## Logarithmic and Other Mathematical Tables: With Examples of Their Use and Hints on the Art of Computation |

### Other editions - View all

### Common terms and phrases

9 Prop algebraic sign ÅRE arithmetical complement cent co-log column complementary angle computation con air corresponding number cosec cosine cotangent Cotg decimal point Diff Entering the table equation Example EXERCISES fifth find log find the logarithm find the number find the sine five places formula fourth figure give log given logarithm given number half a unit HARVARD COLLEGE OBSERVATORY increase interpolation last figure log a log log a+b log cot log sec log sin log sine loga logarithms of numbers mantissa minuend natural number negative number corresponding order of differences places of decimals present value quantities quotient rate of interest result rithms second differences sidereal sin A sin sine N sine or tangent sixth figure square Stirling's formula subtracted logarithm suppose Tang trigonometric functions unity write wwww wwww wwwww Δεν Δίν ΙΟ ΙΟΙ ΤΟ ន ន ន

### Popular passages

Page 4 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.

Page 4 - Since the logarithm of 1 is 0 and the logarithm of a quotient is obtained by subtracting the logarithm of the divisor from that of the dividend...

Page 34 - To find the trigonometric functions corresponding to an angle between 45° and 90°, we take the degrees at the bottom of the page and the minutes in the right.hand column. The...

Page 53 - Conventionally the period is divided into 24 hours, each hour into 60 minutes, and each minute into 60 seconds.

Page 33 - In the case of tangent and cotangent, only one column of differences is necessary for both functions. If we use no fractional parts of minutes, no interpolation is necessary; but if decimals of a minute are employed, we can interpolate precisely as in taking out the logarithms of numbers. Where the differences are very small they are sometimes omitted. Tables of proportional parts are given in the margin, the use o}.

Page 8 - ... immediately following the decimal point. Thus the characteristic of the logarithm of any number between 1 and 10 is 0, between 10 and 100 1, between 100 and 1000 2, etc. Or let it be asked, " What is the characteristic of the logarithm of 5126 ? " Now this number lies between 1000 and 10000, hence its logarithm lies between 3 and 4, and is, therefore, 3 and some fraction. Again, as to the numerical value of the characteristic of the...

Page 50 - Consequently, when the remainder is less than 'twice the part of the root already found, plus unity, the last figure can not be increased. Extract the square root of the following numbers. 1. 4225 Ans.

Page 32 - If che angle of which a function is sought is less than 45°, we seek the number of degrees at the top of the table and the minutes in the left.hand column.

Page 27 - Divide the given amount by the amount o/$l, at the given rate per cent., for the given time. REMARK. — This rule is deduced from the fact that the amount of different principals for the same time and at the same rate per cent., are to each other as those principals. BANK DISCOUNT. Bank...

Page 3 - NUMBERS. 1. Introductory Definitions. Natural numbers are numbers used to represent quantities. The numbers used in arithmetic and in the daily transactions of life are natural numbers. To every natural number may be assigned a certain other number, called its logarithm. The logarithm of a natural number is the exponent of the power to which some assumed number must be raised to produce the first number. The assumed number is called the base- Eg, the logarithm of 100 with the base 10 is 2, because...