Rudimentary Treatise on LogarithmsJohn Weale, 1853 - 68 páginas |
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Página 10
... greater than 1 , but less than 10 , must be some fraction , whose value lies between 0 and 1 ; and in like manner that , since the logarithm of 100 is 2 , the loga- rithm of any intermediate number between 10 and 100 , must have a value ...
... greater than 1 , but less than 10 , must be some fraction , whose value lies between 0 and 1 ; and in like manner that , since the logarithm of 100 is 2 , the loga- rithm of any intermediate number between 10 and 100 , must have a value ...
Página 11
... greater than 1 , but less than 10 , is 1 , 99 100 , 2 , " " 99 10 , 99 99 99 100 , 99 1000 , 3 , " " 99 1000 , 99 10000 , 4 , & c . " " & c . & c . By way of further illustration , we will take the number 67854 , and successively divide ...
... greater than 1 , but less than 10 , is 1 , 99 100 , 2 , " " 99 10 , 99 99 99 100 , 99 1000 , 3 , " " 99 1000 , 99 10000 , 4 , & c . " " & c . & c . By way of further illustration , we will take the number 67854 , and successively divide ...
Página 12
... greater by unity than the number of noughts following the decimal point . Instead of writing , as we have above , 0.8315763 , the characteristic is placed to the left of the mantissa , with the negative sign above it , thus 3-831576 ...
... greater by unity than the number of noughts following the decimal point . Instead of writing , as we have above , 0.8315763 , the characteristic is placed to the left of the mantissa , with the negative sign above it , thus 3-831576 ...
Página 27
... greater than the sum of all the succeeding terms , and therefore 1 log ( 1⁄2 + 1 ) = log ( 8 + 1 ) — log b < 1 1 Α ́ Τ ... [ 2 ] . That is , the difference between the logarithms of two num- bers differing by unity , is less than the ...
... greater than the sum of all the succeeding terms , and therefore 1 log ( 1⁄2 + 1 ) = log ( 8 + 1 ) — log b < 1 1 Α ́ Τ ... [ 2 ] . That is , the difference between the logarithms of two num- bers differing by unity , is less than the ...
Página 31
... greater than the number of cyphers which originally stood between that significant figure and the decimal point . - Therefore the negative characteristic of the logarithm of a decimal fraction , is one greater than the number of cyphers ...
... greater than the number of cyphers which originally stood between that significant figure and the decimal point . - Therefore the negative characteristic of the logarithm of a decimal fraction , is one greater than the number of cyphers ...
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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.