# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068197:0271
# Permalink to this reading: https://leibnizlegible.com/page/00068197:0271?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 136r, page id 00068197:0271
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068197&page=271
# Source image: https://digitale-sammlungen.gwlb.de/content/00068197/jpgs/default/00000271.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 101 lines, status machine
# Lines: 101 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.

y+ a = v0
9+b= ZZ y+ C = V. Est triplex aequalitas; sed ad nostrum scopum
sufficit eam solvi in irrationalibus certae formae. sit Xtm = O XtnD xp= . 
sit y2 1050D + n YOQ + 1 DQ + 13 + 14X + 
1GX +16x rig
vo romatron  2X
21 mp+ 2i nX +2 X
22 np + hX + 2EX
onxtx
5
v 2SOD + 2 +OD + 22190+23 +24X
ZL
P ()
30..
31 1t
82.  33 34..
40. 41.. 42  43+94..
+ 2. 21. 22p SODruX 1OD + 2. WnnioguoumieuxO
+2.224. 
+22B +2.2X +24.2 +22 29X +22 27
Ha B t qt 10 son +15 Z s0n + 11 Soq + 16X1Oet 12 109+ 172
jam ex 1. explica ta per Y et 11, conferendo, fiet 15= 2. 2. 224 2. 20. 24 seu 24 = 15. 2= 21. 2,: 20 simililes
24 = 16: 2 = 20. 22: 21 unde fi multiplicando per 2. 20. 21. fict 15. 21 = 2. 21. 21. 22 = 16. 20 =2. 20. 20. 22
(16)
et rursus 24 = 17: 2 = 20. 21, : 22 Et3, 1(mullip licendu per 2. 20. 22. fiol 15. 22= 2. 21. 22. 22 17242 7
possemus et tertium aeq. formare ex 14 et 16 multiplicatis per 2. 2t. 22, sed hoec jam sequitur ex ipsis 5 et 17
ex 15 est 22= 15. 21 = (6. 20, : 2 2. 21.  + 2 20. 20
(16)
si sit 207 =  20252 et 21. 72 59 2253.7 = 52: 20. fit 20. 53  21. 5ep.  b53
rursus 21 =51: 20. Ergo denique fit 20. 20 = 51. 52: 53 2. 21 51. 53=52 2222=52. 53:51
26)
Si er i Si = 17 - 2. 22. 245: 2  12 - 222235: 2m si= 16- 2214,: 2-
ph. 24  11 - 2. 21. 23 = et 43 = 13- 2.2024 : a = 10- 2. 2023, 
a, 2324(17M = 2. 12. 24 I= 12= 2. 22. 23. Ergo 28= 17 m- 12, :,224m- 29  Ergo fiet
Et sirapliter 23 et 26 fiet
Si = (e 24m - 17. 23 24. 1d + 12F: 2. 2um 2. 23
16n = 221.2An = 11 - 2. 2+23 Ergo 2123(16p - 114 1, 2. 24n - 2. 23. et per 2513. fiet
20= 15 sp - 10, : 12. 241 2 2.3C+ Similiter
523 (16. 24n - 16. 23 (= 1bn. 24) + 11. 24, , 224n a 2. 23
et fiet e (3) =15. 23 + 10. 247: 2. 24 p -223.
Ergo per aegus. (+. 21. 22) habentur
junctis aeqqu. 21, 34, 30, habentur valeres ipsarum 20, 21, 22
sed si ja
t ita novae tres ex comparatis seminis valoribus
prodeunt biter aequationes in quidu aeq e aeq. 8 solae supersunt 23 et 24; praeterea
etiam habentur per X 35, 33, 30.
sunt tres adhuc aequationes po X, X,X. ita nes o tres  lie literae de aeq. H 7 inveniunt
ex quibus
liferas
Methodus melior  videtur, si piis omnes vares in Y y tollamus, quia simplices sunt
1est 10 =, 2. 21. 22 p. + 2. 26. 272 2. 31. 32p + 2. 30. 333 2.41. 425+ 2. 40. 43
11 =, 2. 20. 22n + 2.21. 23 22. 3032n + 2. 31. 33= 2. 40. 92n+ 2. 41. 43
122, 2. 20. 21m + 2. 22 23 = 2, 30. 7 m + 2. 32.33 , 2. 40. 41m + 2. 42. 43
15  2. 21. 22 + 2. 2024=3. 31. 32 +2. 30342. 41. 42 +2. 40. 44
163 2. 20. 22 +2. 21.2423. 30. 32 +2. 31. 34 2.40. 92 +2. 41 44
(24)
17= 2. 20, 21 +2. 22.24L2. 30. 3 + 2. 32. 34 = 2. 40. 41 + 2. 42. 44
sit 2t. 22 51 20. 21 =25) 202252 et 21. 2253 fit 20. 29 251. 52:53. et 21. 21251. 53:52 et 22.27 = 52. 53.5
jam ex 16 sit 3 1= jam in li9 per lib fit 51 = 17. 2 = 22.24 = (per 9g. 7) 12: 2m = 22. 23: m adeoque multiplicando per 2m
ex aeq. 26 fit 17n = 2. 22. 24 m 12 - 2. 22. 23 seu fit 2228)17m - 12,: 2. 24 m - 2. 27 quem valorem
substitutudo in aeq. 25 sit 51= (17. 24n - 17. 23= p. 24 n + 12. 24,:, 2. 24m - 2. 23 Ergo ad Initationem atos
ris ipsius 22, in aeq. 28, fit 21 276m = 11, :, 2. 24n - 2. 23 et 202 15p -10:, 2. 24p - 2. 23. Et ad imulatione
valoris Si in aeq. 29. fit. 5X2 - 16. 23 + 11. 24,:, 2, 24n - 2. 23 et 53 =-15.23+ 10.24, :, 2. 24p - 2. 23
jam ex 2t pe ex aeq. 22 per aq. 29, 32. 33, fit 20. 20 =17,. 33,+ 12. 24, =1623 + l. 24, -2. 2342. 24 P, , - 2. 23+2. 24M
R- 2. 23+2. 2412, = 15. 23+ 10.24. sed rursus ex aeq 31 est 20,70= 18,15p - 10,: (4, 2. 24p -2. 23 Ergo ex 34, 35fil
- 17. 23 412, 24, - 16.23 + 11. 24, (3), - 2. 23 +. 2.24p = = 15, 23,10.24, =2. 23+2. 24M, = 2. 23+2. 24n, 1pule
Ca, quid si sic, ut prius tollamus 23 et 24, ex aeqy. 1, 47, 10, B3, 16. Nempe ex 1. sit 30 - 2. 21. 22p, : 2. 20 = 11 - 2. 20. 22, : 22. 21
Edem modo invenientur duae adhuc aliae similes ipsi 3b
12 - 2. 20. 2m, : 2. 22. Ex lig et 20 fit 10. 21 = 2. 21. 21.22 p = 11. 20 - 2. 20. 20. 22n. Mursus ex ~q. 19 et 21. fiet eodem
modo 10. 22 - 2. 21. 22. 22 p  12. 20 - 2. 20. 20. 21m
denique ex aequ. 20 et 21 fiet: 11. 22
quae tamentres aequs. , L 22, 23, 24 non valent nisi pro duabus
20. 22. 221 = 12121 - 2. 20. 41. 4 M
Ex ha fit 20. 2522 11. 20 - 10. 21 + 2. 21. 21. 22p; 32
ex  fraeq. 23 fit 2026= 12.20 - 1022 +2. 21. 2222p, : 2. 21m Et ex aeg9. 25et 26. fit 11. 20. 21-10. 21. 21+ 2.21. 21p
12. L0. LG 10. 22. 22 + 2. 21. 22p Ergo fid  ex aeg. 27 fit 20 = +. 21. 222. 21322 p - 10. 22 410. 217, 11. 21 - 17
Ansic. P 2 5073, in 31.32 = 21. 22
20. 23-40. 43,:, 41. 42- 21. 22, quae aequando fiet
20, 23. 41. 42(= 20. 23. 41. 22 = 30. 33. 41. 42 430. 33. 21. 22 =20, 23.31.32=31.32.40. 4321. 22.8147
eu 20. 29, 3. 32 21. 2230.33 421. 22. 30. 33  -21. 22. 40. 43
gend3
+20. 23. 41. 4L
33032
=20. 23. 31. 32
+ 31. 32.40. 93125;4013
30,33. 41.4L
2D. ib al 4
2 23402
c
e
s
similis aequatio orietur ex 5 e B; pro 1. L, D. 3 for in cillimus; ponendo O. 2, l. 3, et fiet + 2
et ope aequ. 25. 24, 25. Inveriantr valoes ipsam 23, 33, 34
similiter ope aequs, 11. 14.17. tullantur, 24 et 34. similiter per aegg. 12. 15. 18 lollantur -L 23 30 3
dccedet tertm, nata ex duobus valbubus ipsuu 34 uno per pricres aegu 1. 19. 19. a lle 20 per postem 12. 15. 18
hlerae seu quantitates 5e et 44.in inbemus duas titer aeque sine 14 24 84 cui
12ep
2D 2 4c 43 +3d 3 9 430
412 33 4d 4l 32 334091
Huc puto opluu
astut as aess quidus se rt ) cogus dt s. d s Mod antie   e e sit eue aotu alti col nt