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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 916, page id 1815201908:0973
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910
cum exhypothesiratio A B sic maioris inx gualicaris, pona. urque racio C D maior
PO51+ 2O XCIII.
PR OBOR FIONALLTAFES
racione AB, etiam rario CD, eric maioris inxqualicacis. Acqui per praecedencem
racio B, id eA B F, cune est maioris inaequal. erzo racio P. Fminor est ratione CD.
Acio guxuis ducta in rationem aequalicatis producir sciplam.
dndosatti
Aca sicratio aqualicaris CD, ec alia quauis
A ad B. AacVE A ad B, SC D ad B, PeF 75.
huiusrario C F producieur ex racione AB du-
cta in rationem C D. Sed rario C P eadem est
cum rarione D F (sunt enim D e C aequales)
HOC CA CUMFATIONE AB e CMEFSOratiO A B ducta in rationem equalicatis prO.
Corollarium.
Ie pacer rationem aequallaris in rationum compolicione leu mulciplicarione
ceceris racionibus componencibus adiunctam nihil addere.
PROPOSIFIO XCIV.
AEX SnE 4. rationes AB, CD, F F, GII; S rationes AB, _ G FT in-
cer se mulciplicara letem producane, quod rationes CD, F. Fmul-
Dicorationem AB este ad rationem CD, veracio L. F. est ad rationem
Demonstratio.
lac ve C ad FI, Sic B ad T: per 75. huius AB, OH
rationesincer se mulciplicaca Faciene racionem
AT. RUrSUm ARE VE F ad F, CC D ad R. erie rario
CK productum CD, _ P F racionum: adeoque
exhypochesi ratiOneS AL, CK aequales erun, hoc
est A cric ad I, VE C ad R. Deinde quoniam eA
ve C ad HI, sic B ad P, eric per 13. hurus racio AB
adracionem HIG, ve A ad P. Similicer erie rario
CD ad ratiONeM EH, vE C adK. quoniam erzo
A est ad F, vE C ad R; cricracio A B ad rarionem
EIC, Ve racio C D ad Lationem F F. ergo et ratio AB est ad rationem CD, vE
260 buius. 2 FatIO F. F ad racir C. II. Quod erac demonttrandum.
ducit seiplam. Ouod crat propolirum. i
ciplicatae inter lc:
LaOEOSIIIOKCV.
Acis quaruorrationibus AB, CD, E P, GII.
Oporreac exhibere propotctonem ractonum quas plouucunta
rio AB ducta in rar D, de rario P. F inrarionem 6 II.
Con-