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# Title: Solvtio Problematis A R. P. Marino Mersenno Minimo Propositi (shelfmark Leibn. Marg. 230, Stück 2)
# Folio 28, page id 1815206918:0033
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CONFTRMATIODES
Corodarium tertium.
DAcectertio quis denique excet-
sus, _ quomodo decrahendus
SIE. CCiamimnumerIS, aratione A ac
B, veremancacratio aqualis rationi
A ad BC iuxta lenlum propohtio-
nis. a ratione enim Aad B, item à
ratione Dad B, e aratione L ad B,
detrahendae sune duxe cerrix ratio-
nis Aad B,irem dux tertiae rationis
Dad B, denique dux tertix rarionis
F ad B: quod quidem Hecli A, D, P.
ita diuidantur vei dinila cA P C in B
_c C; hoc est, auterantur ab antece.
dentibus dua tertix, remanebie
enim exratione Aad B ratio F ad
B, hoc est + ad 2; item ex ratione D ad Bremanebir ratio C ad B, hoc est 8 ad 2;
atione F. ad B remanebit cacio LLad B hoc CA10 ad 2, quae aequales crune
rarionibus A ad BC vOI D ad B C, aUE F ad B C singulx singulis, reconsideramei
Ouod h aliud exemplum exercirii caussa pla-
Ceti hErario IadRL vEI2 ad 8i Cic aurem RL. di-
nilum in K2, X I. 6. ratio igicur P ad K adrationem
TadRL CAVEK L ad K, hoc eAt vEB ad 2, sivCVE
quadrupla ad simplam: excestus autem RI. Cuper
R est L, 6. ratio autem L ad R siuc 3 ad r, continet
Les quartas rationis RL ad K. excessusitaquera.
ferantur a rarione Iad Ktres quarta. Quod hech ab L anrecedenre auterantur
tres quarea scilicer gremansul 3, adeoque a racio M ad R 3 ad2 quae x.
 CK
tat patet.
tionis FadR super rationem Tad R L, Cunteres quarex rationis L ad R. itaque au-
qualis es rarioni 12 ad8.
Corolarium quatba.
Lqueexhoclacetquacco codemie
ad decrelcere rationem Aad B, Pel
ablationem factam ab iplo antecedente
Ecurdecrelcit per additionem tactam adB
conlequens: adeoque haec duo in idem
plane eclcleteodo in addicione ad con-
lequens, ee in ablatione ab ancecedente,
autcontra, proportio leruetur: quod qui-
Calcacaclca clclllatur ilis ld liti ee
BC dinilum est in B ex C aut centa. NNam
cercas, quod HeES A ica dinidatE LH L, VI~ F LInEdUIX FCFEIX TOTIUS A, rema-
neble ratio DF ad B, aequalisrationi A ad B C; ita lad B acras Cduplum
iplSB, ACVEC Anc duxe tertixe torius BC, CtCtatI HdetB Per addirionem
C dd consequens B, diminura duabus certiis rationis A ad B. nam ratio
A adBC, peradditionemipsius C, aequalis Acrationi DF ad B, quae dua-
buscertiis minor est ratione D F ad B hoc est A ad B: codem modo hcutratioD L
nioDFadB.
tA a ratione A ad B auteras duas
seu Aad B, per ablationem duarum certiarum torius DF. Scilicet per ablationem
F. F, reddicur diminura duabus cerriis Lalas L leu A ad b, realet c
Lola