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Set one Foot in 90° of Sines, and extend the other to the Sine of 33° 03' ; this Extent will reach from the Tangent of 44° 52', to the Tangent of 28° 30' = AC.

3. To find the Angle B. The Analogy, R:cs BC::C:ct B. Set one Foot in the Sine of 90°, and extend the other to the Sine of 45° 08'; then, with that Extent, set one Foot in the Tangent of 56° 57', and turning the other upwards, it will fall on the Tangent of 47° 26', whose Complement 42° 34'

= B.

Case 2.

Given

The Hypothenuse
and the Leg

8 BC= 44 52 B A = 36 15

1. To find the other Leg A C. The Analogy, cs BA:R::cs BC:05 AC. Set one Foot in the S of 53° 45', extend the other to the S of 90°; this Extent will reach from the S of 45° 08', to the S of 61° 30'.

2. To find the Angle B. The Analogy, t B C :R::t AB:05 B. Extend the Compasses from the T of 44° 52', to the Ț of 36° 15'; this Extent will reach from the $ of go to the S of 47° 26'.

3. To find the Angle C,
The Analogy, s BC:R::SBA:s Ce
VOL. II.

Extend

:

T 2

Extend the Compasses from the S of 44° 52', to the S of 90° ; this will reach from the S of 369 15', to the S of 560 57'.

Case 3.

BA = 36 15

Given { and the adjacent Angle" B = 42 34

{

1. To find the Hypothenuse BC. The Analogy, R:05 B ::ctAB:ct BC. Set one Foot in the S of 90°, and extend the other to the S of 47° 26'; this will reach from the T

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of 53° 45' upward to the T of { 45.59 } = BC.

2. To find the other Leg A C. The Analogy, R:s BA::tB:t AC. The Distance between the S of 90% and S of 362 15', will reach from the T of 42° 34', to the T of 28° 30'.

3. To find the Angle C. The Analogy, R:05BA :: s B : cs C. Extend the Compasses from Radius, to the S of 53° 45'; this Extent will reach from the S of 422 34, to the S of 339 03': Case 4, Ambiguous.

( One of the Legs, as

AC = 28 30 Given

and an oppolite Angle B = 42 34

1. To find the Hypothenuse B Ç.
The Analogy, s B : s AC :: R:s BC.

Extend the Compasses from the S of 42° 34', to the S of 28° 30'; that Extent will reach from the S of 90°, to the S of 44° 52'.

2. To find the Leg A B. The Analogy, i B:AC::R:s AB. Extend the Compasses from the T of 429 34', to the T of 28° 30; that Extent will reach from the S of go, to the S of 36° 15'.

3. To find the Angle C. The Analogy, csCA:R::85 B : sC. Extend the Compasses from the S of 28° 30', to the S of 90°; that Extent will reach from the Sof 47° 26', to the S of 569 57'.

Case 5.

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Given and the Leg

AB= 36 15

AC = 28 30 1. To find the Hypothenuse B C. The Analogy, Rics AC ::65 AB : 65 BC.

Set one Foot in the S of 90%, and extend the other to the S of 61.9 30'; this Extent shall reach from the S of 53' 45', to the S of 45° 08'.

2. To find the Angle B. · The Analogy, sBA:R::CA: 1 B. Extend the Compafses from the S of 36Q 15', to the Radius ; this Extent will reach from the T of 28. 30', to the T of 42° 34'.

3. To find the Angle C.
The Analogy, s AC:R::tBA:+C.

Set

:

Set one Foot in the S of 28° 30', and extend the other to Radius ; with this Opening, set one Foot in the T of 36° 15', and pitch the other in fome Point upward, where hold it fixt' 'till you bring the other Foot to the T of 45, and thereon turn the Compasses, and the other Foot will fall on the T of 562 57. Or you may alter the Analogy, and work it at once.

Cafe 6.

B = 42 34 Given both the Angles

C= 56 57 1. To find the Hypothenuse B C. The Analogy, 1C:ctB :: R:0 BC. Extend the Compasses from the T of 568 57', to the T of 47° 26' ; this Extent will reach from the S of 90% to the S of 4508.

2. To find the Leg A B. The Analogy, :csC::R:cs B A. Set one. Foot in the S of 42° 34', and extend the other to the S of 33° 03'; this Extent will reach from Radius, to the S of 53° 45'.

3. To find the Leg A C. The Analogy, sc:cs B :: R:CS AC. Extend the Compasses from the S of 56° 57', to the S of 479 261 ; this Extent will reach from Radius, to the S of 619 30'.

Thus I have exemplified the Practice of Spherical Trigonometry, by the Gunter ; I shall next proceed to do the same things on the Globe or Sphere.

СНАР.

CH A P. XV.

The seventh Method of Solving Right-angled

Spherical Triangles, by the Globes or
Spheres.

A

S the Globe or Sphere is the very Original and
Foundation of all Spherical Trigonometry ; so

it plainly follows, that a Spherical Triangle is most justly and naturally delineated or represented, by the Circles on (and appertaining to the Surface of the faid Artificial Globe or Sphere. For tho' by the Projections or Planispheres a Triangle may be described in some sort Spherical, yet it is far from being in its due and natural Form, as on the Globe itself. And as the Form, so the Solution of a Spherical Triangle is most naturally performed on the Globe. Of fuch vaft Importance is a due Knowledge of the Globe, and all its Furniture of Circles, that without it I dare pronounce it an Impossibility for any Man to have any tolerable Notion of (much less will he be able to teach ) the Doctrine of Spheric Geometry, and the Theory of those curious Arts which depend thereon.

I therefore take it for granted, that all who under take to learn Spherical Trigonometry are well acquainted with the Nature, Names, and Uses of all the Circles of the Sphere, as has been delivered in the Definitions; and being thus qualified, he will eafily understand what is delivered in the Sequel of this Chapter.

In order to solve the fix Cafes of Right-angled Spherical Triangles by the Globe ; I shall chuse such

a Pogi.

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