then fhall the Triangle ABG be made as required. fet 36° 15' of Chords off from B to A, tive BDEG; 2. Let the Triangle be at the Periphery. Describe the Primi на L D and draw the Right AOF; then with the HalfTangent of 61o 30', defcribe the Parallel HCI, and thro' the Point of Interfection C, draw the Oblique Circle 772 F then is the Triangle made as required. E BKE; Both thefe Parts are found, as in the foregoing Cafes and BC will 44° 524 and C 56° 57' In Fig. 1, E F 42° 34' is the Measure thereof on the Chords; and in Fig. 2, DK to the Number of Degrees on the Tangents from 90°. 1. To find the Hypothenufe, BC wanh This measured on the Chords will be found to be 44° 52'. 2. To find the Leg A B. A Ruler laid from the Pole a of the Oblique Circle B HF, and the Angular Point A, will cut the Primitive in d; then Bd measured on the Chords, will be found 36° 15'. 2. To find the Leg A C. Lay a Ruler from the Pole b of the Oblique Circle Ca D, and the Angular Point A, and it will cut the Primitive in the Point C; then Cc measured on the Chords, will be found 288 30'. С НА Р. CHA P. XVII. The ninth and tenth Methods of folving Right-angled Spherical Triangles, by the Orthohraphic and Stereographic Planisphere. T HE Nature, and Manner of Conftruction of both these Instruments hath been already fully taught in former Chapters; it now remains, that their Ufe be fhewn in folving Right-angled Spherical Triangles, for which they are very apt (especially the Latter) if made large enough for the Purpose. In order to this, it must be understood, that each Planisphere is to be curiously graduated in its outer Limb, or Periphery; that the Semidiameter of the Orthographic Planifphere, or Analemma, is to be graduated both ways from the Center, as a Line of Sines; and that of the Stereographic Planisphere as a Line of Half-Tangents. Alfo, that on the Center of each, there must be placed a Label or Ruler graduated as is the Semidiameter of the Inftrument to which it belongs, in order to be fet to contain any given Angle with the Semidiameter. Laftly, there must be all the Meridians, and Parallels defcribed on each Planifphere for every Degree of the graduated Diameter; or fome Method for defcribing fuch a Meridian and Parallel as is proper to any particular Occafion. VOL. II. Y Having Having given a Defcription of thofe two Planifheres; I have thereto fubjoin'd a Figure of each; in which, that I might reprefent the Triangle in the foregoing Synopfis (which I have hitherto made ute o) I have placed the Label BL to 42° 34' on the Periphery, and defcribed the Meridian which is 36° 15 diftant from the Center B, viz. DAG; and alfo the Parallel E F of 280 30; fo that thereby on cach Planifphere is conftituted the Triangle aforefaid ABC, thofe being fufficient to fhew the Ufe of thefe Inftruments, I have omitted drawing the other Circles which fill up and compleat the fame for univerfal Ufe. As the Manner of using either of thefe Planifpheres is the fame, fo. I have here treated of both thofe Methods together in one Chapter, the Directions which ferve to the one, ferving alfo equally to the other. And indeed were thefe Inftruments made fufficiently large, viz. of 1, 2, or 3 Feet Diameter, and furnished with all its Circles, great and fmall, it would be a moft eafy and expeditious Manner of folving Triangles; and I queftion not but the Ingenious Student would foon be convinced, that the Ufe would abundantly compenfate for the Pains and Time expended in making them thus large, especially the Stereographic Planifphere, which is pretty easily made of any Size. Confidering alfo that either of them may be contrived to anfwer diverfe other Purposes in Aftronomy, &c, at the fame time. But I proceed to their Ufe in folving the fix Cafes of Right-angled Triangles thereby; wherein the Reader muft obferve, that the Directions equally relate to each Planifphere, the fame Parts on each, being marked with the fame Letters. Cafe |