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# Title: Solvtio Problematis A R. P. Marino Mersenno Minimo Propositi (shelfmark Leibn. Marg. 230, Stück 2)
# Folio 14, page id 1815206918:0019
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EOHELRMATTONE
Constructio  Demonstralho.
Ontestuantur rectx C FL, C Lad arigulos rectos, tiacque ve B, ad A, ita O L ad
ON: ex punctis aurem L. Sc NVerisantur I. R de NVM aquales quidem aue
proportionaleslineis A de B, Parallela vero ad G FI, crune per primam huiusR, M
puncta ad lyperbolam cuius alymprori lintHIC, CI. denique hac ve Fad A, ita
CI. ad CI, erectaque 1O aequali iphF, aut certe qua ad K L. candem racionem
habeat quam Fad R C, Par allela aurem lic ad CFI, erit ex O punctum ad eandem
uyperbolam.
Dicoh superkcies kN commensurabilis est superticiei N O, quod F sit in ali-
qua serierum in quatora series A, B, C, D consticui porest repars. Si vero luperti.
cies RN, NOincommensirabiles line, in illo catu linea F innulla Perierum in-
veniri poterit in qua sic series A, B, C, D re pars. Ouod quidem ex pexcedentibus
est manifectum. Demonstrauimus enim Prop. 7. cum CuperticiesRN, NVO com
mensurabiles unt, rectas R P.M NV ese in aliqua scrierum in qua possit exhiberit.
cum vero dua illa superticies incommen surabiles sunt interse, tuc eriam octen-
Tum est Prop. 6. quod magnitudo OInumquam possic exhiberi in vilâ serierum
quae seriem A, B, C, D contincar. Dedimus antem praxim Prop. 8. X in COroII.
secundo quomodo investigari debeat an Cuperkcies KN commensurabilis sit
SuperticiciN O. determinatu est isitur an F. sit in vila lerie reperibile in qua erie
astignare Teriem A, B, C, D, quod erat taciendum.
Scholion.
Busiracior Cetre dignum videtur, quod dat a proorestione Ceriei A, B, C, D,
 magnicue alguat, quod ea quantitas talis esse pos: Venelciogubia
ro, exclula cirnon eus alerie A, B, C, D. Sed ve ean Cu 
lerie inuemripolu, qualcemBCDcopiccaur paste. Nalcc
A e B, non lolum altiguat Pentunem lerle Facios H d b.lel a in lcrie rarionisi
cuius rario A ad Berit duplicaca picaca, Cencaplicata, MCcpal cene
infinitum per Prop. 5. huras. Has CL A ec B, _c B, 8 C, Mcerteri poltunt C dc HI
medim proportionales, cuC ana LCrleS OrICtUF A, G B, TI, C. L Drationis Aad C
cuinsrarionis ratio A ad B crit aupircata: irem interseri porsunt inter A abuua
media R ex L, ite incet Ba C aux medix M e NV, _ tunc oricturenes H, a, L.
,M. D. CMC. rarionis A ad K, cuiusratio A ad B exix erip iaas   Mntinirum
acgC