# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00067993:0426 # Permalink to this reading: https://leibnizlegible.com/page/00067993:0426?run=44 # Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1 # Folio 212v, page id 00067993:0426 # Scan: The same scan is also registered as fol. 215r; its text is given once, here. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00067993&page=426 # Source image: https://digitale-sammlungen.gwlb.de/content/00067993/jpgs/default/00000426.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 44, 2026-08-27T14:25:39Z — 111 lines, status machine # Lines: 111 recognised, mean confidence 0.75 # 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. suopuo =SuIV) EBNISIENY .CIESHBUIPILV D CiESIES qBS,V CiSUISPUSSuEN MeIAjEUV Ur E ry3dGIP V3HOd SBM LT CMNII EIy CunVsNSSE CMIMe rod eabnog vuur vanmaxva ungod uonodX BeSipor SIGeVI PBS INSgCySCBHLIEUE HSLIEI SESresqSIV vOU y 5 10 unus sens chresab BM3ICSyPE+ S 1713S NB SCBrESqBSIV SoUOIEABZ P DBUCHMI HOU XSIEHGSSIY 1B3H: SOSESIMA DE CXSLITBCIOSE r cun3 CnnIsuSS XsneiPp raboyE msiono eod eab cerodiuo sngnuspuosues srams rab pos COrevipso SaBIE OBExS mOU =7 WITBEI LIMSHE Day WBIOBB) Bquab X PBS CLIMSISBTUT CGMPASAIS Jopnr nanposd suiysSuo unconenburdonddu muisiurqureuie cemprojes 3d: uivistouoe) SSOX sis uteretisse Wvoino ss Lab Bisa ieo: Uud3H,DY O3OA UIIVE -nsvuo3 13d pa Cumpmores sod pa sduu curosydnspea b, Bypur 390d (LIMHBCLIEI DE XHUISISGIEIMSAIS PBA CFIISLLEIP CMEAPEAb DE MMSAI SUONES E ApUBd XAB) CEINSI LGIESHIIBSS SAICEIE CLMBEAPEAB S =EABRMTHHSSICIDUOyIBAVOS SaICINESIVOSEMI F CyS LMPUSIS): AuS oropisop prab Copichhsod sues uou soyuur ospin enon b pos niuegoosos Cydjoxur BrpOyBSA SEPBLIEBNV LIIEIS SHHSIESCOSIES SouMOBS) CSBGGOXI SCWOUL ciopues Lydy semoy ens Byens suyd3o( csnurs Sanvor cenuea spempn3 su chus ysosod cnconuo Bens L unvisd sprabrar IIEIISEDLHIOPUENLIBHOS CMMLGUE ET LINIOIIIMU mnges OISISON GIITCSHEIENA XPTAE CsEHESHES inIBuI BOABCHUSGIGXS ESEIET PIGNICS3IIII eopesd enodur ynsuonen burdondde pousalay ainis 00000000000000000000 P0 CIMMNSILCIP DE .3∞ 9t 8E2E61685E59265+ t L. 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BILIMSIM EUISESUI UuON Proporciones currilineorum ad Rectilinea investigare GCometE semper lunc conaci, ec camen nunc quoque, etiam post Algebran adhibicam, nondum ea res Pacis in porestate est, secundum vieem tractenus publicatas; neqre enim haec problemas qua– tiones Algebraicasrerocari poltune: e ulum tamen pulcherrimum habene, inprimis in Mechanica ad pura Geometrix terminos reducen- da quod norune, qui calia profundius inspexère, pauci quidem, sed maxime eximii Machemaricorum. Primus Archimedes, constac, invenit, quae sic racio inter conum, sphaeram ec extindrum ejusdem alcicudinis dc basis, nempe qualis est numerorum exlinder sic cripius Cou celelqaet pharae; unde IpharAN u orum etiam sepulero suo MCBBMIC: SaCIM invenIE quadtaCUTaI Parabolae. Nostro seculo lepettus est MIOCUS Metten SL HBuTAS CUE vilmeas innumerabiles, inpris saliao ortala BC, ISchetale sunem racione urcunque mulciplicaca auc submulciplicaca, directâ aue reciproca absciltarum AB vel DC; eric enim sBura ABC A ad rectan- sulum circumseripcum ABCD, ucunitas ad numerum racionis mul ciplicationem exprimentem, unitace auctum. Exempli graciâ, quia in 132, 3. _c. ordinacae BC, TunE ut eorum quadcata 1,4, 9, dec. Peu in du- plicaca ratione numerorum, tunc numerus racionis mulciplicationem minus. lin Da BCB, ul L ad 2 F. I. Seu VEt ad 3: LIVC, HBUTA CHE LesCa PalS rectan- suli. Si AB vetCDmaneane numeri naturales, de BC hanc cubi, 1,8, 27, _c. (nempe in Laraboloide cubica) Forec racio ordinatarum cript- cara rarionis abseiltarum: Ergo sgura ad rectangulum, uc L ad 3 fl live 4. ted pats qualta- Sin DC sine qradcata, BC cubi, live ratio iplo rum BC, racionis iplarum DC criplicata subduplicata, eric fxura (para– boloides cubico subquadmica) ABC A ad rectangulum, ABCD, ut 1 ad Z Fiseu duas quincas rectanguli constituet. In reciprocis, numero racionis muscipticationem exprimenti praetixicur senum =, sive exprimens eric 2: ergo eric sipura ABC A ad rectangulum circumferi Sed circulus nondum hactenus cogiporuic sub hujusmodileses. quamvis ab omnirecro memoria à Geometris exercitus. Nondum enim inremes pocueerus exprimens racionem Circuli A, ad qua- dratum circumesBc BL Figur. 2, 9rod e qractatum diamecri DE. Recinveniri poruic ratio circumterencia ad diametrum, quae HOI .ox C2E. 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