— = Csp) 



bohi, niit cllipns, proiit maxima eius latitiido fcu inclinatio ad ae- 

 quatorem fucrit =90°, vel ro, vcl =: 90° — A, vcl > 90"— X, 

 vcl dciiique <^ 90° — X. Primo atquc fccundo cafu natura pro- 

 iciftionis non mutatur coni fuperficic in planum cuoluta. Cc- 

 terae \cro lediones conicae cuolutionc coni in lincas ciiucrfae 

 raturac dcgcncrant, in.o ficri ponunt transccndentcs. Si enim 

 (Fig. 3.) AMQ^ fit proictftio circuli Ce (Fig. i.), pe mc- 

 ridianus P f , atquc dicatur QH — QPH — y, HK=f3, 

 (Fig. I.) ps — .x^ (Fig. 3.) ei^.—.y-, et Q proioctio puncli K, 

 habcmus Qp e :rz y^ fin. X, j' zn .v tang. (y^ iin. X), et 



X* -\- y*- /) O- —J^i 



jin. X' ( coj. K^ -hjin. 2 X f ang. j3 ~^-Jtn. X' tang . p-" ) ' 



intcr (3 et y dcniquc hanc analogiam, tting. HKrrfin.CHtg. KCH, 

 vcl pofito KCH=ia, tang.j3 :=z tang. a cof y. Quoniam hic 

 in vna aequatione y, in altera y fin. X occurrit, non nifi ac- 

 quatio transccndcns inter x et _y obtinebitur , nifi forte fin. X 

 valorcm habcat rationalcm. Statuamus e. gr. X=:3o^; erit 



^— rtang.iy, adeoque fin.iyznz -2. , cof. Ji y :r -. * ■• — ; 



vndc ehcitur cof.y =z f^^il]; fietque hocce valoic loco cof.y, 

 et tang. a cof y loco tang. p fubfhtutis, 



2 _4_ .t 16 (y' -t- 3»)' 



x'-i-y 



fcu 16 (.V* -h ,«) — 3ix^ -hyy -h 2 tang. a /3 (a'* —/) -p 

 tang. a* {x* — yy. 



§. 8. Si angulus a crcfcat vsque ad 90°, circulus Ce 

 flhit in Mcridianum P B (Fig. i.'), qui 90° diflafa Meridia- 

 no P f fcu nolho a.KC p e. Acquatio vero nolha diuifa pcr 

 (tang. ay", quia pofito 01=90°^ omnes tcrmini prac \hin-,o cuancs- 

 cunt, pnicbct A* — j- = o, vcl j' zz: :i: .v. Prohcitur itaquc 

 .. Noua Acta AnaiL hip. Sc. T. II. IM INIcri- 



