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# Title: Solvtio Problematis A R. P. Marino Mersenno Minimo Propositi (shelfmark Leibn. Marg. 230, Stück 2)
# Folio 11, page id 1815206918:0016
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Y A D R A F V R R.
HTO TTC. pertertiam huius erune superkcies DR, RF, FMI, M N, H C incert
aequales, onde superficies DK communis est inensura superhent , aVLI.
sed CFI superficies polita crar ad superficiem D C vequacatalus ad eius dia-
deari concincatiadeoque ea magnitudines lune commenturabiles; quod est abi-
metrum, isitur ex numero exponibile est quocies diameter quadrari, lacus sui qua-
surdum non cu C Mee qua sepertuntur dua Dest . MuoCtat
demonttrandum.
TInE denUO VE antE AB, A C asymprori hyperbola DL LL, a MICa
Cu FC, HC aquidistances alymproro A Metcspiant duas III.
emeles DG, CHI commenlurabiles.
DiCODE, FC rectas esse in Peric alicuius Lacterus, ut eua Pocelt ext-
berirecta t.
Demonstratio.
rmenim D G, CFt supertictes commensurabilessine, communem aliquam
maximam mensuram habe duls sic ea superficies O FI, determinata per lineam
ON Parallelam alxmproto AB: que cercio v. 8. contineatur insuperticie II 6.
Iraque per secundam huiusrac L Cad FTC, criccriplicata rarionis NO ad HIC.
Sedeadem superticies bis v. 8. repetita mensurabat luperticiem DC, isitur cum
superticies D C bisconrincar superticiem OFI, etiam ratio D E. ad FC, bis con-
cinebicrarionem iYO ad HIC; liull quod in idem incidit, ratio D F ad F C, crie
duphcata rarionis NO ad II C per Cae. Led d ciusdem rationis crat ratio F B
ad LC criplicatai ergoratio D F. ad LC duplicata est ejus, cuius ratio FG ad
ITC est eriplicata. Traque cum Fe linca verique rationi communis sic, manite.
Aumelelineam HIC esse in serie racteliis in qua sunelineae D B, F. C, quod erat
minetur. Fric enim ratio D F ad PK deNOad IIC. Item si cerrio continuérurra-
per celclam huius omnes superticiesD R, K F. F M, M N, N C xquales inter (c, ac
linea DLTK. F G, LM. NO LBaContiue proporcionales. manifestum isi-
cur est iret D FF. C. Mlleas e  terie in qua est HIC, et quidem in serie racio.
nis NOad HC, lue DE. adt Lh ueuetat demonterandum.
demonstrandum.
Exid quidem manitestius adhuc apparebie, s Per Corr. primae huius. intet D F.
_ F C Consticuntur K Imedia proportionalis quae ad eandem hyperbolam ter-
cio eddem LKad F Cper rationes F C alt L M, I. M ad NO, _ NT Oad FIC, cruit
 uis u   p   a i  t  u         dle  e m e          m