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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 944, page id 1815201908:1001
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27. PY
press.
PRODORLIONALLLATES
quoque AP duplicacam esse rarionis BF. Ouiam AB G eC F F G, Sune quanci.
cares concinue proporcionales, habentes Canem primamiigitur a ratio A ad P.
duplicaca est racionis B ad F, estque exconetdectone D ad C, VE F ad F. O UaEC PTX
b
914
Ricimus postulatum.
PR OP OSITTO CLMII.
cionceius qualae  at.
Inc proportionales quantitares ABC Sicur de DBF.
Dico rationem AD ad C. F. rarionem, duplicatam habere propor-
Demonstratio.
AAEVEF. ad C, ICa DAcF
et
citaquebrario AD ac
ad+
ratiOneM CF,
deinde quia AC, DH rC
Etangulac aequalia lUnC, VE-
DOtC
Equalia cidem quadea
Co C. clerc L. adC ld Aal
caca estracionis A aet D. Oudutu demontrandum.
ROPOSITIO CLIV
D. Sed veF ad C, ita quoque est D ad F, ex constructione. lgicurracio A ad F du-
plicaca estracionis A ad D, hoc est proporcio rarionis AD ad C P rarionem, dupli-
151
Dicbrationem aa quancicaris ad quincam, duplicacam esse ra-
cionis quam lecunda habec ad quarcam.
YI quinque quantirares eandem rationem concinuauerine:
press. demonstrandum.
baenscentie.
DOnaneur quinque quanei-
cates A, B, C. L
CACMHCO
rinuata analosia. Dicoratio.
nem A adE, cAC duplicacam
omnes quinque linc propor
cionales continua, ioMulcliam
EBA _ C D E, lunEPFOPOI
d27. Pro- rionales quancicates. LLa LLad F. duplicara eA rarionis B ad D. Ouod erae
racionis B ad D. cum enim
eR 61O31L1D CLV.
AF rario AB quadruplicara cAt C. D, ratio aurem P. P, duplicara eiul.
dem:
Dicorationem AB duplcaram eeLalo L. al L.
Demon.