§. 2. Theorema I. Si in femicircuh A B D, po- Tab. lll 

 lo C et intervallo arcu circuU maximi A C defcripto , ex ^'S- '♦ 

 pun£io eius quocunque B ducatur arcus circuli maximi ad 

 A D normalis B E , fm 



tang. B E' : I — (In. A C* - fin. E O : cof. A C'. 



Demonflr. lungatur BC arcu circuli maximi, et quum 

 in triangQlo BEC recflnngulo fit 



cof.BE=:?2^; fiet 



fin. B E' = e^i^--:^?^ , 



coj. E C ' 



hincque 



tang. B E* : I =: cof. E C* - cof. B C* : cof. B C* 

 — fin. B C - fin. E C* : cof. B C\ 

 Si ponatur radius Sphaerae infinitus, quo cafu fiet 

 cof.BC^itcing.BE-BE,- fin.BC:=BC; fin.EC — EC; 



fiet B E' — B C — E C% quae eft proprietas pal^naria cir- 

 culi in plano defcripti. 



§. 3. Theorema II. Jisdem pojitis ac 'm Theoremate 

 praecedemi , fi infuper iunganiur A B, B D, arcubus circu- 

 lorum maximorum, eiit 



fin. ^ A D^ r= fin. ^ A B' -f- fin. i B D\ 



Demonjlr. DucHris ex polo C ad arcus A B, BD, ^rcubus 

 circulorum maximorum C G et CF normaUbus, facile 

 liquet efl^e 



AG = iAB; FDzr^BD et AC-CD-^AD. 

 Atqui in triaDgulis recaangulis A G C , C F D eft 



H 2 £0. 



