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prime vertical: celestial great circle passing through the east and west points and the zenith.
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primum mobile: instrument for finding the sines and versed signs of angles, see article on the primum mobile.
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projection: translation of a figure on to a plane or curved surface using straight lines in a systematic way. For example, a spherical surface can be projected on to a plane (the plane of projection) by means of straight lines drawn from all points on the surface to a certain defined point (the point of projection) and marking where they intersect the plane. In a stereographic projection, such as is used for the ordinary astrolabe, points on a containing circle are projected on to an equatorial plane from one pole; in an orthographic projection, such as is used in a Rojas design of universal astrolabe, the point of projection is at infinity and the projection lines are parallel.
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proportional compasses: drawing instrument consisting of two legs each with points at either end; used for transferring dimensions in enlarged or reduced ratio.
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proportional dividers: drawing instrument consisting of two legs each with points at either end; used for transferring dimensions in enlarged or reduced ratio.
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