Mtfcellanea Curio] d. 47 



and leall Diftances from the Pole of Proje- 



dUprLj*L ^ " |-, nE mm , • 



Thus in Fig. 2. and 3. equal to oc and c£ 

 together, is equal to the Sum of the Semi-tan- 

 gehts of the Arches mp pn y the greateft and 

 leaft Diftance of the Circle from the remoter 

 Pole of Projection. 



6. That of every fmall Circle without which 

 the Pole of Projection lies, its Diameter or 

 projected Axis is equal to the Difference of its 

 greateft and leaft Diftances from the Pole of 

 Projedtion, 



Thus in Fig. 4. oq is equal to the Difference 

 between cq and co, the Semi-tangents of pn, and 

 pm, the greateft and leaft Diftances of the Cir- 

 cle from the Pole of Projection. 



7. That of the 2 Poles of every great Circle, 

 and eonfequently of all fmall Circles parallel 

 to it, that which falls within the Plain of Pro- 

 jection will be diftant from the Center by the 

 Semi^tangcnt of theExcefsof the greateft Di«* 

 ftance, of the projected great Circle from the 

 remoter Pole of Projection above a Quadrant^ 

 or the DefecT: of the leaft Diftance from the Pole 

 of Proje&ion to a Quadrant. 



Thus in Fig. 2. d the Pole of the Circle nm 

 is diftant from the Center by the Space of 

 the Semi-tangent of the Arches xp the Excefs. 

 of p m above a Quadrant, or the Defect of pn 

 to a Quadrant. 



8. That its other Pole will be in the projected 

 Axis on the contrary fide of tne Centre, and 

 diftant from t it by the Semi-tangent of the pro- 

 je&edCircle's neareft Diftance from the remote* 

 Pole of Projection, leffen'd by a Quadrant, 



9, Hence 



