# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815206918:0017
# Permalink to this reading: https://leibnizlegible.com/page/1815206918:0017?run=74
# Title: Solvtio Problematis A R. P. Marino Mersenno Minimo Propositi (shelfmark Leibn. Marg. 230, Stück 2)
# Folio 12, page id 1815206918:0017
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815206918&page=17
# Source image: https://digitale-sammlungen.gwlb.de/content/1815206918/jpgs/default/00000017.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 37 lines, status machine
# Lines: 37 recognised, mean confidence 0.90
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

COVETRMATIOHES
PROPOS
51O VI
Ouris AB, B C hyperbola DFFI acympeoris; uni eorum consti-
cuantur xquidistantes recta D E, F C, HIC, continences le suura
commentura biliaDC, CII.
Oporccathorum segmencorum communem maximam mensuram
ed
Constructio es Demonstrario.
DOnatur minorese ratiO D E. ad F G, quam F C ad F C (nam s eadem Sicratio,
erunt superficies ambae aequales per tertiam huius) minoricaque erit (upers-
cies D Cquam superficies CHI per secundam huius. Continuetur ratio D P ad
FCquocies porest, intra terminos D P _ HIC, Scilicet Faciendo reD P ad F G.
sICF C ad TK, TR ad LML. L. M ad FI C, idque per Corr. primae huius. quod si tan-
dem aliqua P NI estadFT C VED F ad F G, cune superticies ipsa D C est mensura
maxima quae seipsam metitur ex superticiem OFI, eim omnes superticies DO,
GTIM.M EI aequales snt per certiam hiius.
Ouod siveroratio D F ad F G quantUM POFCR Continuata Per ratiOneS FCad
K, IK ad L MIincer terminOSD F X HI C, relinquac rationem L. M ad FI C mino-
remquam sicratio D F ad F G (maiorem enim relinguere non porest, alioguin
non esset (eriesrationis D F. ad F. C continuata quories conrinuari porest intra
dictosterminos, quod est contra supposicum) tunc rrendo praxi qua Fuclid.
lib. F0. prop. 3. invenie communem mensuram maximam duarum quanticatum
commensurabilium, ratio F MI ad FT C gux quidem minor est ratione DF ad
FG, auFeratur quories porest a rarione D F ad F G, donec relinquat rationem NO
ad F C: quae si aequalis fuerit rationi LM ad FIC, cririnuenta superticies NC
communismaxima mentura. quod sirursumratio NO ad F C minor fuerit ra-
tione LMad HTC, auteratur rursus ratio N O ad F C quoties porest à ratione
CMadFIC idque semper hac alterna derractione, prour Euclides in lua con-
Aructione Facie, donec tandem relinguatur aliqua vlcima P O ad LTC guX SIEVE
eO v. 8. ad FC. Dico superticiem P C ese mensuram maximam communem
seperclerum DCi, _c G FI.
Postalternas illas rationum derractiones manserine candem rationes vltimae
equales NNO ad F C, S PO ad HIC. Cumitaque rario IM adPO mulciplicet
rationem NO ad F C, sic venumeris lic exponibile quories ratio L. M ad PO
mulciplicetracionem NO ad F C, erit quo juenumeris exponibile quories ra
tio