# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1815206918:0038 # Permalink to this reading: https://leibnizlegible.com/page/1815206918:0038?run=74 # Title: Solvtio Problematis A R. P. Marino Mersenno Minimo Propositi (shelfmark Leibn. Marg. 230, Stück 2) # Folio 33, page id 1815206918:0038 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815206918&page=38 # Source image: https://digitale-sammlungen.gwlb.de/content/1815206918/jpgs/default/00000038.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine # Lines: 57 recognised, mean confidence 0.89 # 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. 111II. LDRALYR A. lacionem coram DIadOI. iOnEMEOtaM A F ad L. O constiui exrationibus cories mulciplicatis rationum ea- rum, qua constiruun rationem cotam CHI ad N S, quories ex rationes qua con- sticuumerationem coram CFI dd N S lunc mulciplicata racionum, qua colticuunt OuopoltO, cumratio A F ad L O non differat a racionibusiis simul sumpris GUa CONSICMUNEraTIONE A F ACLL O PEF COMOMALCIOMCMITAIICAPLICaLAIHCOI rol. 7. quae vera est detractio simul ec addicio, idemque verum etiam sc in rationi- busC H ad N S,e D Iad O T, Daceciam quo senlu verum sc racionE A F ad L O cories concinere rarionem CHI dd N S, quoriesracio C FTad NIS continet ratio- nem DIad OT. continetnempe racio A F ad I 9 rationes cas exquibus consti- euicur, quae quidem tories mulciplicare lunt rationum earum quas concinet ratio CHIadNS e ex quibus ipla costicuitur, quories rationes quas continee rario CFI ad NY S _ ex quibus consticuitur, nulciplicatxe luneracionum quas concinetratio Corollarium decimum. ad NV, ex rursus siratio F ad I Sc duplicaca rationis FTad N, XC. (reliquas combinario. nesomicto re verbis parcam) quoderiam ratiO A F ad L Sc Furura duplicata racionis CFT ad NT: quod camen nonnulli pu- cances sine rilo dubio, ex ab(que controuerlia in hac propositione supxoni, Fallum id camen eAc in numeris inveniumt. neque errant; Fallum id enim vere cA, Patet que idline longis ambasibus. Nam veracioni A ad L. qua duplicata ponitur esse rationis C ad N, addlatur adhuc ria cacio P’ad L, Sic ve contlatum ex illis rationi- bus, Scilicet ex ratione A ad L X alter a illa ratione adiect a. duplicacam HabCacra- cionum C ad HI _ FTad EY contlatarum in vnam rationem, debene imprimis ratio- nes C ad N, _ IIad N coalescere per mulciplicationem: hac icague ve HI ad N. ita N ad Z, cruncque rationes C ad NN, et HIad N sibi ad dica per mulciplicarione, provenietquerario C ad Z. iam vero cum ratio F’ad L posira sit duplicata rario. nis FTad N, hOC CKPTad Z, AaEVEFad L, ita L ad V, crit ex racio L ad V duplicata rationis N ad X, cotaque rario A ad V eric duplicata rationum C ad NV e II ad H Abi addicarum per multiplicatione per 75. lib. de Proporcional. lonse aurem alia est ratio A F ad L quam A ad V. Ouis id iscorat qui in rationum nacura aliquo. modoek verlatus: X id P. Cresorius non animaduerrerie, qui rarionum scien- tiam adeo amplificauie ve pastim nocum est, quique racionibus quibulcumque aque commode reitur ac Luclides lineis: Caussa itaque quare iltx rariones AI ad F I addieae sibi invicem prout rule Propol. 12. licer lingula duplicata sinc rationum Cad N, X FL ad N, non consti- cuant tamen aliquam rarionem A F adt P. quae SiE duplicaca racionis C FT ad N in2- nifesta est, quia rationes A ad L et F. ad Lnon coalescunt per mulciplicationem, led per veram addicionem; sue quia non coalescuneista rationes ve multiplica- ex lune rationum C ad NV, _ FTad N. Sed verationes simplices sunt. Fodemque modorationes C ad NV e FIadEYnon coalescunt permulciplicationem, nam vehC faciumrationem C ad X. veiam ostensum est; coalelcunt aurem et rationes C ad N, XFI ad N per meram additionem rationum, verationes simplices lunt, non aucem vemulciplicantur per rationes alias. Imoreprestius loquar nulla operatio- ne hic opus est, nam cirra vllam addicionem extrinsecam, coaluerunt iam rationes CadN ec FIad N in ratione C FTad N, quia reuera ratio C FTad N eaS actu cOn rinet. idemque est in reliquis rationibus obseruandum. RationeS POrrO A ad L, e F ad L licer reips a duplicatae sint rarionum C ad N, _ FTad N Engula Cingularum, non tamen ve sic considerata mutationem vllam in Cc accipiunt; quare manec racio Aad L, et F ad P. sine considerentur in ordine D Lad OT _ exquibus Connicuitur. J FInC Patet 10. eos Falli qui existimant in hrac propolicione dichdut lalcem debere dici, lrario actL. cpneaca racionis C 1 t 1. 1 . . . 11. 1 1 . 1 1 a t. u 1 1 . . . 1