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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1057, page id 1815201908:1114
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CONOTDES PARABOLLONM.
Demonstratio.
DEr puncta IX K, PONAEuE reCtA OCCUTreNS
perimerro parabolx in punctis LM. Crit Cr-
50 rectangulum F. IF ad C KII rectangulum,
VEL IM ad L. K M rectangulum, ve est osten-
sum lib. de parabola. 2 sed eodem modo est re-
ctangulum CID ad ARB, VEL IM ad re-
ctangulum LR M. IgItUr vE F. PF rectangulum
adrectangulum C R H, ita CID ad AK B rC.
ctangulum.
PROPOSITIO CXXXIZ.
rEctum sic conoides quovis plano obli-
D que ad basim.
Dico per arem heri posse sectionem quae
recta sic ad planum duetum.
Demonstratio.
Icconoides parabolicum A B C sectum sectione
DDEF obligue ad basim A TC, IGICUTAXI OCCUEECE
in aliquo puncto C, cum sectioD F. F axi nom xqui-
distet, erigatur ex G linea CFI normalicer ad pla-
num D E F, ec per FIO, ee lineam P planum po-
nacur: eric illud rectum ad D P F planum, cum om-
nis sectio per lineam CHIb recta sic ad planum
DEF.
eR OPOSITIO CZL.
Mnis lectio conoidis parabolici
adaxem obliqua elliplim FOrmat.
Demontratio.
ctionem DF, ex puncto vero I, quod com-
munc ectaxi ex lince D F, crigacurnormali-
ter TE ad planum AB C, quod factum fuie
peraxem rectum ad D F F planum, pona-
cur denique per PF planum IIF. R, quod
aequidistee bas CL B, Faciens in planis
BAC, D E E seCtIONCS KTFT, E INT. FCquO.
niam IB recta eA plano B AC, cperpendi-
cularis cAt ad DF, KFT. Igieur circulus eAt
Asectio FIR R quare LInCX LK, IF, IFF, IM
aquales sunc incer se. Tandem ponacur planum DT R O PAFAIICIAM EI E. R. OCCurrenS
plano D P. F, secundum communem incerlectionem P R. Ec plano B A C. secundum
rectam
IE conoides paraboneum ABC plano
DE F, oblique sectum ad axem AC. DicO
DE F Mlliplim ellC. AGaEUE enim peraxOm
conoideos planum quod rectum _c ad pla-
num DF. F, exhibens communem incerle.
1057
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1f. 3. 2X
d137. hn-
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