Rudimentary Treatise on LogarithmsJohn Weale, 1853 - 68 páginas |
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Página 5
... raised or involved . Frequently letters are employed instead of numbers as ex- ponents of powers ; thus , a denotes that the quantity repre- sented by is to be raised to the power represented by a ; and b " , that the quantity b is to be ...
... raised or involved . Frequently letters are employed instead of numbers as ex- ponents of powers ; thus , a denotes that the quantity repre- sented by is to be raised to the power represented by a ; and b " , that the quantity b is to be ...
Página 6
... raised , that the new exponent will be equal to the product of the other two ; thus , in the above examples , 3 × 2 : 6 , therefore ( 3 ) 3 = x , and 3 × 3 = 9 , therefore ( x3 ) 3 a . The converse of this rule also holds good , for if ...
... raised , that the new exponent will be equal to the product of the other two ; thus , in the above examples , 3 × 2 : 6 , therefore ( 3 ) 3 = x , and 3 × 3 = 9 , therefore ( x3 ) 3 a . The converse of this rule also holds good , for if ...
Página 16
... = 1 + % . Extracting the root on both sides , we have , 1 b = ( 1 + 2 ) 2 , = and raising them to the power of r , it becomes b ' = ( 1 + z ) ž . Expanding by the Binomial Theorem , we have ጥ ጥ 10 RUDIMENTARY TREATISE.
... = 1 + % . Extracting the root on both sides , we have , 1 b = ( 1 + 2 ) 2 , = and raising them to the power of r , it becomes b ' = ( 1 + z ) ž . Expanding by the Binomial Theorem , we have ጥ ጥ 10 RUDIMENTARY TREATISE.
Página 18
... raised to the power of x , it becomes n * = ¿ 1 * ; then expanding * in terms of x , we obtain ( Prop . B , [ 2 ] ) 2 ηχ - 1 + A1x + 202 + A13 3 203 + + & c . 2 2.3 in which ( Prop . B , [ 3 ] ) a , = { ( n− 1 ) − ( n − 1 ) 2 + } 1 ...
... raised to the power of x , it becomes n * = ¿ 1 * ; then expanding * in terms of x , we obtain ( Prop . B , [ 2 ] ) 2 ηχ - 1 + A1x + 202 + A13 3 203 + + & c . 2 2.3 in which ( Prop . B , [ 3 ] ) a , = { ( n− 1 ) − ( n − 1 ) 2 + } 1 ...
Página 25
... raised to the power of k we have .k pl . * = q . = -p , and But qp , therefore pl . k 1. klog , q . log , p , must equal unity . PROPOSITION I. PROBLEM . To determine the value of log 。 ε , ε being the base of the Napierean system of ...
... raised to the power of k we have .k pl . * = q . = -p , and But qp , therefore pl . k 1. klog , q . log , p , must equal unity . PROPOSITION I. PROBLEM . To determine the value of log 。 ε , ε being the base of the Napierean system of ...
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Términos y frases comunes
added angle opposite annexed table Arith arithmetical complement arithmetical progression arithmetical series base Binomial Theorem calculation characteristic coefficient common logarithm comp constant number cube cubic feet cyphers decimal places decimal point deflexion denoted diameter diff difference divisor equal the area equal to unity equation example feet per second formulæ four figures fraction geometrical progression geometrical series given logarithm given number given sides HENRY LAW inches increment initial figures less logarithm less number loga logarithmic sine Logarithms of Numbers mantissa modulus multiplied natural number negative nth root number answering number corresponding number of integers number required number whose logarithm obtain Prime number PROPOSITION quantity quotient remainder rithm rule SCHOLIUM series of numbers significant figure sixth figure square root system of logarithms tables of logarithms THEOREM velocity weight ΙΟ λα
Pasajes populares
Página 5 - To divide powers of the same base, subtract the exponent of the divisor from the exponent of the dividend.
Página 28 - The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor.
Página 12 - The characteristic of the logarithm of 5673 is 3 ; of 73254 is 4, &c. The characteristic of the logarithm of a decimal fraction is a negative number, and is equal to the number of places by which its first significant figure is removed from the place of units. Thus the logarithm of .0046 is 3 plus a fraction ; that is, the characteristic of the logarithm is -3, the first significant figure, 4, being removed three places from units.
Página 45 - To Divide One Number by Another, Subtract the logarithm of the divisor from the logarithm of the dividend, and obtain the antilogarithm of the difference.
Página 29 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Página 6 - ... number by the exponent of the power, to which it is to be raised; the number in the table corresponding to this product, will be the power sought.
Página 46 - ADD the logarithms of the SECOND and THIRD terms, and .from the sum SUBTRACT the logarithm of the FIRST term.
Página 56 - Multiply the number of degrees in the arc by the area of the whole circle and divide by 360. Example. What is the area of a sector of a circle whose radius is 5 and length of arc 60°?
Página 47 - Divide the logarithm of the given number by the index of the root ; and the quotient will be the logarithm of the required root (Art.
Página 51 - Having two angles, and a side opposite to one of them-, to find the third angle.