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Logarithmologia or the whole doctrine of logarithms, common and logistical, in theory and practice. In three parts / [Benjamin Martin].

  • Benjamin Martin
Date:
1740
Catalogue details

Licence: Public Domain Mark

Credit: Logarithmologia or the whole doctrine of logarithms, common and logistical, in theory and practice. In three parts / [Benjamin Martin]. Source: Wellcome Collection.

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    fappofe a Series of Numbers in Arithmetical Progref fion, beginning from o, and whofe Ratio, or com¬ mon Difference, is Unity or i ; and to them be adapted a Series in Geometrical Progrejfion, beginning from Unity ; and whofe common Ratio be any af- fign’d Number, fuppofe 2, as before ; then will thofe two Series ftand as below : S Arith. o. 1.2.3. 4. 5. 6. 7. 8. gGfc. VIZ. I Qeom.i. 2.4. 8.16. 32. 64.128. 256. 512.^5?^, 8. ’Tis evident the Numbers in the firft Series fliew the Number of Ratio’s between their corre- fpondent Numbers and Unity in the fecond Series. For inftance, the Figure 2 in the firft Series, fhews the Ratio’s between its correfponding Number 4 and I, in the lower Series, are 2 ; the Numbers 5, 7, 9, in the upper Series, fhew the Number of Ratio’s be¬ tween their correfponding Numbers 32, 128, 512, and I or Unity, in the lower Series, to be refpecftively 5, 7, and 9 ; or that the Ratio is fo often repeated from Unity to thofe Numbers, and confequently fo often compounded in them *, or farther, that the Ratio of 32 to I is compounded of five times the Ra¬ tio of 2 to I ; and the Ratio of 128 to i, of feven times the Ratio of 2 to i ; and the Ratio of 512 to I, of nines times the Ratio of 2 to i. 9. Wherefore fince the Numbers in the upper Se¬ ries ftiew the Number of Ratio’s contain’d between their correfponding Numbers and Unity in the lower Series ; therefore thofe Numbers in the upper Series in Arithmetical Progreftion fhall be the Logarithms of the Numbers in the lower Series of Geometrical Progreftion, and that according to the Definition of J^ogarithms beforegoing. 10. From the faid Series, ’tis farther manifeft, that the Produdl of any two Terms in the lower Series correfponds to the Sum of their refpedive Terms in thq upper Series. See the following Ex¬ amples. Arith.