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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1089, page id 1815201908:1146
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OIDES AIYDER BOLLEVM
Demonstratio
1089
rvertcieS ATTCF A AAa in SuperKcieM AFCBFA, aquale a Colidum prO. 245. Dud
ducie magnicudini que oritur ex ductu lemiellipseos AL F ductx in se, cum ex hy-
pochel rectangulum ElF I, aequetur L. R quadraro, et quodliber rectangulum
Oese (dummodo R aequidistae FII) aequecur quadraro S, cum rectangula
HIFBOPR, _C. Sinc Gladracis L R, 9S, dec. proporcionalia: eA enim per 168. hu-
iusrectangulum ITFI, ad rectangulum O PR, ve rectangulum AF C 2d A P C c4S. DuB.
hoc cs reCAHB vIM AL K F ad A S E, hoc cM 4. cllipI. ve quadrarum R I. ad quadra-
cum SO. sed AP L F ductum in sc aequatur solido quod habecbasim parabolam
AM B, de b alcirudinem F B, cum ex hypochehrectangulum sub EB, XC MK x-
quecUE quadraTO LK, isicur eriam AHIC F A superticies ducta in planum AFC
BIA, Equatur eidem Colido quod habeebalim AMB ec alcicudinem F. B.
Similiracione criangulum e FO F ductum in se aequarur solido habenti basim
spacium parabolicum AN B F, ec alticudinem F. B: cu KN, R C (hoC cA FK)
EB sncproporrionales ex hiypoch. ec quecunque SV, ST, F. B, modo ST Scp2-
rallela B B, Simili racione proporrionales AnE. Ouare cum eorum AOCF ductum
in sERQUETuE A O CF A ductoin AFC BI A, e Simul eriansulo AF C F, ductoin
selive in criangulum ABF, cum quadraca HK, aequalia linc rectangulis HFI,
FKO; etam eorum AO CF ductum in se xquatur solido habenci pro basc (uper-
AciCS AM E dE ANB E, hoc est superticiem AME BN A, ex alcicudinem F B.
sed solida illa que alcicudinem habene P. B, communem, sune ve bases AM F BN A,
ANBBS A. ergo e hyperbola AO C F. ducta in (c est ad criangulum AFC F.
ductum in se ve luperticies AM F BN A ad luperticiem ANB E S A. Sed licuE (C d EXIZG.
habCE AOC F. ductum in se ad eriangulum AF C F ductum in le, ica quoque se ha-huius.
DCEC AOCF, ductum in orbem ad criangutum AF C F, ductum in orbem, hoc
est conois facta per eyracionem hyperboles AOCP. ad conum factum ex circum-
ducturrianguli AF C. P, cum quadraca FIK ordinarum policarumm ad quadraTA FM
ordinacim posicarum eandem rarionem concineane quam circuli quorum radii lune
FTK ad circulos quorum radii (une FK. ergo patet conoides ABD C ad conumin-
scripcum AOBD C, cam habere rationem quam superticies AM F B N A ad sit-
perticiem ANBP. S A. Ouod demonstrandum Fuic.
eROPOSITIO CKCI
HIcconoides AB CMtum cylindio F FCVV.
Oporceat aeem Laionem corporum alsignare cxlindri (cilicee e
n
conoideos.
   i      s        .   .  1 t  .   t e  i ie e ptiu.   p  1   u e         u t   e     t an