# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068236:0004 # Permalink to this reading: https://leibnizlegible.com/page/00068236:0004?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 23 # Folio 2v, page id 00068236:0004 # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068236&page=4 # Source image: https://digitale-sammlungen.gwlb.de/content/00068236/jpgs/default/00000004.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 103 lines, status machine # Lines: 103 recognised, mean confidence 0.70 # 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. inucjor nmu uet nen v homns lungn, 5: Ed uae Ess e s 5 e ∞. e s ad ian. 1681. de Sueuienties hextica tis uin e 1. 2 dilit 13. il 21 nsu sisi 55 2. 1C Seriet temminorum 39 194 cot Serie, numerorum : 1. 1. 2. 3.5. X+y aequ. Z et (1 ago Xtyfiet: x+ 29 aequ. (2) 2) aqu. 2X +3y. 1- XD Xt 1 mo 1. (Daequ ary. (3 oqu X+2y geho v . 3(9 atior 3 = v 1 2. 2. 4. 6. 10. 16. 26. &tc. vel 1.2.3,5. 9. 13. 21. Xc. vel 1. 3. 4. 7. 11. 18. 29 2 idem est an orro l aequ fate X jam x+y +2xy, hinc (x equ X jam +x loc loco auli 26 eandem lina yMaego 2X+ 27. ZD) aequ 3X + 5y 1. 1. 2. 3 5. 8. 13 etc ves X + 27. 2XHy. 3x+5 nam (XB) est yxag et yX tryy, et (Y) (V) est (2) +B1) hinc semper prdii s (7) aequ yX + 2yy - XX - Yy - 2Xy y. jamZg etiam XZ 8. 2F 77 etiam aequ. +XX + Xy = yy. EgotZ + 8 7 17 patet etiam ecatummiti exto exsu et 9(X) XY) aequ (Z) et quia (X) aqu. itaque in quacunque serie hujus modi, ut porro quia X2 seu fit ic differentia et l. 12 x accuratius examinetur sumtis duobus prioribus x er y. tertio quolibet fiei semper ent et 10to ab 3i aliisque infinilis locum habet series prima hor modo: X. y. Xty. 1ote 313 (09 oto 4 ergo XX 1 6. ego =()(Z) = (y1Y. Etquidem si primi termini subis extrepporum ex man fcshupis en pibaterer scribatur a. (3b medique haber 2 se Xx +Xy -yy eandem formam habere cum rotabile est aautem formulam 5 eosdem prodituros, si ponantur a def. Quam totum et minor mapor pars tot aequatione aas b aba na x ert e reato furm +1 (21 si unulm vo nb rem aere mois ed 112 2 3 d- u 91