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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
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CONOTDES HRPERBOLTCNH
Demonstratio.
recta plano F. DF, adeoque ad lineam
FF. ergo PO parallela ad MN, eciam re-
Eta eltad F F. insuper quia DP est in super-
sicie conialrmprorici, cric angulus PDO PaF
angulo E DO, hoc CH ML. N. lunEverO e an-
suli DO P, LNM recti ve Facile ex hypoch.
colligitur. quare cum laceraDO, T. N eriam
sinexqualia, crune quoque bO P, NM aequa-
leS. IBICUE NO, P MI, IUNgUNEOP, NM aequa
les e parallelas. ergo ex iplx Cunc parallela
ergocum angulus PON oltensus sic rectus,
etiam O PM reduS erIE. ergOCMBEanSIE CIr-
culum. planum erso D PMcansicconum; de
indequia iam octendiM P ese parallela NO.
estque eciam extrp. DI Parallela NVO, crune
L. D, MP parallele ergo L M, in vno d plano
eA cum rectis MP, PD, D I, in plano scilicet
conumcansence: et quidem paralsela ad D P; cum P MI, D L IUNSANE DL, PNI X-
quales ac parallelaS, erVO LM nON COnCUrTEE vnquam Cum DP, quae est planocan-
senci e superhcici conicae communis; ac proinde, quia planum cansens cum co-
nonon convenier rnquam nih in Cola linea DP, Pacec P. M cum Superticie coninon
concurrere. Acquiper praecedenr. superticies coninunquam concurrir cum conoide.
Ergo P Mmulcominus unquam cocurret cum conoide, ac proindeneque cum co-
noidenslectione GNYT. quod aurem accedac ad inceruallum daro minus, lc ostendi-
cur: planum cangens si verlus balim vna cum cono producatur, ad conum accedic ad
inceruallum daco minus; nam factis sectionibus circularibus basi parallelis, cum cir-
culi hane maiores dacis quibuscunque, anguli concactuum M P R RenEdatis minores,
accedicaurem ex comea superticies ad conoidem ad inceruallum daro minus ergo e
planum canses accedic ad conoidem ad inceruallum daco minus. ergo e linex L. M,
ON L. ad invicem acce dun inceruallo daco minori. Pater ergo proposirum.
OPOSITIO CLXZVI
LDico coni alypoet D FF. sectionem OS R inter alymproton
LM Cecoirura ic L. M eriam elle alymprocon lectionis QSR.
EX O cenerobaleos ponaeur OP, quae sic
parallela PTMI, _ IUHBANEUFD P, P M quo-
niam planA F PF, L. NM recta lune plano
EDF, eric communis eorum sectio MIXY
Demons.
IIdem posicis.
D26. pr imi
Cr6. tersiso
ad L. D, isitur OY ex P D xequalestum. elt aurem L.O dimidium diameeri exint
nON CONCUTrErE Cum lup ertcic coni. quare neque cum sectione SR, qux est in co-
ni GupertCIC, VNGUAM COnVEHICE.
Si Scenimangulus NY LM ex constructione dimidius anguti F D F, quem a Cy mprO-
e complectuneur: vnde SPONAtUE O Y HOMIHaII all L  _ B X; COHCIMB CM
ABC sectionem, erit D B ad BZ, ve F. O ad O T, sed ve B D ad BX, ita cAO T
verlae, de I. D hoc est OT dimidium relle. lgicur L TM alymprocos elt hyperbo
lae SR. Idem paret ex demonstratis t Pracedener, illic enim octenlum cAt I. M
orel
  t     p M  at. te     .    e t     t. H M   A A    B  H     1       A   B  .  B A u   uu   ste n u