66 OBSERVATIONES DE COMVARATIONE 



remoueatur. Quocirca vt haec conftans debite derermi- 

 netur , alium cafum confiderari oportet ; potior autcm 

 non occurrit , qnam is r vbi puncta M et N in vnum 

 coaleicunt , feu quo fit uzzzx, et nx" — inxx-^- i —o. 

 Hinc autem oritur xx~i-^-^j~^y £t x~V (i -f y (l ^_ cc J 

 16. Sit igitur O hoc pun&um , in quo an bo 

 pundta M et N coalefcunt , ductaque applicua OI erit. 



abiutfa CI^VCiH-Vr^) etr ^AO^f + Vfi+^) 

 -f-Conft. Hinc ergo obtmemus conttanrem quaefitarn< 

 ~2AO-r-V(i-f-^J ob V n — V(i-i-cc). Quo~ 

 valore fubftituto erit pro quibusuis punchs M et N 

 diuerfis ? ita fiimtis y vt fit uzzz Vjjjffzrs; fun ma arcuumr 

 AM + AN=r8iy»+2AO-r-V( 1 -{- c c } feis 

 ON-OM=:«V«-f-y(i +«). Sic igitur duos^ 

 arcus nadli fumus ON et OM , quorum differentia. 

 ON-OM geometrice affignari poteft. 



17. Q110 autem facilius pateat , quomodo tam 

 Fig. 7. punctum O, quam ex punclo M punchim N definiri 

 qieat ; engatur in A perpendiculum AD~f, eritqua 

 recta CD hyperbolae afymtota ; tum pofitis CP— x\ 

 PM~ j, ducatur tangens MT, erit ob yzz cV(xx-i) 

 et d r~^ZT) fubtangens PT — "—^ — - x - ^; et 

 CT — *; et ipfa tangens M T — y v ^*,* — -' . Hinc pro- 



j. '/ixi "1 PT ., MT __CA 5 . MT r ~ 



dlt V ^^zr s ~ ^x, ideoque uzzjyi.(7^)—cv..pt — e Q: 



iS. Ducatur ex centro C tangenti TM parallela 



CRzzCD, demiiToque ex R in axeiu peipend^uio KS, 



erit CS — — M '-f", ideoque C Qzl -^- . Quue CQ ca- 



. pjf-nda ent teitia proportionaiis aa CS et CA. Com- 



modius 



