-I^.l ) 86 ( ^'cl^ 



prictatis dcmonnrationcm heic proponamns, primiim inam 

 proprietatcm c;rciiIorum in plano delciiptorum facili dc- 

 monihiUione confirmare placcbir. 



§• =• Sint igitnr bini circuli A G B, D G F fe ad 

 Fi2 I ^"S"Ios redos in G intcrfecantes , ita vt, dudis :td centra 

 circulorum C ct E lineis recflis GC, G F, fit CGE an- 

 gulus redus , tumqiie a verticibus A, B diametri ACB 

 per centrum E alterius cfrculi tranfeuntis , ducantur ad 

 puncflum quoduis iflius circuli lineae rcdae A H, BH, 

 crunt hae redae intcr fe in data ratione, vti AG ad BG. 

 Nam ob angulum A G B := 90° — C G E, ablato commu- 

 ni angulo C G B, cnt A G C := B G E; at A G C = C A G, 

 ob A C - C G, Iiinc B G E =r E A G i et ob ang. G E B vtro- 

 que triangulo G E B, A G E commiuicm, AGBEcviAGE, 

 hinc A E : G E rz G E : B E, per Theor. IV: Lib. V^l. Ku- 

 clid. Vnde duda linca H E ob H E — : G E , erit quoque 

 AE:HEr=EIE:BE, ideoquc A H B E cvj H A E, per 

 Theor. VII. Lib. VI. Euclid , feu angulus BHE~BAH 

 et AHE^HBE, quamobrem fict AH:BH=AL:BE 

 — A G : B G. 



§■ 3« Pro demonftranda autcm ifta proprictate cir- 

 culorum in fupcrficie Sphacrae fe ad angulos rcdos intcr- 

 fecantium, ncccn\ini cft, vt Lemmatis inflar fequens prae- 

 mittamus. 



Theorcma. 



yL z. ' '^^ chciihim gi/eMpia?ii JEB in ftipcrficic Sphjcrae 



dcfcyiptum tar.gat arciis circuli viaximi F E in pun£io E , 



tum- 



