The Application of Spherical Trigonometry to Analogy, Prob. 1. To erect a Scheme or Figure of the Heavens for the Lat. of Chichester 50° 56', May the 12th, at Prob. 2. To find the Pole's Elevation above the Circles of the 11th, 9th, 3d, and 5th Houses Prob. 6. To find the Cufps of the 2d and 8th Houfes 278 Prob. 7. To find the Cufps of the 3d and 9th Houfes 280 Prob. 8. To find the Cufps of the 5th and 11th Houses 281 Prob. 9. To find the Cufps of the 12th and 6th Houses 282 Prob. 10. To reprefent the Face of the Heavens for the given Moment of Time; and to affign the Places of the The Application of Spherical Trigonometry to the Science Prob. 4. To find the Distance and Bearing of two Places, one under the Equator, the other in any Latitude 297 Prob. 5. To find the Distance, Pofition, &c. of any Places differing both in Latitude and Longitude 299 Prob. 6. To Places lying one in South Latitude, the other The Application of Spherical Trigonometry to Naviga- tion; to fhew how to find the Difference of Latitude, Difference of Longitude, the Courfe or Rumb, the Dif tance failed, the Departure from the first Meridian, And with refpect to its Ufe in Sailing, there is taught thefe Things, ibid. 4. To measure the Difference of Longitude 6. To measure the Meridian Distance, or Departure. With feveral other Matters pertaining thereto; with the Globular Chart it felf extending from the Equator The Application of Spherical Trigonometry to the Art of Dialling; fhewing the Nature and diverfe Kinds of Prob. 1. To find the Sun's Altitude by the Quadrant 325 Prob. 2. To find the Horizontal Distance Prob. 3. To find the Plane's Declination Prob. 4. To find the Plane's Reclination Prob. 5. To reduce South Direct reclining Planes to the Prob. 6. To reduce Direct North Recliners to the new Prob. 7. To reduce South Declining Reclining Planes to a new Latitude and Declination Prob. 8. To reduce North Declining Reclining Planes to a new Latitude and Declination Prob. 16. To make a Direct South or North Dial Prob. 17. To make a South or North declining Dial 347 Prob. 18. To make a direct South reclining Dial 353 Prob. 19. To make a direct North reclining Dial 356 Prob. 20. To make a direct Eaft or Weft reclining Dial Prob. 21. To make a South declining reclining Dial 359 Prob. 22. To make a North declining reclining Dial 363 Concerning the Principles of the Doctrine of the Sphere, and Spherical Projection and Trigonometry, in various Definitions. DEF. I. A Globe is a Body perfectly round, every Point of whofe Superficies is equidistant from its Center. See Fig. 1. II. A Sphere is an Artificial Instrument confifting of various Circles, Great and Small, put together in a VOL. II. B pro proper Order and Pofition. And becaufe fuch Circles are called in Latin, Armilla; therefore this Inftrument is commonly called an Armillary Sphere. See Fig. 2. III. Projection of the Sphere, is an artful Delineation of its Circles on a plain Surface; and hence it is called Projection of the Sphere in Plano; this is of two Kinds, Orthographic and Stereographic. IV. Orthographical Projection of the Sphere, is when its Circles are projected on a Plane, by Rays of Light proceeding from the Eye fuppofe at an Infinite Diftance; which Rays are then Parallel; and project the Circles either in Circles, EHipfes, or Right Lines, on the faid Plane. See the Schemes in the Orthographic Projection. V. The Stereographic Projection is a Delineation or Representation of the Circles of the Sphere, as they appear to an Eye placed on any Point of its Surface; the Projection of the Circles in this Manner, will produce either Circles, Circular Arches, or Right Lines on the Plane of the Projection. See the Schemes of CHA P. IV. and V. VI. The Plane of the Projection, is that plain Superficies on which the Circles of the Sphere, are seen or projected; and is fuppofed to be every Way infinitely continued. VII. That Right Line, in which the Plane of the Circle to be projected interfects the Plane of the Projection, is called the Common Section of the Plane of Projection. VIII. A Line of Measures is, that Right Line on which the Distance of the Center of an Oblique Circle is measured off of a Scale of Half Tangents, and this Line always paffeth through the Center of the Projection, or is parallel to the Diameter that doth. |