In the first of which: B: (the Base) being made the Radius, P (the Perpendicular) is the Tangent of the Augle at a, the Center of the Circle, which is oppofite to P, and the Hypothenufe is the S cant of the fame Angle. In the fecond of which, where P is made the Radius, B is the Targent of the oppofite Angle at the Center: C:

In the third of which where H the Hypothenufe is made the Radius, P is the Right Sine of the oppofite Angle at the Center. C

In the fourth of which H being a'fo made Radius, but c the Center of the Circle, B will be Sine of its oppofite. Angle.

CASE. I.

Fig 60. Hypothenufe and Angles given, either of the Legs required.

Operation.

To the Logar of bc 446, 2. 644044 add the Sine of Angle c 22°. 30′ 9. 582840

=

12.226884.

Sum abate, Rad Log. ba 168; 61.

By Gunters Scale.

to

The extent from the Sine 90°, the Sine of the Argle c. 22. 30 on the Line of the Sines, will reach from b c 446. to ba 168. 61 on the Line of Numbers.

CASE II.

One Leg and an Argle given, the other Leg required.

Example.
Sba=168,617

In the A abc, given

Lc, = 22,30

Proportion.

requir'd ca,

Rad: ba:: ct, Lc:ca, i. e. T, 45,: 168,

61 :: T, 67,30: 407,6.
To the Logar. ba 168, 61

add the c, c 22, 30

2, 226884

10, 382776

Example.
ba 158,6

In thesab c, given c=22°,30′

Proportion.

S, Lc: ba:: Rad,

bc.

I

requir'd be

S, 22°, 30': 16801:: S 90°: 446.
Operation.

Add Legar, ba 168, 61

To fr, co. S, < € 22°., 30′

0, 417160

2, 22688

2. 644044

By Gunters Scale.

The Extent, from S, 4 c 22° 30'. To the

S, 90°, on the Line of Sines.

will reach

from ba 168, 61. to b c 446 on the Line of Numbers.

CASE IV.

One Leg and the Hypothenufe given, the Angles required.

Example.

bc=

Operation.

To Ar, co, Legar.bc 446
Add Legar, ba. 68, 61.

Sum S. Lc 22°, 30'

From.90°, co

Subftract 22 30.

7.355956 2. 22688,.

9. 582840

Remainder. 67°30′ = <b.
By Gunters Scale.

The Extent from 446, to 16, 61 on the
Line of Numbers, reaches from S. 90°,
To the Sine 22°, 30' on the Line of Sines.

As Rad, ct, <c :: ba: ca.

T,45:T 67°. 30':: 168°, 61° : 407. 6.

Operation.

To the ct, <c 22°

30'

add the Log. ba 168, 61.

10. 382776 .226884

Sim,lefs Rad, Log,c a 407,6 12, 609660.

By Gunters Seale.

The extent from T, 45°, oo' on the Line of

To the

Reaches from

To

T, 67°,30'S Tangents

168-61

407-6

}

on the Line of

Numbers.

CASE VI.

The Legs given, and the Angles re

quired,

In the a abc,ba, 168,617

given,

requir'ð 2,

b.