} 6^ ( 



S-i 



t)err:oiiJir. In triangulo redangulo G C A efl 



cot. B A C . cot. G C A r: cof. B C 

 et in triangiilo C E D, 



cot. B D C . cot. F C D 1= cof. B C , 



idcoqiie ob 



tang. G C A = cot. F C D fiet 

 c«.t. B A C . cot. B D C = cof: B C'. 



Hinc per niodum CoroUarii fiiiit, fi ducatur arcus 

 circuli maximi LD, circulum minorem in D tangens, at- 

 c)ue ex ilto pundo D bini arcus circuloruin maximorum 

 DB, DA, quorum hic pcr ipfum Polum C iraufit, tum 

 fi iungatur AB arcu circuli maximi, fore 



tang. B D L . cot. B A D = cof B C'. 



Tum vero quoque infignis proprietas angulorum in trian- 

 gulo A B D hinc deducitur, fiet fcilicet 



cof.BACcof.BDC-fin.BACfin.BDCrfin.BACfin.BDC 

 — cof. B C - I : I = - fin. B C* : I , 



atqui efl 



cofABD-cof.BACcof.BDC-fin BAC.fin.BDC, 

 vnde coUigitur 



cof. A B D n: - fin. B C . fin. B A C . fin. B D C. 



'^^'j^- ^^^' §• 9' Thcorema. VIII. Si ciyculo mlnori in fuper' 



'^" •* ficie Sphaeriia defcripto^ infcriptum fuerit triangulum ex ar- 



cubus circulorum maximorum A B, B D, A D compofiium^ 



atque onguhs A C D ad polum C infijlat eidem atctii cir" 



culi nirwris A D cui ad peripheriam infiftit angulus A B D, 



irit 



