# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/DE-611-HS-958803:0011 # Permalink to this reading: https://leibnizlegible.com/page/DE-611-HS-958803:0011?run=74 # Title: LBr. 57, 1 · Bernoulli, Joh. # Folio 6r, page id DE-611-HS-958803:0011 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 5v); this page is its right half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-958803&page=11 # Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-958803/jpgs/default/00000011.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 39 lines, status machine # Lines: 39 recognised, mean confidence 0.94 # 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. sed curva provetiens evodit interdum mechanca secumi generio, id ett quae requirit quadraturam mectam in simplcio inguradrabilis: contra vero interdum agnatio differentialis licet secund gradis per mechatio eam siuplicem conttruntur, qualio illa adds = dygus, cujus construitionem exhibum in schedinomate tratis actorum anni elapa p. 254. quat ediam pridem una cum analyir duo Marchion Horpitalio comunica veram. Hac occasione opportune mentionem injiciam novae mihi repertae speciei curvarum per currentium, quae quati medium teneat inter Geometricas Cartesii et inter mechanicas: Curva geometrica vulgo dicuntur illa quarua natura expritnitur per aequationem certi et determinati gradiio, mechanicu quarum aequatio conitat ex disse, reatialibus: Medias antea vel percurrenteo appello quarum aequatio eit indeterminati gradio, id eit, in qua literae indeterminatae et con– elantes ascendunt ad dimeasionem indeterminata et proinde omnes possibiles dimensiones percurrant: Hae aequationes à Luis transcendens dementionum talibur in eo differunt quod numerus in illis eit vageo et indeterminatus in his vero determinatus sed incognitur. Cua autem hujusmodi curva percurrentes peculiare requiraat syitema ad punita in curvis, ad tans gentec, ad quadraturas i. definiendas, jam ab aliquo tetapore mosii ideam formari non calculi percurreatis, ubi moduta trado sumendi differeatialia aequationum percurrentiua, et conttruendi omnes cur vas percurrentes ope logaritamicae vulgaris quive ut deprehendo etiam ipra ert curva percurrens, ejus enim aequatio positio abscisca, ri appli catâ, y, et subtangente a, eit a a=y. adhibitâ nempe unitate quat dimentio x subintelligitur divisa, ita ut hic non lineatu indem tertinatat sed numerum indeterminatum denotet; Leviscituum ha exemplum adducam: Sit curva queddatu FGH percurreas cujus aequa tio eit hac X =y (pos. Cl. X. et 1H, y.) quaeritur ejus con- Etiuitio. sublangeno et couadratura. Conttruita ad apem prodcntum FCM logarithmica vulgari ABN, cujus prina applicata CA sit= unitati assumtae; deuatur BIH paral lela ipri DC, et BD parallela ipri CA; fiatque CM aequa li ClaCD, et duita applicatae Mne sumatur aequalis CA IH, erit punitum H in curva quaesita: Fiat deinde ut 18+ subtang. logarit. ad eandem subtang eatem ita AC ad IL, erit IC sub. targens ed paritat H. Matium caloeliterum F G tc espectitur per cat