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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William Gardiner
W. Mount, and T. Page, 1742 - Logarithms - 110 pages
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This is a fascinating book. I have a an origional copy dated 1717 and printed in Tower Hill, London.
It is in three sections. The first is " Of Logarithms, Their Invention and Use" the second part is
the actual "Mathmatical Tables" which is nearly 300 pages of tables consisting of Logarithms, NaturalSines, Tangents and Secants, Tables of natural Versed Sines and a Table of Difference of Lattitude. these were printed by S Bridge at Hermitage Stairs in Wapping in 1705. The final section is titled "some uses of the preceding Tables. This section is has a final passage entitled "The propositions of Navigation that occur in the Practice of Sailing by Mercator.
This is all bound in one old volume and I would love to know more about it

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Page 2 - ... 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 45 - But it is to be noted, that both the complements of the latitudes are to beeilimated from the fame pole of the world ; which may be from either ; and therefore if one latitude be N, and the other s, to have their complements, you muft add 90 to one of them, and fubtra<St the other from 90, and then the operation will be the fame as in the preceding cafes.
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 - ... 9" with the meridian. And 3dly. That the differences of longitude on different rumbs, are to one another as the tangents of the angles of those rumbs with the meridian. Hence it follows, that the difference of 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 11 - EVOLUTION BY LOGARITHMS. RULE. Divide the logarithm of the number by the index of the power; the quotient will be the logarithm of the root sought. But if the power whose root is to be extracted is a decimal fraction less than unity, prefix to the index of its logarithm a figure less by one than the index of the power...
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 13 - Step alone is capable to give the Logarithm of any intermediate Number, true to all the Places of thofe Tables. After the fame manner, may the Difference of the faid two...
Page 46 - Alfo when both Latitudes are of the fame name, (that is both North, or both South) you may add 90 degrees to each of them, the difference of the...
Page 12 - Now, though the Notion of an Infinite Power may feem very ftrange, and to thofe that know the difficulty of the Extraction of the Roots of High Powers, perhaps impracticable ; yet by the help of that admirable Invention of Mr.
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.

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