PLA NE -TRIGONOMETRY.

TRACT 16.

J2 66

2 abc

r =

aJ (a z b 2 — (a?+ b' — t*) 2 )

2 abc

s/ [(« + Z>+c)x [a+b — c) x (a— b pc) x ( — a+5 + c)]'

C —

VK + ^-2«V(l-( T - 2 -^-

■&c)T

2.3.4.5» s

Where a, b, c, are the halves of the three sides of the tri-angle, and A the number of degrees in the angle opposite theside 2 a, and c the degrees in the angle opposite the side 2c;also r is the radius of the circumscribed circle;

and n = ... , 180 — = 57-2957795, or ~ = -54567409.

3-t4iS9

105

EXAMPLE.

Thus, if the three sides be given, as for example a = 13,b = 14, c = 15. Then is r = 16^, and the angles by thesetheorems come out as follow ; viz.

Angles by the Theor. The true Angles.

53° 7' - - angle a - - 53° 7’}

59 28 - - angle B - - 59 29|.

67 19 - - angle c - - 67 22}

179 54 sum of all 180 00

TRACT XVII,

ON MACHIN’S QUADRATURE OP THE CIRCLE.

Since the chief advantage of this method consists in takingsmall arcs, whose tangents shall be numbers easy to manage,Mr. Machin very properly considered, that as the tangent of45° is 1 ; and that the tangent of any arc being given, thetangent of double that arc can easily be found ; if there beassumed some small simple number for the tangent of an arc,