# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068195:0210 # Permalink to this reading: https://leibnizlegible.com/page/00068195:0210?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2 # Folio 105v, page id 00068195:0210 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 106r); this page is its left half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068195&page=210 # Source image: https://digitale-sammlungen.gwlb.de/content/00068195/jpgs/default/00000210.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine # Lines: 53 recognised, mean confidence 0.96 # 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. Polygouum inscriptum curvae est spatium meris chordis comprehensum Si recta chordae ac arcus ad angulos rectos occurrat in puncto extra curvam, Si recta chordae et arcui pormalis occuriere cui recta Curva reflexa est quam chorda aliqua fecare potest, in pluribus quam duobus punctis. Sin minus dicetur ad easdem partes cava In curva ad easdem partes cava si recta perpendi phordae perpendicularis inde pducatur ad curvam atque inde ducta usque ad curvam porro producatur, tunc quicquid porro productum erit dicetur esse a parte curvae convexa, reliquum a Conexat rectae, cn a concava. Illud extra hoc, et intra curvam Recta curvae occurrens vel utrinque ante et post occursum, est a parte convexa quae dicitur tangent vel ante occupsuru est à parte convexa, post à concava vel contra; ut autem a parte concava sit tam quaecst secn ante quam post concursum, seu ut tangens detur intra curvam impossibile est. Nam ponatur dari talis tangerns intra curvam quae sit DCF juncta chorda AB erit tota DCF intra figuram ACB cumque sit recta utique utrinque exir utrinque producta e figura, exibit, curramque ejusque circum ferentiam secabit secet ergo u secabit ergo bi vel rect dis rectam AB, quod est absurdam quia recta rectam bis secare non potest, vel bis socabit curvam ACB janguntur puncta nse intersectionis per Thordam novam, ergo et eam bis secabit, quod absurdum, insi ipsa ei coincidit, seu sit chorda, sed tunc curt non esset ad leasdem partes cava, quia eadem recta ei in tuibus punctis occuneret contra hypothesius. vel partim occunet rectae partim curvae rectae in H. curvae in G ergo junctae HG bis occurret quod etiam absurdum nisi coincidans HG et HFCDG. quod non potest, quia recta ex chordat puncto t educta arcui ad easdem partes cavo non nisi in uno punctoque. facile est, quia iHGcurvae si in duobus occurrit contmuetur curva cB ad easdem partes cave quia in nostro arbitio (quod semper fieri potest) infra HB, Hicic utique adhuc oecurret G H s quanodo quamlibee producta, ergo curvae ad easdem partes cavae occurret in pluritus curmum produere quam duobus punctus verimus, neque Demonstranda haec pro- positio quod recta curvae ad easdem partes cavae non nisi in duobus punctis occurrere possit Recta curvam a parte concara tangere non potest enim hic de btqs siecii vel proprie ltatibus quaeritur