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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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PIR ALI5.
PROPOSITIO, VII.
Archimedis r4. applicatur parabola
a revolurione orcam incidane dux linex (AH
VIE parabola ABF. quam
D carisaF AD, secet vero dia-
MCTEF DE; IUnGALUEG) AF. P. X
puncto A cdUCANEUr rectae
AHG ABC, de per punctat,
B ducancur L. HTK, FB C, P2.
Fallelae ad D F
Recta isicur AP circulidia
MCtruM AD; FCCTE VerO AHB
ABC, ductxe a principiolpi
EX ATTI, ABC repraelentant,
linea aurem DIC C, retere peripheriam D C l ac proindercetx DI, DC
arCUSDMI, D MC exhibene. Denique parallela L. HI K, F B C reterune
circulos concentricos (cu parallelos V HIK, FBC:
Dico AL esse ad AF, ve DIad D C: plane ve in spirali A L erat ad AF,
SICUT arCUS D M I ad arCuM DMC.
Demonstratio.
DExS. Archimedis quade. parab. VE AF ad F F ita R FF est ad FL, hoc eA D Tad
TE: _E VE AF ad FF, ita C B cA ad BF, hoc cA DC ad CR: Ouare ex ele-
mentis pacee AF ese ad L. F, ve DB ad LC. Ergo hic erium conveniune spiralis et
parabola. Ouoderar demonstrandum.
metrum, vique primi circuli (in LeC) eandem rationem incer schabe.
buncita in spiralem incidences, quam arcus circuli medis intertermi-
num pirae (D) ee limices lincarum ploductarum in circum ferentia Factos.
Cumplis in consequenria arcubus a line spiralis (hoc est quam arcus
DMLOMC. 
APPLIC ATVR PAR ABOL A.
in spirat
oquod principium est spiralis, et producantur ad peri-
Ex quO SEquituE, SCENEO A per Be HL ducanur circuli F BC, L. HK.
Suoc L uc ad AF
TCUS DML ad arcuM DMC.
ee  eee e5a o 12o 131
P RO