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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 640, page id 1815201908:0697
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onta.
FTY PE R BOL A.
PRODOSITIOCCMI.
gulis G F. F a qualia quadFata F. IL.
Onea vero DC secot circulum in punetis A, C. Ranc quoque recran-
Dico A HIB elle ad candem us perbolam cuius lacus cranluertum AC.
Demonstratio.
Voniam P. FY quadraris xqualia sUnEreCtan-
sula CL Fi quadratis F FI, aequalia quoque
Luncrectansala AF C: (cum AFC, G F F re-
CtanGUIARQUEHEUT) quarCVE, AF. C ad AF. C,
rectangulum, ita quadratum F FI ad HI F qua.
dracumsigieur AFLB sunc ad hyperbolam, cuius
lacus crantuersum, AC.
PROPOSIFIO CCVII
cac aurem hyperbolam AHB
prouucere in infinieum.
EInGENECPOSITa NYM QUC LGNtCE D B, PONANEuT PrETCTCA K P parAIlelX cOn-
tingenti: denique hanc rectangulis DR L aequalia quadFaTA RL. DICO AHBLM
esse ad eandem hrperbolam. est enim rectangulum A N C aequale quadratoNIM, _
ARC xquale quadrato RE, quemadmodum rectangulis A P. C xe qualia lunc qua-
deaca DII: isitur cum rectangulum CF A ad CR A, eandem habeac rarionem
quam quadracum F FT ad R L. quadratum, manifectum es AFTE MI esse ad candem
typerbolam cuius eransuersa diamerer eAt AC.
lROTOSIINOCeNI
Demonstratio.
Vadraris F FY aqualia lunE
Lrectangula A P, C; sCd PH
quadraris xequaeur quadrata FI.
quadratis igieur F Lae qualia (uNE
rectangula A F C: quarECFA
ad C F. A rectangulum est vi
quadracum F E 2d K I quadra-
cum: puncta igicur CTI ad hy.
perbolam lunc. Ouod demon.
Atrandum erat.
Tirculum ABC concingac DB, cuiponaneur aquidistantes F F. li-
Consratio demonstratio.
DEepunce AC delcribatur circulus C A _L cuiuscunque magnicudinis; d con-
Ontingane circuli ABF circulum AD C in A. acta vero communi
AdIaMCETO AE, DOnatuT C C normalis ad AF. occurrens cireulis in
OFI: d hanerectis F FI aquales P. I que aequidistene CC.
Dico C II esse ad eandem hyperbolam cuius latus cransuertum AC.
PR O.