9 , ) we have 1 1 √8a2a + 3—2a . = m m √a ^ = anp . mq 1 25. By using fractional exponents involution and evolution are performed by the same rule ; that is , by multiplying the exponents . Thus , the ...
... evolution of powers , ( Art . 9 , ) we have 1 1 √8a2a + 3—2a . = m m √a ^ = anp . mq 1 25. By using fractional exponents involution and evolution are performed by the same rule ; that is , by multiplying the exponents . Thus , the ...
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.