# The projection of the sphere, orthographic, stererographic, and gnomonical; both demonstrating the principles, and explaining the practice of these three several sorts of projection

J. Nourse, 1769 - 57 sider

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Side 12 - Projection of a great circle is in the line of meafures, diftant from the center of the primitive, the tangent of its inclination to the primitive -, and its radius is the fecant of its inclination.
Side 21 - N1H 26. is as far from the projecting point as QH from its pole P ; and if they be projected into the circles...
Side 16 - The points where an inclined great circle \ \$. cuts the line of tneafures, within and without the primitive, is diftant from the center of the primitive, the tangent and co-tangent of half the complement of the circle's inclination to the primitive. For CG = tangent of half EB, or of half the complement of IE the inclination. And (becaufe the Z.EAF is right) CH is the co-tangent of GAC or half EB.
Side 11 - C, draw the plane of a great circle PED, perpendicular to the plane of projection EFG ; let a plane PHG touch the sphere in P ; then since the circle EPD is perpendicular both to this plane and to the plane of projection, it is perpendicular to their common section GH.
Side 13 - GAH considered as a primitive, and RS its line of measures ; as the circle BGA is on the primitive BIA, and line of measures ID. And therefore the tangent of the angle AGL to the radius GD> set from D to N, gives the centre of GL.
Side 33 - PI be parallel to the plane GF. Then the equal arches PC, CI are projected into the equal tangents GC, CH...
Side 12 - Jphere, is equal to the angle made by the radii of their •projections at the point of interfection.
Side 11 - Through the angular point P and the center C, draw the plane of a great circle PED perpendicular to the plane of projection EFG. Let a plane PHG touch the fphere in...
Side 12 - Plane {hall he in the Line of Meafures diftant from the Center of the Primitive...
Side 17 - F,F are projefted into D and d ; and CD is the tangent of CAD or half BCP, that is, of half GCI, the inclination of the circle ICK, parallel to EF. Likewife Cd is the tangent of CAd, or the co-tangent of CAD.