P LA N E A N D SPHERICAL; WITH THE CONSTRUCTION and APPLICATION OF LOGARITHMS. By THOMAS SIMPSON, F.R.S. The SecoND EDITION. LONDON, Printed for J. Nourse, Bookseller in Ordinary to his MAJESTY. MDCCLXV. "PLANE LANE Trigonometry is the art whereby, having given any three parts of a plane triangle (except the three angles) the rest are determined. In order to which, it is not only requisite that the peripheries of circles, but also certain right-lines in, and about, the circle, be supposed divided into some assigned number of equal parts. 2. The periphery of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 69 equal parts, called ainutes; and each minute into 60 equal parts, called Leconds, or second minutes,, &c. Nore, The degrees, minutes, seconds, &c. conéciseid in ary arch, er angle, are wrote in this manner, 51 18'35'', which fignifies that the given arch, or ang?, contains 50 degrees, 18 minutes, and 35 sez conds, 4. The difference of any arch from 90° (or a quadrant) is called is complement ; and its difference from 180° (or a femicircle) its supplement. 5. A chord, or subtense, is a right-line drawn from one extremity of an arch to the other : thus the right line BE is the chord, or subtense, of the arch BAE or BDE. 6. The fine, or right-sine, of an arch, is a right-line drawn from one extremity of the arch, perpendicular to the diameter passing through the other extremity. Thus BF is the line of the arch AB or DB. 7. The versed fine of an arch is the part of the diameter intercepted between the fine and the periphery. Thus AF is the versed sine of AB; and PF of DB. 8. The |