# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/57310/text
# Catalogue record: 57310 — [De transmutationibus memorabilibus]
# Incipit: x³ - qx - r ⊓ 0
# Date: 1675-07
# Akademie-Ausgabe: AA VII,2 N. 045
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=57310&katnr=Cc2+1014%2FA+%28tlw.%29
# AA VII,2: its series at leibnizedition.de: https://www.leibnizedition.de/de/reihen/reihe-vii/
# Work: https://leibnizlegible.com/work/00068201
# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folios: Bl. 208v (from the shelfmark LH 35, 14, 1 Bl. 208v°.207r°unten): 1 page, canvas 416, page ids 00068201:0416 to 00068201:0416
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068201&page=416
# Lines: 98 recognised on 1 of 1 pages, mean confidence 0.75
# Catalogue: Leibniz-Katalog / Arbeitskatalog der Leibniz-Edition (https://leibniz-katalog.bbaw.de/), ed. Arbeitsstelle Potsdam I der Berlin-Brandenburgischen Akademie der Wissenschaften, CC BY 4.0.
# 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, page by page: a "## Folio <label> — <page id>" line ("## Canvas <n>" where no folio label is recorded), "# " lines naming its source image and model, then its recognised lines in reading order, one per line.

## Folio 208v — 00068201:0416
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 207r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068201/jpgs/default/00000416.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine
X3 - qX  4 = r 1
X+I S + 4 10c
X 13f∞
+910 b
+91() e2
3fg 0 b
bc c
jam (3) b 3 1(3)C
Nam s bH 13) b bc
Eodemque modo 19C⊓  1O b
Hinc ex col. 3. fiet trans formetrta fiet:
8be  t
fiet inquam col. 2., 9feo, +3f co +3fgcC +6fgC0, -99b + 39c b +65gcob + 3fg b .
et col. 1. erit:
-9fC0 + 2f C0 + 3fg00 b +6f9 c0, - 99c, +39 c0 46fg co c + 3 fg E r0
quas duas columnas a seinvicem subtrahendo destructis destuendis habebitur aequatia divisibilis per b -c
fietque, 3fg ab +6) f9c0
+397 cor
sur i1s (159  1d
Notu dum unique purenthesius
intelliitur
H 0, sive b+c = 25 C0 - 39 c + 4
2fg + b
(359 b2b
(359, b) 1659 c0
Easdem duas aequationes non subtrahendo sed addendo fiet.
= 659c0  b+c - 6fgc0
+39c8
a. 3590
6fgc0c b
adeoque b+c p
= 3f2 c02
+ 9fC0
- 6 f9c0
- 3f3c02
+ 4 f c0
At. - 6f gco
- 393cor 1
+ 49 per aeque
2(6+9
69C0 (3f cd) 4 4 16g1 (D 0 C69c0) + 6q, ertque copi
fietque (69c0 351) r  c (- 69 10) +4
-53 2b_ - 65gc + r C 98 -65900 - b
393c02
et erit b+c ( = 18f gCd+ 3fY +6598 + 359c0 - 9fg00
+ 3f=+ 9f90, - 6f94 - 39 c0 + 99 a - 3fgW
qe
eritue Cop 9-63 W r drast
113fC
.35 c0 - 39 c0 + 4
Sed quia cabulus isre feies ninis prolieus opus est quodam contrudendi tentamento, Nimirum ex columna ultima
fociamus: 9 b
922 2bc 29 copo
+ss E 1. e elec sine
12bc 46fgc0 +3fgCd
et erit b+c p- f
-2+9co + lEgra
+8903
- 24529+co
959  +4917
explicemus Cd in vinculo,  euit in viniculo: + f
Si fieri posset in teomino utrima columna
= 293c0 - r + 659c0 70 restat et inea
 g 1 + 353
+2fgco
sive b  - 353 - 3f920 - 3 fc0, 39c0 +9
+9589
- 921 248
+9. 169
2 e+ 53 + (6
1952+ 3f ∞ 399-3699 + g
E+ 2co + 6f20 ros tco  
d +35960 20sis 0 + 4g0r
-3f 20 -39c0 +9
= 383 sed et in proheum
sive -3 f(- 55 9C  ( 35 9 caf - 39 10 r q adeoque c 1 49 +st
adeoque y9 + 25t rf
N - 2929 + 1295 + cf1g H
9- 1249 + 36978
294 465 9
et 39 rf p, . 194 + 119 9665199.-6959 r 169 r
+ 18f39
+3f9 6 -s,g
-3f gco
64910 - 3f c + 94 - 3fco - 39c0 +q
cegea
Quaerenda jam est una adhuc aequatio ex columna ultima per quam
+ b _
2359c0
ve
26+g8
= 3 f3C02
+4fle
- 24g9
= 24, 12996
alteru substitutur
lauditur, alterus non tun
9 - 1249 + 369