or Cotangent of ye Latitude may be easily, as a Sine, transferred into ye limb or mitagurd (?) on ye Sines; and ye Arch correspondent thereto taken in ye limb; for in any one Latitude, there is reqred no more Tangent-points, in this general work, but one. More over ye Line of Sines, if it be of yesame Radius, as ye Sines on the side of ye first Quadrant, in ye Book of Quadrants, serves most easily, wth ye printed Scale trea ted off in pag. 195. to give ye hour and azimuth all over England. But ye Describer does not esteem these Instrumental Conclusions worth mentioning; his Design then being an Improvements of Points so as to lessen ye Charge of Instruments. The Antiquity and Demonstration of Projection. If we consider, that the Azimuths and Altituds have such Habitude and relaon to ye Axis of ye Horizon, as ye Houre Circles and Paralels of Declinaon have to ye Axis of ye Sphere, we shall find, yt whether ye Eye be at ye Nadir or Role-Point, ye Projection will be altogether yesame thing.
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Description of the double horizontal dial presented to the Royal Society by John Collins, 1667. From The Royal Society, CLP/24/6
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