Elements of geometry / from the Latin translation of Commandine. To which is added, a treatise of the nature of arithmetic of logarithms, likewise another of the elements of plain and spherical trigonometry; with a preface ... By Doctor John Keil ... The whole revised ... [with a] preface, by Samuel Cunn.

  • Euclid
Date:
1741
Catalogue details

Licence: Public Domain Mark

Credit: Elements of geometry / from the Latin translation of Commandine. To which is added, a treatise of the nature of arithmetic of logarithms, likewise another of the elements of plain and spherical trigonometry; with a preface ... By Doctor John Keil ... The whole revised ... [with a] preface, by Samuel Cunn. Source: Wellcome Collection.

    391/465 (page 338)
    tinual Proportionals, their Diftances from each other fhall be equal to. one another. And fo it is manifeft, that the Diftanceof the Square from Unity, is double of the Diftance of its Root from the fame: Alfo the Diftance of the Cube is triple of the Diflance of its Root; and the Diftance of the Biquadrate, is quadru¬ ple of the Diftanceof its Root from Unity, <&c. And fo, if the Logarithm of any Number be doubled, we fhall have the Logarithm of its Square; if it be tripled, we fhall have the Logarithm of its Cube; and if it be quadrupled, the Logarithm of its Biquadrate. And contrariwife, if the Logarithm of any Number be bi~ feded, we fhall have the Logarithm of the fquare Root thereof: Moreover, a third Part of the faid Loga¬ rithm will be the Logarithm of the Cube Root of the Number; and a fourth Part, the Logarithm of the Bi¬ quadrate Root of that Number. Hence, the Extradions of all Roots are eafily per¬ formed, by dividing a Logarithm into as many Parts as there are Units in the Index of the Power. So if you want the Square Root of 5, the half of 0,6989700 muft be taken, and then that half o. 3494850 will be the Logarithm of the Square Root of 5, or the Logarithm of V 5> to which the Number 2.23606 nearly anfwers. CHAP. III. Of the Arithmetic of Logarithms, when the Numbers are Fractions. Fig. 3. WHEN Fradions areto be worked by Loga¬ rithms, it is necefifary, for avoiding theTrou- ble of adding one Part of a Logarithm, and fubtrading the other, that Logarithms do not begin from an integral Unit, but from fome Unit that is the tenth or hundredth Place of Decimal Fradions: For Example, let P O be ^00^000, and from this let the Logarithm begin. Now this Fradion is ten times more diftant from Unity to the left Hand, than the Number 10 is diftant therefrom to the right; for there are 10 proportional Terms in the Ratio of to to ?, from Unity to P O. And fo, if A B be Unity,