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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1080, page id 1815201908:1137
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1080
CONOIDES IILILERBOLICYH.
Corollarium.
TXperbolX OSR, ONF similes M, nam iildem concinentur asymproris per
176,  177. ergo per 17 4. Uimiles lunE.
PROPOSITIO CEXXVLII
Alccodoides cono aly piocou, ee hac sectio  lG axi pa-
ralletas quae recta sic ae pranu ABC ductum peraxem, extibens
hyperbolam RL. C in conDLL, d sectionem B N H in conoide hy-
perbolico: _ ducatur ONM P parallela lC Y.
Dico quadratum OM excedere quadrarum ON codem excestu quo
quadrarum lC excedic LHI quadrarum.
Demonstraiio.
DCdNAEE PlanUM R M S baHI DO F, Xqui.
distans, extribebuncur duo circusi TNV
_ RMS, Parallelicirculis AITC, DOF.
erieque quadracum ON aequale TOV re-
ctangulo: quadratum vero ON aquale re-
ctangulo ROS. quemidmodum cciam qua-
deacum TH aequale rectangulo AFC, et qua-
deacum IC,aequale DTF rcctanoulo. (cd re-
ctongula R T S,F CD, sunc excestus rectan-
Suloru R OS, F FD, supra rectangulaTOV,
CTA. ereo rectangula RTS, LCD criar
sunc excessus quadeacorum OM, IC, lupra
quadrata ON, ITI. sed rectangulum R TS
2guale est rectanoulo F CD, igicur eciam
excessus quadraci OM quo exccdic quadex-
cum ON, xequalis es excestui quo quadracit
(O, excedic quadracum LFI. Ouodcrac de-
Alupa in demonstracione rectanonta
CD, excessus ese rectangulorum
ROS, FID, supra rectansuta TOV, CIA.
hoc aurem sic demonstro. rectâgulum ROS.
xquarur rectansulis RT, OS e ZO, OS.
Sed rectangulum TO, OS, aequacur rectan-
suloTOV, _ rectangulo TO, V S, hoc est
led recrangula R FOS, R TO aequantur rectangulo R FS. ergO recrangulum
ROSaequacur recrangulis R T S, LOV. Ergorcerangulum R TS est difterentia
monstrandum.
bCoroll. 1
hypert.
reccangulorum ROS, TOV.
bR FO. ergo rectangulum R OS Equarur rectangulis R FOS, FOV, R TO,
ot sItIOCLXEIA
Mnis lectio conoidis hyperbolici axiparallela exhibet hyperbolalu
ottat eta  PEF AXCII.
Demora