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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 867, page id 1815201908:0924
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PROPORTIONMLLLALES GEOMEFRICA.
DEETNITIO PROPORTIOMCIAIIS
R LIM A
Proporcionalitatem voco proportionum rationem
867
E X P L IC A F
Velides proporrionem detiniens, alc, eam contiltere in d
 racionibus dmilibus, acque adeo necellario quacuor lalcem vIE
uales cenoseam requirere.
Proporcionalicasigicur cum sic racio proporeionum, duasminimum
complectirur proporriches, quocirca octoterminos porturac. Hamracio
incet duas consistil Gllancirares, proportio incer duasrationes vetatu,
quare gauelormeiota requirir. Proporcionalicasigitur duasproporcio
rescomplenu, veldembra seu cerminos exigit: quacuor scilicerrario-
res, quarum lingulx incer duos cerminos consticure Cune; vel duas pro-
porcioncs, quarum linsula quatuocem O em vissuales comipl
auneur. Exemplo Facilius res in-
nOcclcer. SinE raTIONES QUaTUOF
AB, CD, EF, OEI, duo termini
AB, racionem consticuune: sed
AB, _ C D Similes (1 FuerinE ra-
ciones, proportione consticuene:
ita ve diciqueat ve AadB, ita C
ad D, vel ve F ad F, ica C ad H.
veru quacuorrationes AB, C D,
FF, GH, proporcionalicarem
consticuune; que sic efferri deber:
ad racio Ct: Uou caen ide lea ene Mes ena et catu quo
plurima enim raciones, incer e ames, ul propencenateos faceetenstans linea assumenda est
ex z. Parcehulus bIl, et Geouteumque quaruor rationibus expolcis, For- pro unitati
mari pores proporrionalca. Polico enim I, denominatore rarionis AB;
rerir aut provorcio lactentum AB, CD ad proporrionem rarionum
FF, CCI, eAt verario lk ad raltenem L. M. Gua Comdcrallo non parui
ponderis exiltimanla cA, Ccopus enim in quem collimarrocus huius libri
decurlus, incomaxime consistir, verationes dissimiles, ad vlum Ccome-
tricum reuocaripostine: nam in Ccometricis proporrionibus ab antiquis
auctoribus, limilicudo rationum Cola Fuic adhibica; ica ve argumeneum à
proportione nullum posset proterri, quod similesrariones non concine.
rec: iuxra detinirionem iplam proporcionis, a receribus nobisrelictam;
quae
abu5
d
m
H, K, L, M er
eat
ira
nt denominator
Runitatem, ut papior rationis termita
ad posteriorem. Sed itar
B alium habet deromi
torem quam ratio
laeterum hic sensus probu
Cprincipio secundo
bi quod nempe compositio ratis
ex plicatur per multiplicationem
deteominatorum. Nemp
patet haec explicatio deno
minatoris maxime ex princi
quarto, ubi aitinam genominati
lonctis in rationis terminum
consequentem producit anne–
cedentem. Ergo KD= C
Ergo R = E L H
Si denominatores velimus expri
in
artus
quemadmodum estracio AB, 2d
CD rationem, sic CA ratiO F. F
distimiles sinc rariones AB, C D, d F. F, CHI proporrionalicasnon existat, mere per Lineas, una quaesam
ee rationis CD, ixlo K; ex reliquarum EF, GHI iplis L ee M: po.
 e a o s i i 1t pi ta e tuu t   ut  a uli e  ti  pt i   i  e ee  e     ita  t a i . t          a    t   a s it