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# Title: Solvtio Problematis A R. P. Marino Mersenno Minimo Propositi (shelfmark Leibn. Marg. 230, Stück 2)
# Folio 32, page id 1815206918:0037
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VFTF
ATI
e
dD. 8. l. tO. OpeF. GCOM
plicat à ee intellect â prour
cam intesus
C in Corrol.
7. Pacet 9. quomodoincelligenda
 samodo verum sensum
habeat Prop. 12., lib. 20. Oper
Geom
in linc ostenderat Auccor in
casu que proponic, quadolcili
cet lune quatuor ordines conti-
nue provorcionaliui ABCDV
EGTTIV, LMNOV,ORS
FIad S dupicalaracionis IadF.
FV communem habentes rlcimam V, quod ratio A ad L, sic duplicata rationis
C ad N, _ racio Cad II duplicata sicrationis D ad Oi item quod rario Aad0 du-
Plicata Ccracionis C. ad S, ex rario C ad S, duplicata rarionis D ad T. Icem olten
derat quodracio F ad I. duplicata AC Lactos fl ad N, e ratio H ad N duplicara
racionis Tad O; denioue quod racoEad duplicara sic rarionis HadS. Xrario
Tisita exposiris et demonstrac, ICIL Guod ratiO EOT A F ad L. C tories Con-
cineat rationem coram CFCad N S, quories rario C. FP ad N S, conrinet rationem
DIadO Y
Inprimo cum non eNet disticultas, consequentia tamen haec vieima vila est
difficilis, imo e Falsanonnullis, cum eam imnumeris per opcrationes rarias exa-
minare volune. Verum quid s non recte ex operationes acthibeaneur. Nam cum
ex Prop. 8. lib. 10. demonstrecur hxec corsequentia, certe non alium senlum Prop.
hac r2, eiusque vlcima consequentia quam modo polui habere porest, quam ipla
8. Propolitio requirie, alioguin Frustra ea ad demonstrationem adhiberetur. Alium
vero lensum illi s attingas, quismiretur in falsas consequentias, ex ea perperam
intelleet a quempiam devolui: Flicigitur genninus eius propoltionis lentus eA,
aliis verbis in idem recedencibus expolitus:
Focaratio quantitatum A F ad LO costituitur ex rationibus sibi addiris juxta
sensum Prop. B. iam explicatum Corr. 7. quae quidem rariones totiesmulriplicata
Cunc racionum earum qui sibi addira juxta sensum Prop. 8. Constituunetotamra-
tionem quancitaris C FTad NV S, quocies rariones illa constituentes racionem CHI
2dIYS sunc mulciplicarx rationum illarum, qua sibi ad ditae iuxra senlum Prop. 8.
conlticuum coram racionem quancicacis D12d0l.
Ouod quidem verissimum esse demostratur ex eadem Prop. 8. incellect a pTOUE
cam intelligendam diximus Corr. nostro 7. Nam ratiororius A Fad F. O, consti-
enitur exrationibus A adL, A ad O, F ad L, F ad O: item Eotaratio C FI ad HYS
constituitur ex rationibus C ad VT, C ad S, FTadN, FTad S: denique cora ratio D I
ad OT, constienitur exrarionibus D ad O. D ad F, L ad O. Tad T. Ostensum au-
rem eratin catuiam positorationem A ad I. ese duplicatam rationis C ad NV; ra-
tionem vero Cad NY duplicatam cse rarionis D ad O sirem racionem Aad du
plicacam esfe rarionis C ad S, ec rarionem C ad S duplicatam esse rationis Dad Y:
rursus octensum rarionem Fad I duplicatam esse rationis FT ad NV, rationem verd
FTad Hduplicatam rationis Tad O; denique rationem Fad O duplicatam esera-
rionis Elad S er racionem Fad S duplicatum eAc rationis Lad Z. TBicur patexra-
cionem