## Mathematical Tables: Contrived After a Most Comprehensive Method: Viz, a Table of Logarithms, from 1 to 101000. To which is Added (upon the Same Page) the Differences and Proportional Parts, Whereby the Logarithm of Any Number Under 10,000,000 May be Easily Found. Tables of Natural Sines, Tangents, and Secants ... Tables of Natural Versed Sines ... With Their Construction and Use |

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Page 14 - 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 18 - 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 17 - Direction of the Theorem, efpecially where x is fmall and Integer, referving the proper Quotes to be added together, when you have produced your Logarithm to as many Figures as you defire : Of which Method I will give a Specimen.

Page 14 - ... the Logarithm of the one Ratio is to the Logarithm of the other. Thus if there be fuppofed between i and ю an infinite Scale of Mean Proportionals, whofe Number is IOOOOOC^T.

Page 14 - Number. So that Logarithms thus produced, may be of as many Forms as you pleafe to aflume infinite Indices of the Power •whofe Root you feek : as if the Index be fuppofed 100000, &c.

Page 20 - Logarithm, whether greater or lefTer, and call its number a if leflèr, 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.

Page 11 - BCD. But if the angle included be oblique, add the logarithm of the difference of the given sides to the tangent of half the sum of the unknown angles, and from the sum subtract the logarithm of the sum of the given sides, or add its complement ; the remainder or sum will be the tangent of half their difference. Example. In the triangle ABC, having the...

Page 15 - 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 21 - ... this be a matter purely arithmetical, nor properly demonftrable from the principles of geometry. Nor have I been obliged to have recourfe to the method of indivifibles, or the arithmetick of infinites, the whole being no other than an eafy corollary to Mr. Newton's General Theorem for forming Roots and Powers.

Page 16 - ... 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...