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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 946, page id 1815201908:1003
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DIR OPOR TIONALLFATES
Demonstratio.
Voniam ratio B ad D
outeut Guadruplicaca
racionis C ad D, igicur ratio
B ad C est rriplicata racionis
CadD. coaracio A aB Cu
quadruplicata B ad C; igieur
racio A ad B, est duodecupli-
caca racionis C dd D. Leuracte
B ad D, est quadruplicara cinsdemrarionis C ad D. Igiturracio A adD, est sex
decuplicaca racionis C ad D, cuiusracio Bad D, cst quadruplicata: rario vero sex-
AcCplicara est quadruplicara quadruplicatae (cum quacer quacuor proterant sede-
Csanitella carelas PooMioI.
I TIO CLV
Vod si incer A ad B quaenis dux aNumpEx FuCrinE C ee D.
Dicorationes AC in CD, CD in DB, idem producere quod
racio bis dueta in se exhiber cuius A ad B criplicaca est.
Demonsratio.
medix L, X F.
raconibus, quarum rnius est
criplicaca, componstur, hoc est
exiildem inter le nunciplicaris
producicur. Acqui eciam racio
AB compon ud pb
cur exrarionibus AC, C BBB. Lset etBo ProPoltum.
NECF A _ B, Ponantur dux
AF, F F, FB sunc cadem. Ccd
FaCIO AB, COMPONICUE CX Fa
ratione.
tionibus AR, E F, FB. ergO
Cdit.
racio AB ex cribus aqualibus
Ccaric hinc restentooaa nstu et esce  vartum Laveten
Creomerra in mezolabiis adinveniendis, et i quo culcatis cardo verleeur.
F0olane expropositione iam allaca obseruo incer duas quaricates dacaS A, S B, dua5
mediasexhibere, nois au ee quam racionem nllee qua bisn le ducta pro-
quales, quae incer se mulciplicara producane rationem ipsam A a + B. Jam vero cum
quaevis racio diuidi porit in qualcunque ex quorcunque rariones, ex quaru mulcipli
cacione queac oecoau a aclas rationu daram racionem coponen-
cium Ceu producencium, difficulcare in presentinegocio eam parie quam luperare ha-
aenus Ceometre non poruere. Gueamu adcem arcum dacum circulinon est
distreile in cres parces parciri sine vila alia decerminacione, ica neque rarionem in
eres aliquas rationes qua generene rarionem datam nullius negocii cA: Sed shuc-
vique Gcometrarum industria rano labore reneauie in parres xquales dacum arcum
circuli diuidere; mirum videri non debec quod parcicio alicuius racionis in FreSFa-
tiones, qua aequales sint inter se, de mulciplicarxe incer se rationem datam producane,
difficulcarem contincar. Octendimus quidem Facilem Mechodum dinidendi racio-
nem in parces xquales li divisio illa parces considerer qua per additionem GCneranE
Tacio.
ducac racione aaCa A de B, HCLACOHeM A ad B dividere in cres rariones x-
10
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De
ratie