# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815206918:0014
# Permalink to this reading: https://leibnizlegible.com/page/1815206918:0014?run=74
# Title: Solvtio Problematis A R. P. Marino Mersenno Minimo Propositi (shelfmark Leibn. Marg. 230, Stück 2)
# Folio 9, page id 1815206918:0014
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815206918&page=14
# Source image: https://digitale-sammlungen.gwlb.de/content/1815206918/jpgs/default/00000014.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 33 lines, status machine
# Lines: 33 recognised, mean confidence 0.88
# 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.

V AD R A TV R. AE
ROPC
5
F 10 IV
Ara SiC Peries linearum A, B, C. D, E, ac. CoMnuaca secundum ra-
cionem Aad B. Daca Cc inCuper quaevisI.
Oporreat ostedere an F exhiberi pollirin telle rarionis AB C verim-
A ad B, vel minoris B adC.
que liopus fuerir producta, secundum rationem maioris inae qualicaris
Constructio ex Demonstratio.
PIE PCTICS MI GI, MITLMT, MK MS Serici R, D, C, B, A: TumprilqueMN. MD
AO, ME N, quae sint aequales L, D, C, B, A, CrigAnEAEO P, TTV, IX. RB. L dparal
telX rECTR MI N, qUa COnCUETaMC Cum rectISHP, OV, YX, ZB, adqua aquidi-
SEABEM L, in punctis P, V,X, B, d: Crunithaec puncta ve dictum est ad hixperbolam,
cuius alimprori untM PY, M L: Oclendere isitur oporter an Psc in serie A, B, C
D. F, XC. hoc est in serie M NV, M O, Ut Y, MZ. M N. Fiat rectangulum (UPCF F (pO.
Sico quod NM Langulus Sicrectus) d alia recta , Xequale M P rectanigulo: Cum-
Dea deinde MIS qua sic ae qualis O, Crigatur S R aequalis F parallela MN, erir pun-
ctum R ad hrperbolam PBd, cum MIL rectanoulum equale sic M V rectangulo.
vel isitur punctum R est inter pusscla P, e V, vel est ipsum punctum P, auEV
(quod antem dico deP, aut V intellige de quibuluis duobus punctis V X vel Bd,
ec.) Ouod smedium est punctum R incer P, & V, igitur recta R S, hoc CAF, non
estassignabilis in tora serie progresHonISB C, D, F. hoc Csin SCrICM O, MI Y, NZ.
cumque R Smedia ponatur inters O, FThinc maior est R S quam V FI, _E COn-
quan L C ulro minor et sC GuaNs, _C. vnde neque recta R. S hoc cst F est
in serie rationis V FTad P C, _ F C ad n , e c. manifestum igitur est quod non
comhleatur F in serie rationis A, B, C, D, P, exc. nisi recta 1 hoc eA H S xqua-
lis sicrmi linearum progreisionis M C ad M FI.
MN, _c. nam omnes qux sequuntur VEI lunt semper minores quam siE, V II.
sequenter maior quauislinca quae minor es qua sicV FI, quales lunt omnes X I,
BR, dE, _C. Eaurem continuerur rario V FTad P C ve sine proporcionales VII.
PO, N o, CunC Recprocesus a minore ad maiorem. quare cum recta R SminOF SIE
 i  i  1. .  1 1.    1 .   u  .    1 p  1. 1.   b 1. .            1     n p r     p1 m 1r11