the Distance of the two Ports, and the Course the Ship has fleered?

In the Oblique Triangle ACB, there are Given the Side AC=76 Miles; and the Side BC=134.1; and an Angle oppofite to one of them, viz. the Angle CAB; for Cis five Points to the North, and B two Points to the South of the East Point E; the Angle A then is feven Points or 78° 45': Whence by Cafe II. of Oblique Triangles; there will be found the other Side AB-126.4 the Distance of the two Ports; and the Angle ABC=33°45', confequently the fecond Ship's Courfe was on the Rumb BC parallel to c A, NW b N. as required.

III. Admit I fail from a certain Port A, 126.4 Miles ESE; but by a fudder Change of Wind, am obliged to traverse that Course on the NW bN. Rumb 134.1 Miles; how far am I from the Port A, and on what Point have I made my Way good?

By the two Given Sides AB=126.4 Miles; and BC=134.1 Miles; and the Angle included ABC= 33°45', the Difference of the NW b N. and WNW. Points; there will be found, by Cafe III. of Oblique Triangles, the Angle BAC-78°45'; and therefore, fince AB is ESE. the Courfe from A to C is NEON; and the Way made good from the Port A to C, will be found AC-76 Miles, as required.

IV. There are two Ports A and B lying ESE. and WNW. off each other, and diftant apart 126.4 Miles; and there is an Island Clying Northward, diftant from the Weftermoft Port A 76 Miles; and from the Eaftermoft Port B 134.1 Miles, it is demanded on what Points the faid Island C bears from either Port A and B?

In the Oblique Triangle ABC, having the three Sides given, the Angles are to be found by Cafe IV. of Oblique Triangles; thus the Angle A fhall be found 78°45', and fhews the Island C bears NE b N. from the Port A; and the Angle B will be found 33° 45', and therefore C muft bear NW b N. from the Port B, and thus the Problem is fatisfied.

These are all the direct or moft ufual Cafes of Oblique Sailing, which are fufficient to fhew how the whole Doctrine of Oblique angled-Triangles is concerned to refolve Problems in this Sort of Navigation; and alfo how any other Cafes of Oblique Sailing, like to these here fpecified, may be easily refolved by any one who has learned what hath been before delivered of Oblique Trigonometry.

Thus I have finished a copious Application of the whole Art of Right-lined Trigonometry to the various kinds of Plain or Rectilineal Sailing; what relates to great Great Circle Sailing, and to the making and Sailing by the Globular Chart, will be delivered in the Second Part of this Work.

CHA P. II.

Plain Trigonometry applied to Cofmography, in Measuring the Globe of the Earth, and its feveral Parts; alfo of the Atmosphere, Rain-bow, Clouds, &.c.

Cofmography, according to the Etymology of the

Word, (which is compofed of Koou, Mundus, the World; and vegon, Scriptum, a Defcription fignifies a Defcription of the World in general, including all that is known or to be known of the Heavens and the Earth. But in a more limited Senfe, it is taken for the Science of this terreftial Globe on which we live, with its Appendages, as the Atmofphere, its Meteors, &c.

I fhall apply the Doctrine of Plain Trigonometry to Cofmography only in this latter Acceptation; and fhall fhew how by its Service, the Dimensions of the whole Earth, and its several Parts, as the Torrid, Temperate and Frigid Zones; the Height of the Clouds; of the Atmosphere; the Dimensions of the Rainbow, &c.

And first of all I fhall fhew how by Trigonometry, the Circumference, Diameter, and confequently

the

the Magnitude of the whole Earth was attempted by the Ancients; who for that Purpose used feveral Methods; as

I. Suppofe, in the adjacent Figure AEFG represents a great Circle, or the Circumference of the Earth; and BD the pèrpendicular Height of fome Mountain, as Teneriff for Inftance; and A the farthest Point of Sight, from the Top thereof.

Now by good In

ftruments, the Angle ABD may be taken, and the Side AB may be known, and the Angle at A being a Right one, there is, in the Right-angled Triangle ABC, Given the Side AB=179.5 Miles fuppofe; and all the Angles fuppofing B-87° 25', to find the Side AC or Semidiameter of the Earth.

Then by Cafe II. of Right-angled Triangles, fay;