Mathematical Tables: Comprising Logarithms of Numbers, Logarithmic Sines, Tangents, and Secants, Natural Sines, Meridional Parts, Difference of Latitude and Departure, Astronomical Refractions, &c

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Benjamin B. Mussey, 1842 - Logarithms - 11 pages

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Page 4 - Greek proportion, and apie/nf;, number). " The logarithms of numbers are the exponents of the different powers to which a constant number must be raised, in order to be equal to those numbers ; the principles, therefore, which apply to exponents in general, apply to logarithms." To constitute a logarithm, it is necessary that the exponent should refer to a system or series. These exponents, therefore, constitute a series of numbers in arithmetical proportion, corresponding to as many others in geometrical...
Page 4 - ... Hence we see that the logarithms of most numbers must consist of two parts, an integral part and a decimal part. The former part is called the characteristic or index of the logarithm. The characteristic may always be determined by the following RULE. The characteristic of the logarithm of any number is equal to the number of places by which the first significant figure of that number is removed from the units...
Page 4 - That is, to multiply numbers, we add their logarithms; to divide, we subtract the logarithm of the divisor from that of the dividend ; to raise a number to any power, we multiply its logarithm by the exponent of that power; and to extract the root of any number, we divide its logarithm by the number expressing the root to be found.
Page 52 - I .64301 .76586 .65628 •75452 .66935 .74295 .68221 .73116 .69487 .71914 59 2 .64323 •76567 .65650 •75433 .66956 .74276 .68242 .73096 .69508 .71894 58 3 .64346 .76548 .65672 •75414 .66978 .74256 .68264 .73076 •69529...
Page 47 - II 10 g 8 7 6 5 4 3 2 1 0 Cosine. Sine. Cosine. Sine. Cosine. Sine. Cosine. Sine. Cosine. Sine.
Page 2 - ... Tangents, and Secants, Natural Sines, Meridional Parts, Difference of Latitude and Departure, Astronomical Refractions, &c. By SP Miles and T. Sherwin. Stereotype Edition. 8vo. pp. 88. $ 0 88 " The tables comprised in this volume have been very carefully compared with the best English and French . tables ; and they will be found, it is believed, not inferior, in point of correctness, to any similar tables in use. Prefixed is a short introduction, explanatory chiefly of the methods of using them.
Page 5 - Naperian logarithms muy be calculated with a very small fraction of the labour which they cost their inventor. This having been done for all whole numbers within the given limits, the logarithm of any fraction is readily found by subtracting the logarithm of the denominator from that of the numerator. It must be admitted that Briggs, by his construction of the decimal system, divides with Napier the merit of inventing logarithms, considered as an instrument of calculation. In the Naperian system...
Page 11 - The Miles and Parts of a Mile in a Degree of Longitude at every Degree of Latitude.
Page 9 - It is to be observed that when the two places are on the same side of the equator, the...
Page 7 - From 0 to 45, the degrees are placed at the top of the page and the minutes in the column headed

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