# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/1023099829:0069 # Permalink to this reading: https://leibnizlegible.com/page/1023099829:0069?run=74 # Title: [Traite Du Triangle Arithmetique, Avec Quelques Autres Petits Traitez Sur La mesme Matiere] Traité Dv Triangle Arithmetiqve, Avec Qvelqves Avtres Petits Traitez Svr La mesme Matiere (shelfmark Nm-A 605) # Folio 19, page id 1023099829:0069 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1023099829&page=69 # Source image: https://digitale-sammlungen.gwlb.de/content/1023099829/jpgs/default/00000069.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine # Lines: 52 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. GEHERALIS RESOBIIIO Postulatum. Hloc autem praenorum esle postulo; Oux sic radix quadrata nume. Ei, 2, nempC, 1. Ftenim, I, est radix maximi quadrati in 2. contenti Sic de quae sc radix cubica numeri, 6, scilicet qui ex multiplicatione erium numerorum, I, 2, 3, oritur, nempe, r. Sic dx quae Cucradix quarti gradusnumeri, 24, scilicet qui ex multiplicatione quatuor numerorum, 2, 233, 4, oritur nempe, 2, d sc de caereris gradibus. In vnoquoque enim pero nolci radicem istius gradus, numeri qui producicur ex mul- ciplicarione cor numerorum conrinuorum ab rnitate quor exponens gradus propolri continet rnitares. Sic ergo in inveltisarione radieis V. 8. decimi gradus, postulo noram esse radicem ictius decimi gradus, numeri 3625800, qui producitur ex mulciplicarione decem priorum nu- merorum, 1, 2, 3, 4,5, 6, 7, 8,9, 10, nempe 5. Fe hoc vno verbo dici Porest. In rnoquoquegradu, postulonoram esse radicem iltius gradus minimi producti roridem continuorum quor exponens gradus conti- neernicaces; Minimus enim productus continuorum quorliber, ille est cuius mulciplicarores ab rnicare sumune exordium. Nec lane molesta haec peririo est, in vnoquoque enim oradu vnius cancum numeri radicem suppono, in vuleari aurem merhodo, muleo gravius in rnoquoque gradu, nonem priorum characterum, poresta- LeS exigUMEuT. Nocum liC ergO. PEoducti nUMCEORUI, I, 2, Peoducti num. Producti num. PEod. BU. Prod. M. PF. H. ecC. nempe 2 rad. quadr. este, 2,2,3, nempe, 6 rad. cub. esse 13 233,43 nemp. 24. rad. 4. grad. esse 1,2,33 435, nempe 120 rad. 5. gr. 1, 2, 3, 435, 6, Bem. 720 rad. 6. gc. esse 2, 33435,6,7, nem. 5040 rad. 7. Gc. eAtC Problema. Daro quolibet numero invenire radicem proposiea pote- Racis maximx quae in dato concineatur. Sic dacns numeTUS V. 8. 4335, ex invenienda Cic radix gradus V. 8. quarci maximi numeri quarri cradus leu quadrato quadrat qui in daTO HMICTO CONTInCATUE. Inveniantur, ex praecedente rractaru, quaruor numeri continui, quia s psecedente quartus gradus proponicur, quorum productus scmaximus eius spe- ciei oui in 4535 Contincacur, lineque ip(1, 6, 7,8,9. Radix quaelira est rnus ex his numeris. Ve vero discernatur, (iC pro- cedendum est. Sumatur ex postularo radix quarsi eradusnumeri qui produeirur ex defu radicum extractio tracte