Mifcellanea Curiofa. 4.9 



PROPOSITION II; 



The Angles made by the Circles on the 

 Surface of the Sphere, are equal to thofe made 

 by their Reprefentatives on the Plain of Pro- 

 jection. 



The Reafon of which is evident from the ge- 

 neral Definition and laft Propo- 

 fition : For (in Fig. 6.) let e Fig. 6. 

 reprefent the Eye, be the Plain 

 of Proje&ion, opc the Angle to be proje&ed, 

 draw pn parallel to fo, pd, and pf^ Tangents to 

 the Circles p c and jpo, and continne them till 

 they meet the Plain fe, in the Line df ; 

 Becaufe the Angle dpm is equal to npm^ and 

 dmp equal to npm, therefore is tnd equal to 

 fd. 



Wherefore in the Triangles dmp and fmd are 

 dp equal to dm, df common, and the Angles 

 fdm r fdp both right ; therefore the Angle dpf is 

 equal to the Angle find. Therefore, &c. 



Whence, and from the firft PropoKtion, ; 

 it follows, 



i* That if every great Cir- Fig. 7. 

 cle to be proje&ed (which does 

 not lie in the Plain of the Eye) the Tangent of 

 the Compliment of itsDiftance from the Pok 

 of Projettion fet off in the projeded Axis, on 

 the contrary fide of the Interferon, will give 

 its Centre. 



For cn is equal to the Tangent of can, the 

 Complement of dac. 



£ 2, That 



