# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068217:0063 # Permalink to this reading: https://leibnizlegible.com/page/00068217:0063?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4 # Folio 31r, page id 00068217:0063 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 30v); this page is its right half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068217&page=63 # Source image: https://digitale-sammlungen.gwlb.de/content/00068217/jpgs/default/00000063.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 31 lines, status machine # Lines: 31 recognised, mean confidence 0.87 # 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. Re recti consideinta patet omnu brevius tractam, et ad unam tantum arbitrariam reduci posse sit laequ X a. mX + nX + p XB+ EmXe + 24X + 2pX +X X +qX + YX+ sx + +x + v + x_ + l Mr + imx Z mpa X _ qu + rX + sxt + tX L VX An X+pX Ap + lX Alq Xt +liX +ISA A LtXFII X+ iMX tinX Fip X trnX X ImpX +mpXAp aqu 2m X L 2nX + 2pX tinnX + impX + ampX + pr ne xt + n X Sed hihil hic tucramurt Nota m X + n2. - 9 X6 - rX - s xt - + x3 - v M = It X - lv -19 - Ir. -1 si aequatio X2 +gX + rx+s aquo sit redacta ad posit (posito X aequ atb +C +d.) sit redacta ad hanc: a =2 Ba = 4 a +5 aequ. 0. seu ad has. a + b + C+ d aequ. 2 20 et ab+ aE + ad + b+ b d + cFd aequ. 3. et ab + a5d + bcd aequ. 4 et aeb d aequ 5. Et aequatio a-2 a etc. possit deprimi, poterit etiam aequatio X + qX etc. deprimi, et contra ponamus enim aequationem datam X + qX etc. posse deprimi, utique dividi poterit per aliam quae sit: in duas alias, quarum si inveniatur radics si quaerantur partes a. b. c. occ. utique necesse est oriri aequitionem v.g. ad a. quae in illam a - 2a etc. dividere debet. Et ideo quia duae sunt aequationes ipsam X +qu dividentes etiam duae erunt aequationes dividentes ipsam - 2a et. pec referre videtur quod pro inferiotibus non suit tor necepariae rndicis partes.