# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068250:0004 # Permalink to this reading: https://leibnizlegible.com/page/00068250:0004?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 37 # Folio 2v, page id 00068250:0004 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 3r); this page is its left half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068250&page=4 # Source image: https://digitale-sammlungen.gwlb.de/content/00068250/jpgs/default/00000004.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine # Lines: 98 recognised, mean confidence 0.86 # 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. siguorum tantum pegula determinanda, superest Et hic quidem video cum sucimas didisa est ut paates atosomax pares, oppositum esse signera eru meutri naequalium graduum membri in quo summa notarum gradua in quodivisa est in empares Si fuissent aequationes duae XLMFIXHIOX =0 et 2F 2X = ofvet ne mutare signa opus sit 22 + 21X + 20XX = 0 fiet 12, 20. 20 + 11. 2021 = 10. 21. 21 seu + 11. 20. 21 2∞0 Hs sunia congrunt prioribus, nisi quod pondum deprehendo motam G regulam communem signoum poteramus et per gradus ante sublationem literae omnimodam, uti depressione ad Gradum inferiorem Sit 12 + 1X +10X = 0 et 21+ 20X = 0 multiplcando illud per 20, hoc per 10x fiet + 1g.20 + 1t. 20X (F 102OX) =0 et multiplicando utrobique -10. 21. = 10. 20 53 illic per 21, hoc per 12, fiet : (n. 21) + 1. 21X + 10. 21 X = seu 111. 21, 4 10, 21X = 0 quae duae aequationes sibi imvicem respondent per inversionem Termicorum, vertendo sed n manet. quod si Eas rursus inter se sungaraus fit 10_ (1. 12. E1. 20) = 210., fl. 21. 2) (F 10. 1p. 20. ED + p. 1. 20. 21 - (. 12. 20. 20 10 in 12, et 20 in 21 et X in 1 Signorum regula nondum salis apparet, video ubi sunt quadrata, ibi esse sigulum conhariim ei, ubi non suit quadrata, sed tamen in gradu primo, nulla sunt quadrata, et tamen est signorum mutation itaque glntiatius aliquid concspi quiet. An semper est mutatio de gratu g signi de gradu in gradum ut a 10 ad 11, vel a 20 , 20 ad 2) Et simeter ab 11 ad 12, et ab 21 ad 22 412. 12. 20. 20 tum urbat tamen 0: B 13 + 1 X + 1X + 10X o= 21 + 20X seu x= - 21: 20. 2t fint 13, 20 - 12. 20. 21 + 11 20. 31 - 10. 21 =0 Sed pergamus ad gradum ontium: Et diminuendo ordine aequationes 13. 20 +12. 20X + 11. 20 X (1 10. 20 X -10, 31 X - 10. 20X =11. 20. 21. 2) =0 se + 10. 2. 8.21 EI 11. X 13, 20. 20 + 12. 20. 20X A1. 20.20X) = + 12. 20. 20. 2) o= 13taX+UX + X Ex 1 et 2. + 13. 20 + 11020X + 11. 20X=0 = 11. 20. 21. - 11, 20.20..) =10. 21. 21 +19. 20, 21. 0 = 22+ 21X + 20X ex ret 3 fit 11 20i 10 2. G Ex 2el3 fit _ N or 13. 20 c (F 13, 20. 22) + 12. 20 10, 22. 22. - 10, 21. 22. = 13, 20. 22, - 13, 20.21. - 13, 20.20. Ex det 4 fil p 1. 21. 2LXE +. 10 21 21. 2r X 413 20. 203 13. 20 20 32D. a o= l3 +IX + IIX +10X 10. 21. 13 = 10. 12. + 13, 20. 21 +13. 20. 20 Ego landem ex 4 et 5. fint. 10. dB. 2.21. 2222 10. 14 30 22L 2 +10. 13, 20. 26. 2222 + 1. 12, 20. 20, 22. X2 = (12. 13, 20. 20, 20. 72 + 10. 13. 29. 21, 21. 21 =11. 13, 2020. 22. 2 4 13. 13. 20, 20,20. 21 (410. 10. 21. 21, 22. 22 +11. 11. 26. 20, 22. 22 113. 13. 20, 20. 20. 20 =(10. 11. 28, 21. 22. 22 +(210. 13, 20, 20. 21. 22 22. 11. 1320,20, 20.22 + 13. 13, 20, 20.20 videtur in calculo peccatum esse. Nam aequ. 1. multiplicetur per form. unius gradus prodibunt quinque termini. multi sunt 4. sed literae ex formula uniue gradus sunt 2, ex formula 2 graduum sunt 3, Ergo sunt literae 5 aeg. E sit gradus n. ducatur aequ. 1. nt eti hugohoc Cate. Ergo fit e= naI, al g - men +1 Maltiplicetur aq. 1. per formulam gradus , erunt termini et 3H Ergo literae debent esse Ar A aequalio- plicetur aeq. 2. per orm 2 graduum; prodibunt termini quinque. Ex quibus tollendi quatuor, ergo aequationes sublatitiae fiet e =1 et 9= 2 + 10. 1021. 21. 22322 = 10. 18. 20, 31, 22. 22 + 10, 17. 20, 20. 21. 22 +1. 12. 10. 20. 22, 2 =12. 13, 20, 20, 20. 2 +13. 13. 2420. 20. 2 410. 10. 21. 21, 22.22 10. 12. 205 21. 21. 22 =10. 13, 26. 21. 21. 26 HI. 12. 20. 10. 21. 22 = 11. 13, 28, 20, 21, 21 = 10. 10. 26, 22, 22. 22 + 2 (410. 12. 35. 20. u. 21 (+ 10. 12, 20. 20. 21 = 12. 12. 20. 20. 20. 2 +12, 13. 25. 20. 20. 21 mulliplicetur aeq. 2 per sem. form. gradus g. euul termini 912 +91 = C+ 3+1 fit g - et 1 o= 22 + 21 X + 20 X nes sublatitiae etunt ex omnibus terminis uno demto, ergo erunt e+ 3 1+ 3+1 sed eago eodem literae sunt 1+1 + et 1 = et 1+ 1 + C + 1 = 2C + 3 Ergo De + 3 = (et 3 + 1 in formutam gradus e, prodibit famula terminorum m+ eti ducatur aequ. 2. in form. gradus g. fiet quod sufficit perdratiter. prodibit ae quata terminoum n +9 +1. debet esse m+0+1 = n + 9+1 Ergo fit 9 = m - n + C Generaliter aeq. 1. sit padus m