# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068231:0020 # Permalink to this reading: https://leibnizlegible.com/page/00068231:0020?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 18 # Folio 10v, page id 00068231:0020 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 11r); this page is its left half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068231&page=20 # Source image: https://digitale-sammlungen.gwlb.de/content/00068231/jpgs/default/00000020.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine # Lines: 57 recognised, mean confidence 0.92 # 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. refutatur Hypothesis, quod contine in alcuti scilicet cationule omne, contireAtru tantum in partibus formis seu summis homoeoptotis, ut STab Siabe Ai abcd. Unde sequetur ponenti xomne rationate Cum enim sit gus Va +d b4 C esset Nia la be ) S) abed sequetur et X’ ego SVa ab Gs abc Hinc omne rationale ipsius X contineretur in Nabc. Ergo nihil rationale continetur in S Erqque omne rationale quod in et continebitur Saeb es ab In fo summa cujus forma vensim est pg homogenea est ea membra quinto gradui, necesse est tas, quae in se dctafinvicem ducta faciunt solidum expressum esse simul rationalia ut si Saeb ost rationalis erit sa b etiam rationalis, quia invicem ducta faciunt a b seu ab. H + similiter si sab est rationalis Hinc porro sequitur illud Saeb, sui respondem etiam Sa a b rationalis + 4 Etiam ex diversis gi etiam Sa b c. erit ratioralis si Ya bc est rationalis Si ab est rationalis, tunc utique sab non est rationalis (alioqui et a foret rationalis) Ergo Sab irrationalis ducta in Yae rat irrationalem facit rationalem Sab. Sed eadem Tab duc irrationalis, ducta in SKirationalem, facit etiam rationalem Sab videndum nic an hoc sit dic possibile, ut eadem irrationalis ducta in diversas irra tionales faciat rationalem. nimirum ostenti possit ex alio capite videndum etiam an non abjurdum sit, a b et Tab esse simul rationales seu extrahibiles, dividatur enim una per alteram fiet a: b3 arationali autem diviso per rationale, prodit rationale ergo a ent a: b erit rationalis Ergo Sa: b erit etiam rationalis quod an absurdum demonstrari possit videndum si a b est rationalis, utique s ab non ationalis at b non estra– tionalis, smultiplicata enim per Tra irratioqe rationalis saeb per sa irrationalem, utique dast irrationalem) Sa ab est irrationalis, tunc ab est etiam irrationalis (quia in senivicem ductae faciunt rationalem, et contra. Ergo si _Saeb est rationalis, tunc ab nox est pationalis, si enim simul essent rationales, foret ssa: b rationalis Ergo Yab abt foret etiam rationalis, ergo S a b foret etiam rationalis, cum tamen absurdum sit sa b et es ab simul rationales esse. Hinc ergo demonstratum est formas similes duarum earundem literarum, non esse simul rationales nisi quando in se invicem ductae ex ipsa forma fiunt rationales, tunc enim siml rationales ambae sunt, quando una est