# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068235:0035 # Permalink to this reading: https://leibnizlegible.com/page/00068235:0035?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 22 # Folio 18r, page id 00068235:0035 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 17v); this page is its right half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068235&page=35 # Source image: https://digitale-sammlungen.gwlb.de/content/00068235/jpgs/default/00000035.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 109 lines, status machine # Lines: 109 recognised, mean confidence 0.80 # 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. a lequ. (- X aequ. + 1 4 2 79 t 1.9 f- 3a aequ + 1 = seu major quam Z s - 6a aequ + 1 - .3 S. ba aequ - 3 + erc. Si bina Gungas, exhiberit 130 semper +. 15 Eci (.3 1.5 Fri7 Ing. adhuc procedit, quia tmais quam 1- 4 est majur nihilo 1 + 4 5- 4a q ego +1= 6 1.13 4 + E 1.. 3 +5 err. ad huc procedit, quia 1 majus quam ers ad huc procedit, nam quia 1- L aequ 0. fe reliqua ntius 1.5 sunt nihilo majora. 7 a = β3 aequ 1. 3 1.3 non procedit quia -= += est quantitas 1.. 3 1.. 5 nihilo minor. Ergo et b aequ. 5. Il12, 3,45 +30- 15 48 i 3 Ergo is 21 1201 0 17. 5 1. - 3 620 + +.3 - 13 + 13 erc. quod non procedit quia B 1. XcB aqu. V aequ quod procetir, nam 1.. 5 aequ 6, 20 ergo p + aequ 5 16, 20, seu 1. 5 1.. 7 X - 2 (3 aequ aequ 20- 12 aequ. 920 6p0 25 ci non procedit, quia 220 mina quam 25. Hinc provideri 1 a - 3β aequ. 1. 3 1.. 5 poterat, quousque progredi liceret. Em Eritque 1. 3 X - 4 (3 aequ 1. 3 1. 5 19 + erc seu; OB-dy aequ. 6-946+ d.ad + 6 + 9d - 6+ gd erc. debet d tmaijo unitate 1. 11 A. _ - cβ aequ. p. 3 1. 5 1.17 1.. 7 1..5 1.. 9 1.. 7 4. et substituando pro d substituendo d +1. sit eadem quantitas pinor unitate 42 19 1.5 sit quantitas 6 - d - 1 6 + 19d +d + 6 + 19d +d minor unitate. 61 1.. 7 11. 5 lateram autem d ita inveniemus situr d fit integer experiamur et in sequentia conditione su d sit fractus, sumamus 1.7. 1.. 5 intemum proxime fiet : 612 16 = 6, 7, d = 6 19d fiet: 48, 6 aequ 61 d Ht ergo 41, 6 aequ. d. ubi si d fieret integer hic finiretur tota series nam residuum foret 0. sd quia est fractus, sumi debet integer il assumeretur, sed, proxime major, p16+4. Nempe 5. Jam sumamus alterum terminum ubi adhibetur d +1. et cum multiplicemus ubi si a daequ 5. foret 6 - d - 1 aequ. 0. 1.. 5 et 6+ 19+d aequ Ergo fit utique reliquum minus unitate. adeoque numerus 5. succedit. Si vero substuto 5+ 1. in locum d+ 1, temminus ille in quo d +1 non fuisset quatuor primos terminos ponere assumere proxime majorem intemum eam d minor unitate, tunc debuissemus non duos ett valorem postea in quinque priagibus experiri, an pro dponendo d +) Ex his ergo et modus aequales 0. Et in vestigare valorem d, et secundum valorem repertum, fiat quantitas nihilo minor. lapparet divi dendi seriem per seriem infinitam per sediem infinitam ita ut investigetur quotiens verus numeralis, residuumque sit proe minus intate quod imprimis puliare procedit hac methodo si sit signa et- alternent. 7 2 Concludo igitur esse 01 + 101 101 etc. et d aequ. 5. p. e8 aequ. 1 - e + 194 101 e - 194101C + 19 + 101e erc. abi patet si sit aqs. 1. fore 1..5 = . 1. . 7 .15 1-. 11 1.. 9 1009 8, 9, 19 + 8, 9, 101e = 194 101C quia 42 1(01C quantites g 2864