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Concerning the Principles of the Doctrine of the Sphere, and Spherical Projection and Trigonometry, in various Definitions.



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




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


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.

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