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# Title: Solvtio Problematis A R. P. Marino Mersenno Minimo Propositi (shelfmark Leibn. Marg. 230, Stück 2)
# Folio 13, page id 1815206918:0018
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   i d
tio EMT ad FTO MulEipLICCEFALIOHEMP O ad FTC. Sedrursus numeris erAL ex-
Ponibile quories rario DHaNO mulciplicarctrationem I. MadIIC; igitur
et numeris exponi pocest, quloriesrario D E ad NO mulciplicer rationem PO ad
FI C. itaq; curatio N Oad F C aequalis sir rationi P Oad HI C ex suppolico, eriam
innumeris exponetur, quocies ratio D F ad F C mulciplicer rationem PO ad
TTC. isicur exponi pocelt per numeros, quories superficies DC concincactu-
perticiem OHI, per seccam huius; ac propcerea superticies OFI meritursu-
perticiem D C. Jam reto quoniam CuperticiesFR, KL, LO aequales Punt An-
sule superticiei D C Pel tertiam huius, cum ex conser. ratio D P. ad F C continua-
ea sic perrationes FC ad LK, IK adTM, IM ad P O; eriam ergo superticies
OII mecietur toram superticiem O P: Sed ex superficies OHI meritur seiplam
igicur superticies OFC, toram luperticiem OII mecitur. Ouod crat primo de-
Ouod autem superhcies O Ehemaxima mensura superhcierum D G, G FI, SC
quidem ostendetur. Si enim luperticies OTI non lic maxima communis mensu-
rasponacur si fieri porest maior luperficies SFI, determinata per lineam SR
alnI BEoco B A parallelam, qua veramque commensuret. Tortur superficies HIS
aliquories reperica commentutat superticiem C TI, vei ex luperticiem DG. led d
De haperticies aliguoties repetita metiebatur superticiem GL per secundam
huius, (nam ex constr. ratio D L ad F C aliquocies continuata, Faciebat rationem
FC+ adL M) igitur ex FTS superficies commensurat superticiem CT. sed d
cadlem superficies FIS mensurabat superticiem CFT, igitur eade superticios IIS
aliguoties repetita, menlurar superhciem M II. Sed ratio L M ad HI C aliquories
repelica consticuebatrationem D F ad H O, igitur per secundam huius, TupCrA-
AciesFIS aliquocies repecita mensurat superticiem DO. Sed eadem superticies
HS mensurabat quoque corant superticiem D C; igitur etiam superkicies FIS
memturabie superticiem N C, Hoc eA ex constr. et secunda huius, superticiem
EIO.naior minorem, quod est ab surdum. Non igitur alia quam FIO Superhcies
est communis maxima menlura supertcierum DG, GFI, quod secundo locode.
monstrandum.
Monleracum opoccuu.
Corollarium primum.
Exhis Facile intelliges idem ele pCterE MEn SuTAMI MTAMIMTAI CBMMUHEM I-
perticierum D Ed CTI, quodl pecererarionem aliquam L V. 8. ad LLC, cl-
ius ratiOneS D R ad F C, _ LC ad FIC sint aliquories mulciplicata.
Corollarium secundum.
Iinc eriam manifectum est, Gusa uratio nulla reperiri possitper alcernam il.
lam rationum detractionen cuius veraque rario D P ad F C, _ F C+ ad TIC
sc aliquories mulciplicala, lpexticies D C C FPere incommensurabiles.
OS1
X
Acâ serie progrestionis A, B, C, D, de quauis magnitudinc F, quxe
non sic in seric rarionis A, B, C, D. dererminandum est an in vIla
Ceriepotire C eBC.
Constructio
  m