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, Rcs BC: tC

57′,

Set one Foot in the Sine of 90°, and other to the Sine of 45° 08′; then, with fet one Foot in the Tangent of 56° the other upwards, it will fall on the 47° 26', whofe Complement 42° 34′

ct B.

extend the that Extent, and turning Tangent of

B.

1. To find the other Leg A C.

The Analogy, cs BA : R::cs BC: csẠC.

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, BC: RtAB: cs B. Extend the Compaffes from the T of 44° 52', to the Ț of 36° 15'; this Extent will reach from the S of 90% to the S of 47° 26'.

3. To find the Angle C.

The Analogy, BC: R:: SBA:s C,

VOL. II.

T 2

Extend

Extend the Compaffes from the S of 44° 52', to the S of 90°; this will reach from the S of 369 15', to the S of 56° 57'.

1. To find the Hypothenufe BC.

The Analogy, ResB:: ct AB: 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

08

of 53° 45′ upward to the T of {45 02

52

2. To find the other Leg A C.

The Analogy, R: s B A :: t B: t AC.

The Distance between the S of 90o and S of 36o 15', will reach from the Tof 42° 34', to the T of 28° 30°. 3. To find the Angle C.

The Analogy, R:cs BA:: s B: cs C.. Extend the Compaffes from Radius, to the S of 53° 45'; this Extent will reach from the S of 42o 34, to the S of 33° 03′· ·

1. To find the Hypothenufe B C.

The Analogy, s B: SAC:: Rs BC.

Extend the Compaffes 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, B:t AC :: R:s AB. Extend the Compaffes from the T of 429 34', to the T of 28° 30'; that Extent will reach from the S of 90, to the S of 36o 15'.

3. To find the Angle C.

The Analogy, csCA: R::cs B: s C. Extend the Compaffes from the S of 28° 30', to the S of 90°; that Extent will reach from the S of 47° 26', to the S of 569 57'.

1. To find the Hypothenufe B C.

The Analogy, Rcs AC::cs AB: cs BC.

Set one Foot in the S of 90°, and extend the other to the S of 61 30'; this Extent fhall reach from the S of 53° 45', to the S of 45° 08′.

.

2. To find the Angle B.

The Analogy, sBA: R:: t CA: t B.

Extend the Compaffes from the S of 36° 15', to the Radius; this Extent will reach from the Tof 28o 30', to the T of 429 34.

Set one Foot in the S of 28° 30', and extend the other to Radius; with this Opening, fet 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 Compaffes, and the other Foot will fall on the T of 56° 57. Or you may alter the Analogy, and work it at once.

Cafe 6.

Given both the Angles

B = 42 34
C = 56 57

1. To find the Hypothenufe B C.

The Analogy, tC ct B: Rcs BC, Extend the Compaffes from the T of 56° 57', to the T of 47° 26'; this Extent will reach from the S of 90% to the S of 45o 081.

2. To find the Leg A B.

The Analogy, sBcs C: R:cs BA

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 csB:: Rcs AC. Extend the Compaffes from the S of 56° 57', to the S of 47° 261; this Extent will reach from Radius, to the S of 61° 30'.

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

СНАР.

.

CHA P. XV.

The feventh 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; fo

it plainly follows, that a Spherical Triangle is moft juftly and naturally delineated or reprefented, by the Circles on (and appertaining to) the Surface of the faid Artificial Globe or Sphere. For tho' by the Projections or Planifpheres a Triangle may be described in fome fort Spherical, yet it is far from being in its due and natural Form, as on the Globe itself. And as the Form, fo 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 Impoffibility for any Man to have any tolerable Notion of (much lefs will he be able to teach) the Doctrine of Spheric Geometry, and the Theory of thofe curious Arts which depend thereon.

I therefore take it for granted, that all who undertake to learn Spherical Trigonometry are well acquainted with the Nature, Names, and Ufes 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 folve the fix Cafes of Right-angled Spherical Triangles by the Globe; I fhall chufe fuch

a Pofi