# Leibniz Legible — https://leibnizlegible.com # Page: https://leibnizlegible.com/page/00068255:0137 # Permalink to this reading: https://leibnizlegible.com/page/00068255:0137?run=74 # Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5 # Folio 69r, page id 00068255:0137 # Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 68v); this page is its right half. # Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068255&page=137 # Source image: https://digitale-sammlungen.gwlb.de/content/00068255/jpgs/default/00000137.jpg # Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 95 lines, status machine # Lines: 95 recognised, mean confidence 0.84 # 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. Ex aequ. pro aeq. 5. articuli 19 inveniendas oay aqu rur c pl siis mno Crnginid uis onsce -23712, : 9, 127234 237126312 923) esCgala A 712 2. 152 2723 f 2 p2. 22SI2. 2342, : 2513. 2372 F 1712. 23 512. 12723 - 13723- 14712, ., 1 723 + 23712 (2. i se quigrlut eo bd q ur es-l uinderiu pro aequ. 6. articuli 19 invemiendam it isi r + 1729. 23512. 12723 4 1712. 12525. 23712,:,7 7125. 23512. 23712 4 7112. 12513, 12723 = 12723 - 23712,:, 12723+23712 Ergo tandem mundando al + bm me cemeat Ct a b. ad Ad artic. 21. aequ. 1. F seu in t a = mt 1 aat b + bbr Bla + Hmb = fnu F Ib fit a = B5l-Bgm, et ast= atm = 6fl - bgm tam aglebum = afm+ us fmx + fly- - glX. + gmy siu colas fma = f1b gmb seu 4 E Aid artic. (23. pro aeq. 2 vel 3 arlic. 22. scibatur =Cx + my erpo seu X, = et 292 = les 3,2 4+ 5e2 = 3in - (= 15, 125: 122a) seu 212 (6) 3 12123, 312 a = 15. 235, : 123 a et 22318 112. 323a - 15. 125,: ma. seu se quia 1232 (323, et 112=8,12, et 15. 235 = 37. 235 et 15. 125 = 37, 127 hinc ut omnia enuntientur et 123 + 313 = 3131723 ex artic. 3 articuli 29 isp secundum justitiam fieb: 212= (123. 312 + 112. 323) a - (15. 23524 37. 2372), : (123+ 323) a, id st _ 212 - 12 123 a - 15. 255,: 123 a et 3232(112. 323 + 1230312) a = ((5. 125 4 37. 127),:, (112 + 317) a dest 223-712 323a - 37. 175:, 312a ope ergo aequationum 6. nempe duplici aeg. 2 hic, et duplici aeq. 3 ha, et ope ag9. 2, et harticuli praecedentis, id est 14 et 15 huius habnimus, 2, et quae sunt 6, habuopus ae99. 8, et 18 et 16, et r7 859, E0, 18 8, 18, 16, 17 et 11, et 13, quibus invenimus nondum habitos valores, ipsarum 312, 323, 212, 223 37.15, et 237: 127 vide post 1 aequ post aeg. 13. ubi feliciter evenid, ut valor ipsius 2377. 123, sit idem superest um ut praestemus qui jamante fuit repertus, evitaturque contradistio, in quam alias incidi potuisset. 2p 513 f313 = - 13 + 113. suastituamus valores s -2t 12. 123. 313Ar d = 37. A7 11579 431 323 19 7 quo aqu qui valor aequandus equ. l. articuli hujus pro 213, 513, 313, 713, 13 In aequ. + segtago ipsarum 513, 713, fet 1seteS as per aequ. 20 ut usqe articuli 29) valori aequationis 18 articuli praecedentis 29, in qua evanescit 312 et 12 quia aequales et sir explicando seu 313 :13 = b9no) 15, 125 - 235 + 312. 323 Trr, :, 37. (27-237 4 112. 1231YY, secundum aequ. 12 articuli 28, prudit nova aequatio ex his duobus ruboribus, per quam non video quid impediat determinari aliquam ex is Inveniri aliquam ex lis quae supersunt quantitatibus 15, 37, 112, 123, 125, a 235, 127, 237 de quibus nihil ad huc habetur quam 37: 15, et 237: 127 si in aequ. 19 7) Hic jam tentemus periclitemur novalo H pothesie, et faciamus (20mo) 6 125. 235 = 39) Hic jam periclitemur nova Hypothesi, et faciarmus 15. 125 - 295 = 37. 127-23,, ita enim ob. 312, 323, = 112. 123 freiet per c9. 19 artic. 30. fieret 313 = 113. unde (3ho) ex aequ. 18 artc. 20 faeret (125 - 235) 115 1300 nn -200 um = (45o) 12 (127 - 237) 537 11ool-2oomm. sed hoc non licet nam ex 4 et ) hujus, fieret 14390 nn -200 min = S100 l - 200 mm quod est contro hypothesdi prestat ergo redire ad aequ. 19. et explicando, et faciagnas n :a et ex ev. 18 artic. 29, fiet ampendio 125 - 235 vocemus 25 et 127-237= 27 erit a+ vere vt + uvoreu 17 l’ex aequ. Yise Y300 nn -206 mm, 8 15 :, 100 ll- 200 rum, 37) quod est contra intentum per et 125+ 235 21 et 127 -237= 23 erit per 12 ee arstic. 29 125- 235, 4,:, 127-2770 19 artic. 30 fiel 15. 25 + 112. 123, 21. 25 ) B, :, 37 C 37. 127. 237. 27 4 312. 323. 23. 27 a 313: 113, C introbique dividi potest per 25 et 27, fiebus 27 + . 923. 23. as 37. 127. 13 15, 125. 235, 25 + 112. 113 2. a i2 (idest ur. 123 vel 3123d9 unde tandem habebitur n2. 123 Ere. 125. 235 - 37. 27. 17. 237 ita taudem . 23 ab - _2 2) a es in quibus nondum implicantur et reliquae i seu 312. 313. eu fiet 112. 123 4 312. 3 25, 225, 17, 237 (ex quibus pendent 25, 27, 23, 21, B, V) sumi possunt pro arbitrio, quantum patiuntur jam habitae deter 112, 123 vel 3(2323, habemus per Pitera nn = 2od um et similiter minationes, et scopus. licebit etiam ponere 15Brest DDag:, 3de et atu inventas quantum quat conditiones postu laut, determinatas 112, 2n, 31E, 18, 213, 313, 123, 213, 323; jam absolvamus substituendique erunt hi valores ubique pro 37 et 15. opieri pretins upere u utile erit i exprimi tam vec v quam et 171et 3 artic et init. artic. 8((pro 4e, esp (19to), , 3 explimere ipsas v, Z, y inde terminatas ubi fors et dendo aeq. 1. et 2 artic. 16 pro ut tandem obtineamus irrationales Suy, Y0Z tyZ cum ipsis pqdere Mer y, adeoque et reliquas vide antur aequ4. artic. en artic. 30. et nitio deinde an sabis fiat initio articuli 10, b. tum pro valore possumus intir dissimulare quae instituimus riationabs in aquiutio sata Hi pu n idalonis pratio dantur irrationab, in aequintio dati His podib, um q cemratius parte ulie eiupari aibenta salisfacunt eq altuonali 12723- 23712.23 12723 + 237125312. 313)