# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068241:0009 # Permalink to this reading: https://leibnizlegible.com/page/00068241:0009?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 28 # Folio 5r, page id 00068241:0009 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068241&page=9 # Source image: https://digitale-sammlungen.gwlb.de/content/00068241/jpgs/default/00000009.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 173 lines, status machine # Lines: 173 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. sit Aequatio fiet o 0X + 1 aequ. eihil. et 10 X + u aequ. erih.. Artic. 1 1. 10 = 0. 11 aequ. nih. seu 1. 10 aequ. 0. 11 (1 C Aitic. 2. sit aequatio 0X +1 X + 2 aequ. nih. et 10X + 11 aequ. niho fimulliplicando 2 per Xfi et (3 et addendo 11t3 fic 8 10X + 1 qu. N et a 1d X +, 10X + 2. 10 aego N. Ergo . Ergo 1. 10. 10 equ 0 +o 0. 11. 11 - O. 11 X (5 Ergo ex 4 et 2 fiet 2, 10. 10 aequ. 1. 10. 11. 0. 11. Aliter idem: mulliplicetur aequ. 1 per 11. et aequ 2 per 2. fi adtantur subtrahantur a se invicem producta, et residuum dividatur per X, fiet: +n X + v 10. 1X + 1. V aeq. Nik. Ergo ex 2 et 6 fiet: - 2. 10 1. 1D11 aequ. 2. 10, 10 O. II. H1 (2 sit aequatio: 0 X + 1X +2 aeq. N. et 10 X+ n X + 12 aequ. N a mult. R qu. 1. per 10, et aequ 2. per: 0 et anferendo invicem, fit: +1. 10 X + 2. 10 aequ. N. unde per praecedentem articulum: ex 1. et 3 fit: = 0. 11 X = 0. 12 + 1. 1. ∞. 10. 10 aequ. 2. V. 0. V 11 =0, 1. 1. 10. 12 = 0. 1. 2, 10. 11 40. B. 1. 11. 12 =(2)2. 0.1, 10. 11 2. P. P. 10. 10 Sed cum in aequ. 4. 10. 11. 12. non tractentur ut 0. 1. 2. signium est calculi imperfecti, uti etiam deprimi potest. Itaque aequationes 1 et 2 multi. plicemus per illam per 12 hanc per 2 sintu et oductum peu per pucem et productum unum ab altero aliferendo, sufferenitium dividendo per X fiet +0. 12 X + 1. 12 aequ. 0. et combinando aequationes 3 et 5 habebrinus = 2. 10 X = 2. 11 per articulum primum. +1. 1. 10. 12 +0. D. 19. 19 16) -1. 1, 10. 12 seu quadr de 10. 12 aqu +1. 2. 10. 1 22. 10 + 0. 1. 11. 1 = 0, 2. 11. 11 ∞1. 2. 10. 11 5= 0. 2. 10. aqu. N. =0. 1. 11. 12 2= 0. 2. 10. 12 40. 2. 11. 11 4 2,2. 10. 10 ubi nota si in aequ. 6. ponatur 12aeq. nihilo redibit aequatio 5 prioris articuli divisis omnibus per sit aequatio DX L q N OX +, X + 2X + 3 aequ. _ 10X + 1 aq. a multiplicentur per crucem in ultimos fiet + B. 11XF + L.HI X + 2. 11 aequ. N. Rursus eodem i modo multiplicentur 2 et 3 per crucem in ultimos, fiet: 8.11. 11. X + 1. 11. 11 aequ. N ~. 2. 10. 11 et rursus multiplicando 2 et 4percrurem in ultimos fiet: + 1. 10. 11. 11 = 2. 10. 11. 11 +3, 10.10. 10 = 0. 11. 11. 11 ubi si ag. 0. 4 3. 10. 10 Atic. 1. OX + 1X + 2X 13 aequ. N. D0XZ IX + 12 aeq. N Arlic. 5 multiplicentur per crucem, in ultimos fiet. ex 0. 12 X + 1HX + 2. 12 aequ. N, et res redacta ad artic. 3. - 3. 10. = 3. 11 Ergo adimitationem aequationis 6 articuli 3 fir aequationem scriberemus a 12 tunc displicet, quod video incognitas it 1. literas eo ven literas quales 10. et I1 et 12 assurgere ad quartum gradum, cum tamen non debeant assurgere ultra tertium. Itaque aequatio 1 et 2 rursus multiplicentur per crulem in summos, fiet: +Il0 X 4 2. 10X +3. 10 aequ. N. = D. H1 X (∞. 12 X conjungendo aequ. 2 et 3 per crucem, sultura summarum, fit: O. E + 1. 1012 X 4 2. 10. 12 -3. 10. 10. = 3. 10. 11 15g. N. conjungendo aequ. 2 et 4. percrucem ultimavum fit: 41. 10. 12X 42.10. 12 aequ. N 20. 11. 1 = ∞. 1. 12. = d. 12. 12 O. 1 12 23, 10. 10. ~3, 10. 11 Unde deniqe multiplicando per crucem, habetur quaeduae quationes coincidunt Unde exaequi2 45 ad exempulum articuli siet: conjungendo aequ. 2 et 4 per crucem summorum fiet 42. 10 10X + 3. 10. 10 aey N. et ix aequ. 5 et 6. per crucem multiplicatis fit: + 0. 0. 11. 11. 12. 12 1. 10. 11. 12. 12 destinendo L= 6 1. 10. 11. 12. 12 10. H1. (+7. 12 4 1. 1. 18. 18, 1. 12 =P. 3, 10.10. 11. 12 via possunt L = 0. 3. 10. 11. H1. 12 2= 1, 3. 10. 10, 18. 12 43. 3. ∞10. 10. 10 0.0. 10, 12, 12. 12 4 0. 2.10. 10. 12. 12 40. 19. 10, 10. 11. 12 0. do. 11. 1. 18. 1 =0. 2. 10. 11. 1. 12( quet 10 lu =9. 19. 12. = 1. 10, 12 + D. 2. 10. 10. 11. 12 ∞0, 3. 10. 10. 11. 12 = 1. 3 10. 10 11. 11) 42, 3. 10. 10, 10. 11 = 2, 2. 10, 10. 10. 12 = O, 11. 12 +9. Vd itaque vertenda liters numeros 40. 3. 10. e1. 11. 11 (2)0. 2. 10.19. 12. 12 ∞0. 1. 10. 11. 12. 12 ∞0. 2. 10. 10. 12. 12 = 1. 10. 1 n : f(1) 0. 0. 11. 11. 12. 12 = (2) 0. 1. 10. 11. 12. 12 +; 2mr 12 = 0. 2. 1C. 11. 11. 12 4 1 12 4 1, 1, 10, 10. 12. 12 ab ea quae est in actis Einditorum, quae tamen deberet coincidere, ponendo a et 10 esse unitatem +2. 3 10. 10, 10. 11 tesse nihilum 2 esse p. et B3 esse q. et 12 esse y + a et 11 esse Z quia hic predit yyz7 quae illie diessevidetur utroviq descresidaa 1 dividi per s = 1. 3. 18. 10, 18. 12 Artic. 3 ubi nota omnes terminu quadratum non con- tinentes affectas signo signa-videntur oriri a terminis i quo rum signa mu- tata radice mutari possunt Nam si ambarum aequationum signa mutata radice vera in fal sam mutare tur, endem tamen prodiret aequatio uttima sublata incognita ipsius et autem valor fieret contrani is non sequem tin apparet. haec. inductio Isulende prmen oligutur ex multiphici modo quo eadem qua Eycrplicens latis titas produci potos 0.0. 11. 2. 2 pro 0 adhibitis 10, pro 1, _ H1. et v2, 12. dit 2 p bis 0. 811. 11, 12:12 B puto ex his series in infinitum scrrbi posse videtur haec equatio differre