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.

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    Here they leave us firft to calculate that un¬ known Angle, before we fhall know whether we are to take the Sum or the Difference of the Vertical Angles or Bafes* for the fought Angle or Bafe: And in the Calculation of that Angle have left us in the dark as to its Species •, as appears by my Obfervations on the two pre¬ ceding Cafes. * / * •»' ■ i ' • > ' ’ > * i • ■ The Truth is, the Queefitum here, as well as in the two former Cafes, is fometimes doubt¬ ful, and fometimes not*, when doubtful, fome¬ times each Anfwer is lefs than 90 Degrees, fometimes each is greater*, but fometimes one lefs, and the other greater, as in the two Lift» mentioned Cafes. When it is not doubtful, the Qucefitum is fometimes greater than 90 De¬ grees, and fometimes lefs. All which Diftinc- tions may be made without another Opera¬ tion, or the Knowledge of the Species of that unknown Angle, oppofite to a given Side ; or, which is the fame thing, the falling of the Perpendicular within or without. For which fee my Dire&ions at Pages 324, 325. In the Solution of our iff and 5th Cafes called in other Authors, the 5th and 6th j where there are given two Angles, and a Side oppofite to one of them, to find the 3d Angle, or the Side oppofite to it; they have told us, that the ^ Difference \ Vertical Angles, or Bafes, according as the Perpendicular falls < within } be t]ie fought Angle or Side j < without b o a and that it is known whether the Perpendicu¬ lar