# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068196:0146 # Permalink to this reading: https://leibnizlegible.com/page/00068196:0146?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1 # Folio 73v, page id 00068196:0146 # Scan: The same scan is also registered as fol. 74r; its text is given once, here. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068196&page=146 # Source image: https://digitale-sammlungen.gwlb.de/content/00068196/jpgs/default/00000146.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 196 lines, status machine # Lines: 196 recognised, mean confidence 0.78 # 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. Sidua sint aequationes, continentas Z, Aqe, do simplici ratione, possunt inde fieri aliae binae, quarum uni desit d, alteri dpsit dez Itaque jam tum sic scribamus 100 + 10Z + 120 d 2( = 0 200, + 210ZH 2o rorto f ita in priore millimus 10r dyx. disserentiam dugues note mtir 2, peste tagriloi enq noiti) posteriore rior 220 dZ prior dabit compendio 10 + dno voleituus 130 et 201 + d eor voce mu) 203. Et quatuor istas pric2es equationes e multiplicatas respectiva per l, m, n, p, addamus n unum. fiet: 100l, + 1101Z + 101 lv + 120l. 1Z 200ma +210 m Z + 201 mV +2o2m do deo B vid 1202l 3(7) Tentemus an haec aequatio possit rrodi tractabilis seu ec Dentificabilis tractabili diaonaranonz =+ le1KV+ on dZ = 10In du + 12on ddlk + 202 dlv) troopa Hlno pZ toloipV + 20 p Aq + 203p do 0o ha +310fZ + 301. fB +320f dZ + 302 f du )(1) 50+9d0 +00h = 8 = 0 faciendo O = 9 = 310Z + 301V + 320dZ + 302 du. unde dispereatiando Hyo 9Z. + d 30190 +3109 17 + 301 g dv + 3rogultzu 1302 g dldv =0 fiet d(= d310Z + d301. V + 310dZ. + 301 dv + 320 ddz + 202 dax d320 d d302 dv Et hos valores D et do substituendo in aeg. 8. fiet.- Et aequationes 7 et 1 ientificanda punt inter se, contrahetur autem alcilus facilndo hoco 302=0 fint etiam p=0. fice ob quanesci ergo terminus ildo. Et perinde est as acti non tantum aequ. 1, 2, 3, multiplicatas respectior per l, m, n, in unam aeg.7. composuissemus Omisso ergo termino dao, relque ut identificemus aequ. 7Z et 1, aequabimus coefficientes reliquorum termiporum. Ob Terminum habentem ddque, fint n = 14 = 3209: 120 +d3209dZ d3orgdv Ob terminos et V, erit 110. cuol +210. n + dy0. 320g 210s, +.d310q et 101 L+201 + Ao1. 3109 = 31 f id 301g quaerum binarum aequatiogum epse invenitutm et m Ob terminum Y F Ao, cum evanescat p, et fob 202 = o) etiam pruodibit sine litins 101.3r ag orgor , 2o 30cg Ubi feliciter omnis abistdissernisfis. Ob terminos dze et av, habentur singulatim valoras psarum literarum L et m; et ob aZ firt , nol. . (30: 120) 320.. + 320 f +3109 +d3209 Et 202M = -(01: 10) 3209 +3019. Quos valches ipsarum literarum , et m, substitie us in aeg9. pe 15 et 6 prius per 202 multiplicatis , ex eu apis fiet in 2o B. 3og. + 10. vo. 320)- H0 202 3lg + o 202 d qag ti. 1 bo va za g + 12 2B2. 32s , 120 202 d30g + 202 12C 3209 hlaq ib fir l 101 202 2C9209 + 101. 262. 520f ,rot 202. 3109+ 101 02 d3209- 120. 20t Siog to. e1 3019 = honot 101 f 19 1. 202 d301 g 20c 10. 202. 120l 202 320f s + 210, 120. 202M = 10. 202. 130 3209 + o2 B∞ f F 40 02 yege + 110. 202320F + 110. 202. +110. 202 89 Ex aeju. 1 6. 101. 202, 120l = 101202 Bo 3209 +101. 202. 320f +101. 202. 3109 F101. 207. 13269 Etexaqe 2d vidi nanss. Et ex ay 2a ordinundo fit: +1d. 210. 161 3169 + 120. 210523019 l. 202m - 120. 201. 1 3209 + 120. 201. 3019 -120. 120.502. 310 C-atro or tes 2og Et exay. 19 firt: porrrb. 40 3olg Et rpaey. 20 fiet + 3320a + 202 d 110. 3209 120. 202. 310 f + 120. 202 d 310g 1202d110. 3209 120. 202. 310f + 120. 202 d3109 +202 dio1. 3209 = 120. 202. 301f + 120. 202 d301 g +202. dio1. 320 g (20) 120. 202. 301 f + 120. 202 4301g siata et 5H. 310 ono. es a + 110. 120. 202. 320f, + 110. 120. 202 d320 = 110. 130.202.3209 = 120. 210. 101. 3+09 (=5. 30 +120. 2041103209) 1620 (20oC (=L212 dx - 10I. 120. 202. 320f, + 101. 120. 202 d dibe + 120.120. 201. 3019 = 10on2v. 102 d301 9 =120. 120. 202. 304f =101130. 202. 3209 = 120. 101. 201. 320924320 invenio autem nullo fructu 350 et 301 reduci ad se invicem +120. 202d01. 3269 seu fieri 301 = 5t. 310, vel contra, sam ita a quando loefficientes ipsorum d31o in diversis aequa- tionobus tit 51 200 seu 51: 00 = 1, sed aequando coefficientes ipsorum 310, coanescunt f, et 1 nec possunt inservire ad aequationem. Ergo reducamus 310 ad 320, seu frat 310= 8t, 320 + seo d. SP 320 a + 110. 120. 202. d3209 +120. 120. 20. 3019 +110. 120, 208.51 3209 = 120, 120, 2025 dg20 G = 120. 120. 202. 51. 320f = 120. 120. 20t a 56. 3209 + b1. 120. 202. d320 9 + 120120. 201. 3019 = 12o. n0. 2e2 4309 0 = 120. 120. 202. 304f it bis dabus aequ aequemus harum duarum aequationum termues d320, et 320, Ob dero fiet 51 == 00. 10 -00. 101, :120 Aequenus has bines aequations 3 10]. 120. 202. 5 3209 Terrinos 320 mop aequationibi aequaba. interim ex refiduotum aquatione, fit d301 (5) 2019 - 202f - 2109. Et posito f:g hubetur 301 Jam f. g inveniemus aequando terminos 320, hoc modi X+ 00. 110. Ro. 202f 00. 10. 10. 2020 -00. 120. 210. 101C +00. 120. 202. d110C A+0S. 101. 120. 202f d unde fiet 00.1205+202 d101 +120 C2f. . 5, or auo . -00. 101. 130. 2029 .-00. 120. 101. 20f - +00, 120. 202 d10t . +101. 120. 202. 51 G habetitur fe + 210. 101 120. 202 520. 51 = 120. 20r 4 d sedita evunescet f et g ob evanesceatem nom 1I. comparundam cum aeg.7. fietus ob taz, n mrog: 120 et 2) Jorg: 202 tut 1olL ob dq fiet nol of + 3log. L d3rog - (130: 4120) 3209-(150: 212)302g ob de fiet 202 m ) vorfF 301g +d 3029 (101. 120) 32og - fro 3. 202) 3org Ejm non licet omittere 302, sed redenndum est nobis ad aequ Hag secundum Z, fiit: 110. 202. 320 f. + 110. 202. 409. + 110. 202 d320y - 110. 202 (130: 170) 3209- 110. 202 (210. 2023029. + 210. f9 D. 30r5 , 210. 120. 3019 (+. 20 120 d362g. 210, 120 (101: 129) 3rog- 20. 1 20 (203. 202)3029 Ae superest a supersunt aequationes ex coefficientibus ipsorum Z et v, quae multiplicentur per 120. 202 Et ex ap scudmu, fiet. 101. 202. 320 f + 101. 202. 3109 + 111. 202 1329y - 101 202. (130: 12o 13209. - 101. 202 (210202) 32g, + 201120 3ors pro112o. 30191 201. 1o deorg- 201. 1 40 (1o1. 20) og - 2o1. pro (203. 102)9029 + 120- 202 (a110: 120) 3609 + 120. 202 (d210: 202) 302f 3 19 120. 202. 310f + 120. 202 4310 + 120. 202fl101 : 120) 3209 + 120. 202 (d 20] - 207)302y (7, -110. 202. 3205- 110. 202 d 320g + 110.248. 3029 20. 210 dv25 120. 202. 301f + 120. 20243019 Ex aeg. 16 ordinando firt 110. 202. 3109 =120. 202 d 3109 120. 210. 3019 l E. ex aequa simndo fiel: C 31 =101.202. 3109 Hiora 12o. 210. 3028 +120. 2102 3C2 = lec. 210 - 610C) 400.8 a + 120. 28. d 510 +110. 202 (130 ) posroa + 120. 210 (106) 3209 -120 d2103029 216 dirS. 3209 +120202. 301 f + no202 dholg. - 101. 202. 32ofu = 140. 202. 13209 + Br 210. 3org, - 120. 2o) 1302 120. 201-. 3019A Fiut 2 vs, 310 = 3to 20 1507 302 et 0g. 301 = 1y 20 t60. 302 sit ex aeg. 18 firt - 110. 282. 5109. 320 + 129 202 510 F .. -- -120. 201 3027 fint Exaeg. 15. a 2, 20 202 hof A1on or 43103 +0 eq oi 2) lO1, 201. 3209 2 202d10. 32 tas jam bini XI. 10. 20Y 22g 13oca + 10 120d20. 30 aequationes aeque mus inter se pens sadem ut terminia 302, et termini 302 utrobe 1302. f. t 60p= ob. (201 - 210) + 202. 5017 : 202 30 ut 21. Et ita qu oi Dloroni G+a atipduc 120.4105 I6. 2 hol. 501 ) 400. ror d a v1. 202. 5019 +00t 202 la +, 20g def 2019) (0201. v0. 20 + 202 501) Bt )urtoctsom ngetouohomon 20. 202 d cot =D orre 2 2um 1209 Morsooo vi eo 501 Edere de Die 29ceetre o vorlood d30 + 10 022 nu tareii ponumm sai itit io aspioiin tod =1812022 3209 173104 eliuosimu (= 101. 120202- 3109 eo o no ga e por +110. 120, 20451 =1 20. 120, 202.5,F = 120. 120, 202. d510 = 110. 202. 501g. 302 - v0. 10. 202 9d320 -1 (30) + 120. 201611. 302 4 120. 292 5e .. . . 410. cdt 3169. 1. 4+ 128. 202. 302 = 120. 210. 809 +00 I a + 129202 d5019.-. - - 00. 11. 2029320 -00. vio. 2019. d302 in ussoatvroed A exagitospit +00. de ja =1012d2. 5109. 32 - 101. 2c. 50 +(2b. 2006109 111 4 l∞. 202 46 . . .. devau