This is found as in Cafe 2, and is equal to Cf= 24° 04'. 2. To find the Angle D. This is alfo done as in Cafe 2; for it is equal to cd = 46° 18'. 3. To find the Angle B CD. Measure KL on a Line of Half-tangents from 90 downwards, and you will find it to be 769 00', whose Complement 1049 is the Angle required. Cafe F draw the two Oblique Circles BC F, DC G, fo fhall the Triangle be made or projected, as required. 1. To measure the Angle at D. Measure KL on the Half-tangents, and 'twill be found 46° 18'. 2. To measure the Angle B. Measure RI in the fame Manner, and it will be found 369 08'. 3. To measure the Angle C. This is done as taught in Cafe 1, and is found to be 104°. Cafe This Cafe is to be converted into the laft foregoing Cafe, by changing those Angles into Sides, by Theorem 13, taking for the greater Side 76°, the Complement of the Angle C 104° to 2 Right-angles. As in this adjacent Scheme, the Triangle BCD has its Sides, BC, CD, equal to the given Angles B, and D; and the Side BD, the Complement of the Obtufe Angle C to 180°. Wherefore if the Angles of this Triangle be measured, they will be found as follows; viz. B = bc= 30° 00'; D = dc = 24° 04'; and the Complement of BCD = b d = 428 09'. So that the Sides fought in this Cafe are those which conftitute the Triangle bdc, and are to be measured as before taught. And thus much for the Projection of Oblique Spherical Triangles. The Learner may vary the Method of Projection, and Form of the Triangle, fometimes if he pleafes; but this is here omitted, and left for his Exercife. CHAP. CHA P. XXI. Of the Menfuration of the Area of a Sphetical Triangle, and the Completion of a Solid Body. T LEMMA I. HE Lunary Superficies of Hemifpherics, is as the Angles of the fame Superficies. Demonftration. Suppofe the Meridian Semicircle AED to be moved over the Longitude of the Equator BEC, upon the Poles A, D ; then fhall the An- B gles on each fide the Meridian at the Poles, viz. F, and G, be as the Times in which they are generated; the Superficies alfo K, and M, -------་་ A F E fhall be as the Times; therefore F:G:: Superficies K: Superficies M. And G F M: K and fo it will be how foever they are taken. For Thofe |