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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 906, page id 1815201908:0963
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+iMtins
906
PR OPOR TIOHALLTAPES
EROPOSITIO LXXI.
Vicratio AB ad CHI, ve eltrario DF ad I L. rationem. Sic inluper
Oratio BC ad HTI, vees P F rario ad racionem L ad HI.
Dico proportionem rationum AB, DF, eAc ad proportione acte
num BC, L F, reproporriorationum G LI, K L. ad proportionem ratio.
NUM HII, LM.
TuFPaI
Demonstratio.
GTaEVEE ad D, SiCB adN, ee ve
E ad F, SC C ad P, VEVeH P.
ad K, SC FI ad O, vedemum ML
adF, ACPad O. Duoniam exhy-
Pochesiratio AB est ad rationem
GFI, ve racio D P ad rationem
K L, cric permucandoaratio AB
ad ratIOneM D F, VeraciOO HIad
racionem R L. crg0b A elt ad L,
veKadOhocclerario ANEqua-
modo ostendam rarionem B P aequari rarioni FIO. ergo
eadem cum racione B l. en Propoctoracionum Ci H. R L, eadem elt cum racio-
ne C,O, proporcio denesde racionum IIL. L. ML eadem cum rarione IIa. ergo
proporciorarionum AB, DP. est ad proporcionem racionum BC, F. F, veproporcio
racionum C LI. KL, ad proporrionem rationum LII, I. M. Guod eracdemonAtran-
dum.
O, vi
Fatio AN eAt ad FaEIO
BP ad racionem IIO: _ PeFMIHE. TatiO
AN est ad rationem BP, veratio CO ad racionem FYO. Sed peF Y3. huiuSPEOPOE-
eio rationum AB, D F. eadem est cum racso LLL a proa BC3 LL
eROPOSITIO EKLII.
rationum, quantirares C _ II.
AEA (IMEFreSrationeS AB, CD, E F; denominatores aurem AB, C D
hacoris rarionis AB, etlat o Calle euancitas I denominacor rationis
E F respectu F denominatoris rationis C D.
Dico liquancicas l sic denominatorrationis P. P respectu C denomi-
Lemonstat.
Voniam ponicur C de
nominacor racionis AB
respectu II denominatoris
C DracioniS, ISIEUEVECCD
racio ad rationem AB, ita
denominaror FTad denomi-
natorem C; cumque Racua-
cur racionis AB denomina-
TOF C, respectu quanciratis L
qua est denominacor rario.
nis P F, eric quoquere ratio
B adracionem PP, ira demominator C. ad P denominatorem. erso ex aquo etur
ratio
in