# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068255:0138 # Permalink to this reading: https://leibnizlegible.com/page/00068255:0138?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5 # Folio 69v, page id 00068255:0138 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 68r); this page is its left half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068255&page=138 # Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000138.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 129 lines, status machine # Lines: 129 recognised, mean confidence 0.81 # 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. Quemlibet jam valrem ipsius 513: 113 repertum in 8gy. 13 et 14, articuli 18 aequabimus valori invento aequatione 16 articuli 14. Et similiter quem libet vactorem ipsius fient aegq. (1) et (2) articuli hujus. Unde so ex quibus consequitur aequatio qu (3) hujus quae oritur ipsos duos valoris in aequ. 13 et c4 articuli (8 aequando inter se. Et a similiter quemlibet valorem apsius 713: 113 repertum in ag9. 11 et 12 articuli 18 aequabimus valori invento aequatione 6 articuli 15 fient 094. (4) et (5) articnti hujus. Ex quibus consequitur, aequ. (6) hujus articuli, quae oitur ipsos duosvalores in aeqq. 11 et 12 articuli 18 aequando interse.. Et has 6 aequatiomes distincte scuibtre supersedeo prate 3 et b. ubi videndum an non compendia prodeant Nempe ae 0 aeq. (3) R. 1123. M (23. 513. 312.712 7 17 2. 112. 512.323. 723 + 7112. 7123 (112. 523. 312. 723 + 123. 512 . 523. 712) C15) 1723, 118. 512 323. 723B1 712. 123.522. 312. 712 1712. 1723 (112. 523, 323. 712, f 123. 312. 312. 723) et -71 23 + 1723 2) = 1212 - 71 et sed ex aeq. 8 articuli 16 est 112 Si2. 323. 723 = 133.523. 312.712 et -1712. 1723 f 7112. 7123(2L - bis 12+512, 323+713, 123+523, 31 2 F 7 (2 lurgo ex aequ. 3 sic explicata 1234523, 3121712 1124512, 323+723 Lit ) 12. 513. 312. 712 + ()12, 512. 317. 723 = (2) (1124 51, 323 +123 4. 123+ 51Z, 312+712) (112.523. 312. 723 = 123. 512. 323. 712) ̀ qu. 0 Et pari jure ex aequatione 6 explicat a debet oriri aeq. (11.) nitilo differens ab aequ. 10. sola permutatione +523, 312 +712 112+512, 923+723 inter 1 et 5 cum 3 et 7 in notis initialibus, sed ita pulchre evenit ut aequ. 11 et aeg. 10 coincidant quoniam aequ. 10. eodem se modo habet ad 1 et 5 Ut ad 3 et 7. Unde cum aeq. 3 resultans ex 1 et 2 idem Det quod aeq. 6 resultans ex 3 et 4. consequitur aega 1 et 2 itemque 3 et 4, revera non tam pro quatuor quam pro tribus aequationibus esse habendas. Unde ex his 4 aequationibus possent excerpi decussatim duae ex 1 et 2 aiticuli hujus et eis conjungi aequalio 10. commode, etiam sic procedere licebit, ut loco aio psiqus 713: 313 per valorem excerpendae, consideremus dividamus ex vt a si C D. S. sIE S valorem primum aequationes 13 Ipsius 513: 113 ut fiat ceq (12) hic, et nursus ax artic. 18 dividamus valorem aequationis 12 ipsius 713: 313 per valorem aequationis 14 ipsius 513: 13 ut fiat aequ. (1) hic. nempe rursqualor novo ipsiq. 13. 7B3; E3 Hos duos valores sed aequando cum velore ipsius aequando inter se fieret (15) quae tamen videndum an non redeat ad aeq. 10. hicjuse 113. 713, :, 513. 313, ducto ext 17 aiticuli 14 et ex ag. 6 articuli 15. habebimus aegq. (17) et (18) hujus ita aeq. 15 non coincidit cum ae. 10, poterimus conjungere 494. 10, 17, 18 onquam sufficientes ad omna determinanta videndum tamen an non ex i’et 2, itemque 3 et 4 huju non possit fieri aliquid simplicius quam aequ. 19, 17, 18. imo re considerata apparet nit posse fieri melius; ob aequ. 8t articuli 16 nobis profuturam. Nempe dividento aequa per aeq 112 (2) 2123. 112a723 = 2112. 123.712. sed per aequ. 8 articuli 16 fit 112.723, 1,523. 312 = (1440) 123. 712 :, 512. 323 = (1gno) 17. 55. 18t ex aequ. 12 Denominator voloris ati aequ 1 articuli 18 per q aequ. 13 ejusdem fit 2. 323,512 scribi poterit 7123. 112. 129 (53 : 17) - 7112. 123. 712 (53.17). Ergo jam praeclaro tam exitu evanescit numerator aequationis 2 de primitu denominatorem, et it tos jam ex articulis = (17mo) 171= (pero, 31 1d. 727. a qua Et ex equ Himc itaque aequ. 15 est denitica nec quicquam faci (12. 123. (12523 +23512)537(12723 - 23712) 12723. 23(12 (312), 323. (12723 +23712), 15 (12523 - 23512)12523. 23518 523. (312 =15. 4) 12523: 112 (21mo) et 223 = (3724) 127235, 3 12 et ex eq. 17 articuli 14 e st 523f qu. 9 112. 127232373 : 312. 12515. 15 unde ex aequ. 17 tandem fiet 123. 312 (12323+29512) (12723 - 2512) 12523. 23712 = (2284) 112. 323 (12723+ 22712, 1252. 22512) 12723. 23512 non differt aqu. (18. 723: 523= je, aequatis cum aeq. 17 articuli +4, et aequ. 6. articuli 16 oriendis, et fiet - 7123. 342. 523 +7112. 323. 512,:, 12. 323- +2251Z ubc Ro esta 1712. 123. 312 = (1mo) (51. 13 L) - 15. a () 12523 - 23512 (12519 - 13512) 2, 12. 123, 12 315G ubi pro 523 et 512 substituendo valores (15: a) 12523: 112, et - (151a) 23512: 1237 ex aequ 1 fie 2 00 equ, + 7123. 123. 312. 12523 4712. 112. 323, 23548 (2 3t0) 12523. 23512 (12532 23512) + et stiuendo 3 et 7 fet 12523 + 23512,, quas Aegq. 23 et 4 seponamus et deu 12. 1C13 (21 2523 = 123 23712, :, 323. 385 1 at a qull ent Eili s egrienti dug +123 s (2sto ex t. eZ isto B523. 21712,: 52723 23512. 12724 (113523 + 235I2 C, 127 (3- 23712 under rereausi seu 12523+23512, :, 12623- 235(22 223+ 23712, :, 12725= 23712 12628 a Eeden 2tme ) 7123. 112. 323. 12) 23 - 7112- 132. 312. 23713 fiet: 7129. 123. 312- 1252547412. 112. 34. 23512 23. 112. 323 - 1712. 123. 312 et27 437(2, 1725. 13. 3M - 1112. 1123 13 Ar9. H nug un r f1235 17 27r2 eq 12727 Toestuendo ubique 1igi B3, fiet (1251 1 (23312), inum n + manenim 12523. 23712 171t a =(272 (23712 seu 2Z. hur. 25 S12. 1371 = seu 13 1s 23 f 1 vel Yi 1 (sis) L 112. 92. 232 17 11 123- 23512 X a) : 123 3. 112. 123 + 1252 65. a),: 112 H SI ZBa 127L3 323. 37 312+712, 1323+723 = 312. 32 a -23712 15 (2. 375:, 31 4 5 a t. 725. 313.37 f312 a, 112. 285(2. 12723, 123 (312) 12523. 23712 HE 2572 (3123h.1. X35IX. 12723 :, (31da. 15. 312. 12525 2p112 + 1272 3. 52 57. 113(19 1251G X(112. 112. 1 2512. 12713 Sen f 12. ct. 128. 12. 14523 ~ 3B12. tereBESI 2 M. 31. 2s En A has EsuIE.n reS. HE. Msi. AEYEa H 12. 128. 37 ag 3 3sr2. 1425. 23 2 teur 351323A2 nSL3. 12723 ed per aeq. 25 323 = + 123. 3(2. 12523, 23712, 7 12. 23512, 12713 quo subst luto sit 312. 123 a. 12523. 23712= 112. 312. 25715. 23M. 12723. 37: eue qo 512. 712 A seu 2a = 2351R: 112. 15,:, 112. 12Bat 125 . 123. 15B L 11I 45I2,: 11345,8 3. 212. 723 + 13. (512. 323. 712 = lis 112. 723 + 123. 712 (Exl ergo (29no) al sernetrum geluditur s15pE. 22712 + 21512. L2p. 12322(127~). 712 pr anenter ulbamus et p2At 13 + CB in eadem eu. 10 funt jam 112 = 31Y. 120 1E. a et 523 (1 ee. 12) is. a aambus 19.7 123. (31: 4) 237122. 313 eL:, 12s u Zmmnunrhtn us. 2n es + in as seufps)Binm cm Ear. 12725 = (ob 25 hic) 4 12. 922. 12725d. 12523. (237 12 = 4 12523. 12 magu m 2 Nunc superest ut coy. 10 evolvatur, et ut alterutra 23 vit 24, sola. Et pringum pro aqu. 10 tollamus 512, 523, 53. 2 et ibi habebimus inter alia +13 Z et 712 = 65: a) 2351 enfunde 123. (12712 2.73 1(2 (37. a) 127237312 qq. 23 et 24, et ope aeq 2b 2 utAI. . 2IEy B 22. 1 351226s tuendo valaem ex aequ. 25 unde ubi pro 3F 123. 312 173812. 23512 qu. 25. fdebuis et jam institur articulo ficerente post 6 post eg. 8. 723+ 23712 123, 711 27iZ. 112. 93 1212 _ -2112. 15. 3I2. 23718 1ngrg. 23712 (12733 -25712) Se Redeamus jam ex aeq. 22. proqua consideremusquod 1723. 112. 323 = 1712, 123. 312, hujus fed ex aeg. 14 hic pe 112. 323 placet tamen ad huc a actu ipso exhibere aequ. 1. hujus articuli quoniam hactemis quator aequ. ex . 11. 12, 13 articali fiet: n seu ipusa 113(713, : 95B. 313 = (20mo) = 17: 52 vel distinctius 113.713, .9 513 315= e3. 5o C. nisi a alitums ipsum paatmerato rem 13. 712 7112. 42. 723, ubi in dem de nominatore rursus ob a9. 14. 15 pro 512. 323 ponendo ex aequ. 12 fit 123. 712 (53: 17), et pro 523. 312 poneldo et