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, ... The Third Edition. Carefully Revised and Corrected, by William Gardiner

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William Mount and Thomas Page, 1742 - Logarithms - 110 pages
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Page 34 - Wherefore to the complement of the confiant log. ю 1015104, add the log. of ihe difference of the log. tangents of the half complements of the latitudes, and the log. tangent of the courfe, the fum (abating radius) will be the log. of the difference of longitude in minutes. Example. Given the latitudes 49 55...
Page 47 - Number propofed, there be taken any infinity of mean Proportionals, the infinitely little augment or decrement of the firft of thofe means...
Page 35 - 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 7 - 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 31 - 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 17 - ... 2-2951271 log. of 197-3 9-8961369 sin. of 51 56' 2-4012760 log. 251-9278, as before. But if one side and the angles of a right-angled triangle be known, and you would have the other side, as in the former example, the operation will be easier thus : Add the tangent of the angle opposite to the side required, to the logarithm of the given side, the sum (abating radius) is the logarithm of the side re* quired. 10-1061489 tan. 51 56
Page 50 - Curiofity of any Gentleman that has leifure, would prompt him to undertake to do the Logarithms 'of all Prime Numbers under...
Page 7 - 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 47 - 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 47 - Momentum is directly ; that is, the Logarithm of each Ratio will be as the Fluxion thereof. Wherefore if the Root of any infinite Power be extracted out of any Number, the Differcntiola of the faid Root from Unity, haJl be as the Logarithm ofthat Number. So that Logarithms thus...

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