Rudimentary Treatise on Logarithms
John Weale, 1853 - Logarithms - 68 pages
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Common terms and phrases
added addition angle answering applied argument Arith arithmetical complement base becomes calculation called CHAPTER characteristic column common comp constant number contained continual corresponding cube cubic cyphers decimal definition denoted derived described diameter difference divided employed enters equal equation example exponent expression factor feet fifth figures five four fraction geometrical given greater half head II II II inches increase increment integer length less less logarithm loga logarithm look manner mantissa multiplied Napierean natural number negative obtain opposite performed places portion Prime number progression Prop proportional PROPOSITION quantity quotient raised ratio remainder result rithm root rule SCHOLIUM series of numbers shown sides significant figure solidity square subtract surface system of logarithms taken THEOREM true units unity weight
Page 5 - To divide powers of the same base, subtract the exponent of the divisor from the exponent of the dividend.
Page 28 - The logarithm of the quotient of two numbers is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 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.
Page 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.
Page 29 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 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.
Page 46 - ADD the logarithms of the SECOND and THIRD terms, and .from the sum SUBTRACT the logarithm of the FIRST term.
Page 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°?
Page 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.
Page 51 - Having two angles, and a side opposite to one of them-, to find the third angle.