# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068212:0003 # Permalink to this reading: https://leibnizlegible.com/page/00068212:0003?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 19 # Folio 2r, page id 00068212:0003 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 1v); this page is its right half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068212&page=3 # Source image: https://digitale-sammlungen.gwlb.de/content/00068212/jpgs/default/00000003.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine # Lines: 63 recognised, mean confidence 0.91 # 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. 9 Interio utenue pre ductae. VAB ad hibentur infimne una a positione data, seu semper eodem situ manens altera BPtransiens per punctum datum sed convengens manenteque puncto B, varians situm. Et pi et primum quidem convergens ipsi rectae A ejqus concurrens ut BC7 s in puncto C, deinde si angulus file inclinationis, con- concurrens eidem finue minuatur in puncto aliquo remotione (C) donet per P non convergit ex BD per(B)P perveniatur in BP, ubi recta simpossibiamaginar cumqfit punctu amplius ipsi A, sed ei est parallela, dH His positis, licebit una aliqua ratiocinatione complecti tum tum casus omnes intermedios ut (B) quam ultimum B. Et hinc etiam fit ut una ratiocinatione complectarum veluti. Ellipses et parabolam, si scilicet consideretur frcens alterum alli ocum A esse focum unum Ellipseos, (cujus vertex i datus sattum qui maneat fixus, alter quemadmodum et beu alterum focum C esse mutabilem dum transitur de Ellipsi in Ellissin, donec tandem (in casu quo recta Bpintersectione cum recta VA focum fi variabilem faciens ipse focus C fiat evanescat, seu fiat impossibilis, quo casu Ellipsis in parabolam evanescit is lae abela Et ita licet ex nostro postulato Elli parabolam una ratiocinatione cum Hac methodo etiam Geometrae Ellipsibus complecti. in constructionibus uti solent, cum scilicet diversos casus una constructione, complectuntur, et ductum generali notando in certo casu conversentem rectam Taliam abire in parallelam angulo rectae ad rectam evanescente Ex hoc autem postulato oriuntur quaedam locutiones quae videntur aliquid continere absurdi, do commoditatis gratia adhibitae, quae videntur aliquio continere absurditassed su signisi qua significatione substituta cessente. Nempe si dicatur punc de puncto icur em Concursus imaginario tanquam de equodam reali loquamur a uti in Algebra recepta radices imaginariae adhibentur Eaclo dicere ssolemuls e Pa Et hinc analogiam rectae VA servando dicimus Rectam Dcum in parallelam desinit habere focum esse convergentem, ad ipsam, e sive cum infinite parvum insigite, nit vellociratom ea angulum facere perinde ac si diceretur corpus quiescens, motum habere, sed corpuso infinite parvam et rectamum alteri aequalte esse inaequa on elle, sed disfereatia infinte peria, et tor att