# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068241:0014 # Permalink to this reading: https://leibnizlegible.com/page/00068241:0014?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 28 # Folio 7v, page id 00068241:0014 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 8r); this page is its left half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068241&page=14 # Source image: https://digitale-sammlungen.gwlb.de/content/00068241/jpgs/default/00000014.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 107 lines, status machine # Lines: 107 recognised, mean confidence 0.85 # 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. (11) 10 + 1 X, rX ag N. 20 + 2IX + 22X aequ. N. ergo L10M + IIX (F 1. 22X (12) Mustiplicetur aequatio (12) per X et aequ 4) per 21 et aequ. (11) per - 11. et producta in unum addantur, et prodibit Aequatio (13) talis: +10. 21 + 11. 21 X (+ 12. 21 X - 11. 20 = 11. 21 X = 11. 22X + 10. 22X + 11. 22X = 12. 20X -12. 21 X7 aq N. seu +10. 21 + 10. 22X aq. N = 11. 20 = 12. 20. Jam ex aequ. (2) et (3) faciendo novam (14, ut ex aequ (i et (2) supra fiebat 3 pro 10. 11. 20. 21. scribend: 10.2=2 12 29 loco 10. 21 - 11. 20 scribemus quadrat t (4 ~ (11) (14) - 10. 11. 21. 22 aequ. N. (4 11. 11. 20. 21 + 11. 12. 20. 21 20+ 21X + 22 X aequ. N. ergo + 10. 22 +11. 22X + 12. 22 X -13.20X - 13. 21 X 10 + U1X + 12 X + 13 X aequ. N. (15) aequ. N 1. 13, 20. 13. 13. 2020, 20. 21 211. 13. 2 quam aequationem 15 nacti sumus multiplicando 7 et 1, per crucem secundum tem no altissimos; poterimus vero et aliam naucisci, multiplicando secundum beti . . 20.20. 21. 21. quam infimos. ita poterimus multiplicare (7) per 20 et (11) per 10. et fiet + 10. 20 + 11. 20 X + 12 20 X + 13, 20X aequ. N. seu fallendo et dividendo + 10. 20+ 12. 20X + 13, 20X Y6) u essu = 10. 22. X - 19. 24 - 10, 21 jamut aequationem quantum libet simplices nanciscamur, in quibus sola extet dimensio simplex, X. jungemque aequationes (1) et (16) per conem secundum terminos altissimos, et fiet: +13. 20. 20 + 13. 20. 21X (+ 13. 20. 22X) aequ. N. Oritur et h9c aequatro 17 exaeq. (11et 15) ad imitationem 11. 20. 22 12. 20.22. - 13. 20. 27 aequationis ((3) dite ex aequ. (11 et 4) + 10. 21. 22 + 10, 22. 22. Jungemus er et (11) et (15 (per crucem secundum terminos infimos, et fiet: (+ 10. 20. 22 + 10. 21. 22X + 10. 22. 22 X aqu. N. quae aequatio coincidit cum praecedente = 10, 20.22 - 11. 20. 22X = 12, 20. 22X + 13. 20. 20 X + 17. 20. 21 X jungamus ergo A1) et (5) secundum termines et (16) certo modo secundum ter- minos altissimos, fietmultiplicando (15) per f0, et (11) per(12. 20 et (16) per 21 fietque: +19. 20. 22 + 1 13. 20. 20 X - 13. 20. 21∞) (cavendam fuit in hoc calculo, ne 10, 1, 12, 13. (18) - 12. 20. 20 (-12. 20. 21 X) - 12. 20. 22 X2 aequ. N. +11. 20, 21 + 12. 20. 2∞ + 13. 20, 21X2 - 10. 21.81 - 10, 21. 22X ante tempus altius assurgerent sed conjungendo aequationes (17) et (18) scontingit quidem ut ante in aequ. 12) et (13) ut absolutus terminus uniue coincidat cum coefficiente alterius; verum quia ita assurgitur ad quadiato quadratum litera . alicujus, ut 20 quae tamen coerceri debet intra cubum. Jungamus 2. H. 16 secundum ideo calculum reassumere oportet. terminos altroos et sui multiplicem et per B- 20, et (16) alinquams quala est 10. 20 - 11. 20X - 12 20X- 13 20k at (11) multialicemus per arbitrarium fet: e rro MO 41. 20 3n22 +2 l sx +lix Ut ergo timplicissima ratione procedamus primum relinquendo aequationem) qualis est, jungimus ei aequationem (11) ut inde habeatur aequatio 15 vel 16. sed si velimus duos terminos X et X simul tollere, et invenire aequatinem il simplicem in qua sola, extet X, ita procedemus: atHollatur aequata 7 ad quadrabo quadratum scribte 20 l + u L X + 12 X 1 13lX - 131 + com+ un X F AmX+ 1sm X 20a + 20 a X + 22 aX +20 bx + 21bX + 22b X + 20CF AZL, CX) + ex et primum = aequ 22D. unde commo dissimum erit facere qu. 22. et baequ - 13. se vel etel l aqu 20, et a aqu - 10. omissis nete quid si supponantur ambo simul, rest priori modo fit aequ. (15) posteriori aequata (16) Si pamo conjungamus ambus hypotheses sicunt, habebitur aequatio simplicissima in qua sola restabit X. denique si faciamus bequ 1 barom + 21a vel baequ prodine debebit idem nempe aequatio in quam ot sublata erise X. s. Al pro invendia XX f, poterimus omittere m et et fiet At pro inventiendo X poterimus negligere tam in quam C et facere laeq. 7r et b aequ 3+ 10. 22 1022 et a ag 12. 22 = 13. 31, : - 22. et habebimus 413. 20 21 =1. 21. Et X Aoliter equ - 20a : 10 aequ = d2 b: 13 seu a aeque 1042 b, 1. 20 13 20. 22 mutus laq. - 10. Mrb. r adrem aobinsu lar vam put: mes2 Ed ve per ol irpoando 12r = 13. 21. sit 0.2222 7 11.21. 2222. 22 10. 13. El. 21. 11. 11. 20. 22222 FII. 13. 20, 20. 2