# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068235:0012 # Permalink to this reading: https://leibnizlegible.com/page/00068235:0012?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 22 # Folio 6v, page id 00068235:0012 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 4r); this page is its left half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068235&page=12 # Source image: https://digitale-sammlungen.gwlb.de/content/00068235/jpgs/default/00000012.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine # Lines: 54 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. bb + 8 a b aequ 105 aa. sit brgo ha+ c Sthhaa et Byhe a + cC + dh aa, + 8c a + 105 aa -sit aa = 8t aa debet esse 105p hh + 8 vel 105 p hh + 8. rursus sit baeqo ha + a + d fier + hh aa + (2hda + dd aequilios a a (2)h aa + (2) d a + aa + 8 a d gh aa +e aa 105 aa 105 hh 105 p hh + 8h seu 105 p h 48 105 r hh + 8h + 1 + 8 105 - 8196 5 hh + 8h hh +Bh 96 Numerorum autem ab _ 105 inclusive ad 96 exensive, nullus est qui sit hh. + 8h praeter ipsum 105, posito h esse . unde CH0 eganescit ernm terminus ultimus hh + 8h. Ex Nimirum ex 105 extrahatur radio affecta secundum hh + dh neglecto residuo: is erit quaesitus. 105 hh++ ICEC. Ergo generaliter si sit aequatio: bb + lab aequ in aa fiet. et fiat dividatur b per a, erit ut sit h quotiens, C residuu fiet. ttr ut lh m tunc hh + Ch cadet intra m et m - l - 1 five sive faciendo ch + Ih +f aequ m et hhe ls gaequ n et f+9 aequ m n. in= lant + seu hh + Ch aego mf hh + th aequ 1a g fit gppri n trb thago maf thh+ th aeqo n. + m. n-f sed hoc non determinat rem satiperacte quia inervallua inter intervallum in quom consistit h seu itaque h tam habetur exacte ut error sit miner unitate. Cumue quotiens semper debeat esse numerus integer satis de terminatus est si dicatur consistere inter esse radio jaffecta seu pronica extur. ex numero inter m et in - l-1 nam in nostro exemplo h est 7. ex 105. si sumatur vero 6. sunc cadit infra 96 fit enim sih + gh aequ. 28 Et sufficit, dicu data aequatione bb + labrgo maa. fore bb + b aequ M. et h quotiens b divisi per a, popim rationalis scilicet proximus vero, erit etiam radio aequationis hujus aa bb +l b aequ m. rationalis prexima vera, ita ut enor scilicet sit minor unitase. unde habetur met hodus generalis pro aa qualibet aequatione reperiendi quotientem seu tih +haego qpemid. n haec fonnatio eandem habet formam cum ipsa data Ag de