PLANE

AND

SPHERICAL;

WITH THE

CONSTRUCTION and APPLICATION

OF

LOGARITHM S.

4

By THOMAS SIMPSON, F.R.S.

The SECOND EDITION.

LONDON,

Printed for J. NOURSE, Bookfeller in Ordinary to his MAJESTY.

MDCCLXV.

Plane Trigonometry.

DEFINITIONS.

LANE Trigonometry is the art whereby, having given any three parts of a plane triangle (except the three angles) the reft are determined. In order to which, it is not only requifite that the peripheries of circles, but also certain right-lines in, and about, the circle, be fuppofed divided into fome affigned number of equal parts.

2. The periphery of every circle is fuppofed to be divided into 360 equal parts, called degrees; and each degree into 60 equal parts, called minutes; and each minute into 60 equal parts, called feconds, or fecond minutes, &c.

Note, The degrees, minutes, feconds, &c. contained in any arch, or angle, are wrote in this manner, 50° 18' 35'', which fignifies that the given arch, or angle, contains 50 degrees, 18 minutes, and 35 fe conds.

4. The difference of any arch from 90° (or a quadrant) is called its complement; and its difference from 180° (or a femicircle) its fupple

ment.

5. A chord, or fubtenfe, is a right-line drawn from one extremity of an arch to the other: thus the right line BE is the chord, or fubtenfe, of the arch BAE or BDE.

6. The fine, or right-fine, of an arch, is a right-line drawn from one extremity of the arch, perpendicular to the diameter paffing through the other extremity. Thus BF is the fine of the arch AB or DB.

7. The verfed fine of an arch is the part of the diameter intercepted between the fine and the periphery. Thus AF is the verfed fine of AB; and DF of DB.

8. The