TABLE II.-For the Solution of Oblique-Angled Spherical Triangles.

An angle or a side being divided by a perpendicular, the first and second segments are denoted by 1 seg, and 2 seg.

the side contain-i ed between the given angles.

Sin 2 seg.

tan ang. opp. given side

ngles Third side.

and

sin 1 seg. x tan ang. adj. given side

Let fall a per. as Cot 1 seg. of this ang. = cos giv. side × tan adj. angle.

Sin 2 seg.

sin 1 seg. x cos ang. opp. given side

Sines of sides are as sines of their opposite angles.

Cot 1 seg. ang. req.

dicular from the included angle.

Cos 2 seg=

Let fall a perpendicular as before.

tan given ang. x cos adj. side.

cos 1 seg. x tan giv, side a lj, giv, angle tan side opp. given angle

Let fall a perpen. Tan 1 seg. of div. side = cos giv. ang. x tan side opp. ang. sought.

from the third

cos giv. ang. x tan other given side. cos side not div. x cos 2 E cos I seg. of side divided

angle.

Afides und the

Let fall a perpen.

Tan 1 seg. of div. side

chided) angle.

Third side.

on one of the giv. sides.

Cos side sought

to one of the

third side.

A side opposite Let fall a perpen-Cot 1 seg. of div. ang. = cos giv. side a tan ang opp. side sought

given angless

Third angles

jacent

V.

An angle by the

The

み

of its halt

dicular on the

be the sides; A, B, C, the angles, and, uskoling de angle at

of its half,

TABLE II.—For the Solution of Oblique-Angled Spherical Triangles.

An angle or a side being divided by a perpendicular, the first and second segments are denoted by 1 seg, and 2 seg.

ities required!.

Sines of angles are as sines of oppos. sides.

}

Cot 1 seg. of this ang. = cos giv. side x tan adj. angle. sin 1 seg. x cos ang. opp. given side

Sin 2 seg. =

between the

}

cos ang. adj. given side

Let fall a perpen-Cot 1 seg. ang. req dicular from the

included angle. Cos 2 seg =

= tan given ang. × cos adj. side.

cos 1 seg. x tan giv, side adj. giv. angle tan side opp. given angle

req.

= cos given ang. × tan adj. side.

cos 1 seg. x cos side opp. given angle

cos si e aj. given angle

Tan 1 seg. of div. side = cos giv. ang. x tan side opp. ang. sought.

from the third

angle.

Cos side sought

cos side not div. x cos 2 seg.

cos 1 seg. of side divided

IV.

Third angle.

Let fall a perpen.Tan 1 seg. of div. side = cos giv. ang. x tan other given side. on one of the

giv. sides.

dicular on the third side.

=

Cot 1 seg. of div. ang. = cos giv. side x tan ang. opp. side sought.

=

tan giv. side x cos 1 seg. div. ang.

Let fall a perpen.) Cot 1 seg. div. ang. = cos giv. side x tan other giv. angle. giv. angles. from one of the Cos angle sought

Let a, b, c, be the sides; A, B, C, the angles, b and c including the angle sought,

A side and the

to one of the A side opposite given angles.

Let fall a perpen

sine or cosine

three

of its half.

three

of its half.

angles.

An angle by the and s = a+b+c. Then,

Let s be the sum of the angles A, B, and C; and let B and C be adjacent to a the side required.

Then,

TABLE III.

For the Solution of all the cases of Oblique-Angled Spherical Triangles, by the Analogies of Napier.

Given.

Required.

Values of the Terms required.

By the common analogy, sines of angles as sines of opp. sides.

{By the common analogy.

By the common analogy.