# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068201:0396
# Permalink to this reading: https://leibnizlegible.com/page/00068201:0396?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 198v, page id 00068201:0396
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 199r); this page is its left half.
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=396
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000396.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 85 lines, status machine
# Lines: 85 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.

20
= (( - 4 qu s5 1 29 + 4 8 55  + 29. (557 - 4 5 9  
seu 520 =  59) - 4 qu (597 109 =+ 4 R9. 109 + 2 qu 5109 7 - 4. (59 - po)
=4. ( 9  +. 1. 6259 - 4. 25 (104 + 4. 5. 109 + 2. 100g0 - 4. 5. d9 + 4 prc
.
2
25 1000
= 59 + 4 pt0
200
200
40
est rationalis in X ergo quod est rationale in
20 erit q + 4 pro
10110  10155
sed rationale in xo est a + β a b + Va b + dabc +B a
sed a = 4 et ab -0 et a bC = 0. Hinc indestigabimus 
a = _ qu sa
seu ab -0 ergo a = a
Hinc quaeramus a, etc.
1513
0
res
20
20
15
a = q et ab =0 abc =0
1a =
= qu+ 4aebcd
20
o
10 = qu- 4 ab c
re
20
15)
10710
20
cope
a in a = a +2a  seu a b - 4ab0
20
ergo fiet 4 = q - 4abcd + 2a
re
10
10
+24 abc205
20) = (490) C6abed + 12abcd +n a 65 +24 abcd
Ergo
20
5
015
110
-(1+1 +2) abcd = absd a b5 = - 4 ab c
10 (+20
+aβabCd +7 abed- 4d a bC d + D abcd
-4595
Ergo habetur ab cd
a - 4g’a +0 a - 0a +. d 3 p: D  =0
20
Quaeramus jam β, V, 5,  per regulam alibi invendam
creum nniones totidem
Potentiae a b e d corficiens prodit ducendo invicem m + np+q quiterciones,
MCn + P +9 rerum niones m+ sp + q rerum pniones m + greum quiqniones
ipsi a. b3 praefigitur  20. 19. 18. 17. 16- a. b praefigitur 20. usque ad 11. =
2. 3. 4.5
1. 2. qu ad 10
ipsi a b c proesiptu 20 usque ad 16 15 .sqadic d (abC d prosipta 0
insque ad 51
1 usque ad 5
abC d praefigitur 20 usque ad 16 15 usq ad 11 10 usqu ad 6 = D
1. usque ad 5.
1. usque ad 5
1 usque ad 5
fiet 4, 20 19. 18. 1 +. Hic quivis triminus mulliplicatur per 20 usqu d 16,: ce1 usque ad 5
rostat  4 + 2. iusque B11 + - 4. 15 utq ad 11 + 15 usque ad 6  Dousqu ad 16 = aβ + 2) -4d +
6 usque ad 10
seu 4. qu. 1 usqead 15 +2. qu. ( usqu d )
1 usque ad X
qu. Insque ad S
Iusque ad 5
625
100
f 10023
1020
E2o
Unde C20
20