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# Title: Solvtio Problematis A R. P. Marino Mersenno Minimo Propositi (shelfmark Leibn. Marg. 230, Stück 2)
# Folio 35, page id 1815206918:0040
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Corollarium ondecimum.
TX HIS PATEEET. CEFArE FUESUIS COSGML Ex PFOP. F2. DUTArNE sequITatIOneS A F
L, C FIad NI; D. Pad O esse rationes corinue proporrionaleas inquiunt
ratiO AF adI duplicata est rationis C FTad NI, ex ratio C II ad NV, MMplicara ratio
nis D Fad O. isitur rationes ex sune continue proportionales. Lcque hoc mode
ad NV, D Lad Onon esse contince proportionales.
Sed quidlMiFLM (ICZ CETOTE LupPOSIEO, Veritatem, quat HOIIMaSitancut lequi
Deinde vehocallumeretur, tamen Mmme regueretur laliones easene com
nue propercoates. Suba qudem innumeris priusoltendo, deinde id iplum
rurlus Propolitionem r2 examinare dum volune, inveniunt rationes AF ad L, C: 1)
debere, noneliciane: Nam imprimis nusquam altumpcuni est rationem A F ad L
duplicatam esse tationis C FIadH L hane turrus duplicacam racionis Dlad.
namhoctacumelle iam oenaimus.
Ccomerrice demonstraturus.
Suppono ex l. de Proportionalicactous P. Cregoris, utres concinueproportio
halesrationes exhibita  actelem mediam in se ductam, idem producere,
quodu prima ducta in tertiam.
Siciam A, B, C, D, F. Ordo quinque Proportionalium. Latio A ad L auplicalaci
rationis C ad F: ratio autem C ad LMaplicata estracionis D ad Fi. non tamen ideo
rationes A ad B, C. ad F, D ad P concthue proportionales crunt. quod sic Patet.
4 32 16
LiaCVE C adL, IEa L ac His culle racio
C ad P. ducta in se producet rationem
C ad F. Irem duCatuF FALIO D Ad P in F2
tionem A ad F. SIVC AaE VED ad F ita F. alt B prodibirque ratio A ad C, hoc eAB
ad F. Patet aurem rationem B ad F candem on en Cmatione C ad f. Ho
cara lic ratio A ad F. rationis C det L. Guemadmodum haec iplarario C ad F, est du-
tur Cunc rationes Aad Fi _ C ad F, deinde D ad F proporcionales, quamnis dupli-
plicata rationis D ad F.
Contirmabitur hoc iplum simili
Fere discurli. Ponantur denuo qua
cirates A, B, C, D, E. continuare eandem rationem A ad B. erir itaque ratio A ad F
duplicata eius quam habet Cad P: _ similiter C ad F. duplicata rarionis D ad B.
cumque habeanteres hae rationes commune consequens crie ratio A ad P ad ra-
tionem C ad F; He A ad C per propolicionem secuidam libri de Proportionalitati-
bus: _c ob eandem caulam erit ratio C F ad D F, vE est C ad D. Gua vetoae
nes cadem ese (upponuneur propter concinvationem, crieratio A ad C dupli-
cara rationis Aad B, hoc est duplicata C act D. GualC TaCIO H adt L C adt L D au L
proportionalesnon Cunt, cumcerm  operales essenon pote