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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 953, page id 1815201908:1010
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GEOMEFR IC
est F F ad GHI: elt aurem racio AB ad CD. duplicara rationis B. F al LL. 17
rur eciamrario AI ad C K, duplicara est rarionis P. I. ad CM. Ouod Fuie demon-
Itxandum.
Ouod in scholio peacedenci dictum eA de 169. intellisi erlam voluimus de PrX.
Tenri cheOrCIaCC.
PROPOSITIO CLLAI
Vtracio A ad B, duplicara lic C ad D, ratio quoque C ad D dupli-
caca racioris quam habet F. ad L.
Dicorationem Aad B, quadruplicatam esscracioris F. ad F.
unde ve A Fad CK, ica AB ad C D. Eodem modn intereur eNe L L ad OM, vE
Demonstratio.
in concinua proporcione, scilicee
G, TI, de P.igicur racio A ad B, du-lsC
plicaca eAt racionis A ad FI. sed
racio A ad B; ponicur duplicara.
Facionis C ad. D; igitur racioC
ad D, est eadem cum ratione A
ad FI. Cum ergoratio A ad FI
duplicaca Cicracionis A ad G, CFL
iam ratio C ad D, est duplicaca
racionis A ad 1. sed racio C ad
D. ex hypocheh eriam duplicaca
est rationis D ad F. igiteur rario A
2d C, Cadem el CUM FAEIOHC P
ad F: est aurem ratio A ad B,
quadruplicata racionis A ad C.
Isicur cciamrario A ad B; qu2-
druplicata cs rationis P. ad F. Ouod Fuie demonstrandum.
Scholion.
TAec ratiocinatio habet locum non solum in casu quo prima ad secunda duplicatam rati
nem habet terriae ad quartam, exc. sed vniver sali sima est in quauis mulsiplicata ratione.
nam demonstrandi ratio omnibus casibus insernit, modo artendatur ad numerum mediarum
qui interserendus est inter terminos datos prima rationis.
PROPOSITIO CLZXII
Trratio A ad B, duplicara rarionis B ad C, se
Dratio B ad C, duplicara rarionis C ad D, &
racio C ad D, duplicata rationis D ad F, d sIc
consequencer in infinicum.
Oporceat vltimum siveminimum cerminum
extribere (cilicet F, truius progrestionis in infi-
nicum procenla.
TOcpoemu reperies libro quem praemi-
simus de hyperbolapropositione 133. vei e alia plu-
lalruie smilias
NCerpOmancurintet A ex B FrCS
LQUAnEIEACES, GuIX CU A _x B, GInE
Constructio e cmonsraio
     .       e e  t  .   . 1 1 1 t p     t 1  i ee A     e  t    e t .     t   .     et e