Sherwin's Mathematical Tables: Contriv'd After a Most Comprehensive Method: Containing, Dr. Wallis's Account of Logarithms, Dr. Halley's and Mr. Sharp's Ways of Constructing Them; with Dr. Newton's Contraction of Brigg's Logarithms ...

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W. & J. Mount, T. Page & son, 1761 - Logarithms - 110 pages
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Page 7 - And if the given number be a proper vulgar fraction ; subtract the logarithm of the denominator from the logarithm of the numerator, and the remainder will be the logarithm sought ; which, being that of a decimal fraction, must always have a negative index.
Page 15 - But the demonftration, as I conceive was never till now perfected, without the confideration of the Hyperbola, which, in a matter, purely arithmetical, as this is, cannot fo properly be applied. But what follows, I think I may more juftly claim as, my own, viz. that the Logarithm of the...
Page 11 - Now thefe rativncula are fb to be underflood as in a continued Scale of Proportionals infinite in Number between the two terms of the ratio, . which infinite Number of mean Proportionals is to that infinite Number of the like and equal...
Page 43 - ... the log. tangents of the half complements of the latitudes, is to the difference of longitude a ship makes in sailing on any rumb from the one latitude to the other, as the tangent of 51 38...
Page 41 - Seek the given difference of Latitude and Departure taken together in their columns, or the neareft numbers to them, and the Courfe is even therewith at the fide, and the diftance at the top and bottom : But if the given difference of Latitude and Departure cannot be found nearly, take i, f, sV.
Page 14 - If the curiosity of any gentleman that has leisure Would prompt him to undertake to do the logarithms of all prime numbers under 100,000 to 25 or 30 figures, I dare assure him that the facility of this method will invite him thereto; -nor can anything more easy be desired. And to encourage him, I here give the logarithms of the first prime numbers under 20 to 60 places.
Page 2 - In multiplication the work is the same as in whole numbers, only in the product j separate, with a point, so many figures to the right hand as there are fractional places both in the multiplicand and multiplier ; then all the figures on the left hand of the point make the whole number, and those on the right a decimal fraction.
Page 9 - Seffa declared, that he would be contented with this fmall one. So the Reward he had fix'd upon Was order'd to be given him : But the King was quickly...
Page 2 - In division the work is the same as in whole numbers ; only in the quotient, separate with a point, so many figures to the right hand, for a decimal fraction, as there are fractional places in the dividend, more than in the divisor, because there must be so many fractional places in the divisor and quotient together, as there are in the...
Page 17 - Logarithm, whether greater or lefTer, and call its number a if leflr, or b if greater than the given L, and the difference thereof from the faid neareft Logarithm you call /;. it will follow, that the Number anfwering to the Logarithm L will be either a into if 1-\-\П-\-\1г-{-^'\-,\^ &с.

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