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# Title: Solvtio Problematis A R. P. Marino Mersenno Minimo Propositi (shelfmark Leibn. Marg. 230, Stück 2)
# Folio 10, page id 1815206918:0015
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CONETRMAL
B5
PROPOSTTIO
VIc rurtasa leries continuè proporcionalium A, B, C, D, d c.
Dico infinitas exhiberi posse series, quarum parres line linex A
B, C, LaC. HCvEFacO A ad B sie duplicara vel eriplicata vel quincupli-
caca, vetcemuplaaa aC. rarionis quam habet prima ad secundam al-
cerius seriei exhiBICE.
Demonstratio.
InElinea F, FI, I, R MediX inteF A, B, C, D. _C AanEL, M, N, O,F aquales rectis
A, B, C, O, F. CTUHEISITUF L ad MI, MT ad N, N adO, hoc est A aet B, Bad C. C ad
D induplicata rarione Lad F, aC PrODterCa A, B, C, D, XC. erunc partes seriei ra-
tionis L ad F. Sed eodem Hiodo A ponantur media inter terminos huius serieiL,
F, M, FI, N,eC. Peries haec secunda parscrit serieiillius terrix, ac propcerea et ie.
ries As B. C, D pars erit sericitertiae; cum ostensa Ac esse pars secundae. cum au-
temintiniex medierates polsinta (signariinter duos cerminos, imo sc infinita bi-
narie medixe, cernariae, quaternarie, de c. patec seriem A, B. C in infinities infinitis
Seriebus alsigtari posle cuius (ic pars, Prouc propolicum erat demonstrare.
PROrOSICIO VI.
LDDE, PC, HIC quae aequidistenc alymproro AB auterantque super-
sicieshirperbolicas DC _ OFI, ica tamen verario superticiei DC ad
OHI, eam obcinearrarionem quam latus quadrati ad luam diamerrum,
Eue re superficies illae sine incommensurabiles.
Dicolineam HC non eAC in rlla ommino seric in qua reperiuneur li
REXDP AFO.
CIncAB, AC alymproritiyperbolx DFHI, de posirx sine rres linex
Demonstratio.
Penim inaliqua serie rationum continue proxortionalium sine eres illae linea,
ponantur esse in serie rationis D F adTK, _ TR ad FG; F C adLM; I. M ad
NO; HO adFIC. itaGuC cum ContinnE proporcionales unc D E, TR, FG, L. H,
es