# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/51975/text
# Catalogue record: 51975 — [Overbeck] für Leibniz
# Incipit: Aeqvatio 1. ayy = x³+aax
# Date: 1715-01
# Sender: Overbeck — Addressee: Leibniz
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=51975&katnr=36922
# The Leibniz-Archiv's transcriptions of the letters of 1715 (pre-edition): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-transkriptionen-1715
# Work: https://leibnizlegible.com/work/DE-611-HS-861255
# Title: LBr. 705 · Overbeck
# Folios: Bl. 115 (from the shelfmark LBr 705 Bl. 115): 2 pages, canvases 229–230, page ids DE-611-HS-861255:0229 to DE-611-HS-861255:0230
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=229
# Lines: 154 recognised on 2 of 2 pages, mean confidence 0.84
# 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 115r — DE-611-HS-861255:0229
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000229.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 150 lines, status machine
Calculus Surdorum
Donamus 2 + Y3 =m.
Aequatio 1.
Multipl. utrinque per Z- YZ
fit 4+ 2(3 -33 3 = (2- Y3)m
id est d = (Z - Y3)m.
Seu 1: m = 2 - Y3
Horu quadrata 1: n1 2 = 7 - 4Y3
Divisis E. e X per m
fit 1: m = (2 - 13): m
MiM =I: M = (2 + YZ): M2
5 Suma 1: m  + 1: m = A: m
addontrinque AWZ. um
a 1 1
Aequ. y -b +213) 2 + 20 +6 +2r3) a
(2+ r3) n.
+ a a X
Aequ.
(3
X -(4 +2V) Z +v + (4 1213) a
Pono 2 + r, =m vid. Liter~. Iem 2+ a = W.
fit y -(Em +1) WV +2V
mn
X = 2M W + B
Ergo per Aequ. 1.
fit (Em +B) e +2V) 23
Dfit aW: vm +1:m B. m = 4: m. + 4N: vm
ME vE
a
fit ((2m +1) W +20) 2
(2 +r3)v.
mi seu y = (Em + 1) W +2B,
a
(Em + V)3 3
m313
mv
X = ZmW +V
moa. Et omisso communi Multiplicate a3
= (2mW + D 2m u +v Et Involvendo Explicite
MEvE
md v3
MD
Mn.
Multipl V utrinque per Zm: D fit am + amWer, +W+emtqu + qu = 8m  = 12 m H  +6mHo qV L 2mW+ V
_ fit 2: m D +2: D = B: mv.
Addo utrinque 4: m v.
a fit 6: m v +2: B Z8: mv +4: m v.
Multipl. V utrinque per(2m)
D fit 2: m +Z = 8: m 3
Ex 8
4r3-5 p
m2v2
 a a
a + 4: m. quae ad Literam Dvalent 4Wm +I: m + 1: m
fit 4N: DE L WE: m v + 8W: mo + 4W: m B = 8WV3: v + BW: om +6N: mn +2WV: B
Divido utrinque per W. fit 4W: v L W: m B= + B: mv + 4: m B = 8W 2 v +8W: v m + 6: m v +2: p
((2 + Y3) 8W): 413- 5. perr. fit
Multiplicetur
explicite 2+Y3
AV3 -5
3Y3+4, 3
= 10 - 513
16+8, 3
d per X3
fit X - 10V3+15
16 + 8r3
et 13) +4. (4r3, - 5)
facit 4V3 - 5 = 8N: D
sit 4vr3, - 50 = 81
fit v = 8W Hic Valo
Hoc abbreviatum
C8+ 43): (r3, -5)
-
4Y3, -5.
a
Itaque in Valoribus 8, 4,
Abbrevia dop 5. &t  fit 15. -for3
satisfactum est Problemati quo exigebatur
inveniendus Valor v. ration aliter per 7.
B + 413,
et per 43
a
= 5V
qui V’alor vocetur 
X
8 + 4r3= a
X
a
Hoc abbreviatum per 33 - 2, vel 8 - 413
16Y3 +20
vel X - 1613 -20
a
16.
Posterius abtireviando per 4
Hem X et y. pure rationaliter per a
excepto irrationali 13
40Y3
Ergo y = 15 vel y
a 8V3
fit 313 +2
Vael a = 2d
quod hirc non estimatur.
facit 75
per 10r3- 15 vel per 16- 8r3
X
Abbreviado p multiplicans (4V3. - 5) fit  +r3), (a 3, - 5) +4
Fac. 313, -2 qui Valor s
nom W est a +Z.
2 + (2: m)  8: m ad Literam C
sit 2-(1: m) = 8W: v
Item per Multiplicatem (413, - 5) abbreviando, prodit (5+213, 413 -5) +1b
Facit 10V3, -n. qui Valor sit 
tertia ex e restituta
4Y3- 5. Abbreviando (
B
1  6: mB + 2: v.
Restiant AW: v= + N: mv = 8N E v + 8W: vm,
Aufero utrunque
C
Sumo alore 1: m ad Liter. T. fit 2, - 7 + 4r3 = 8W: 1
(16 + 813): (413-5)
20r3 +83-23 - 10r3
Pro Aequatione
(4 +213) W. + 8i
.
y
Divido totum per W: v2) fit 4. + (1. m) = 8W: v + 8: m
Altrreviando pW. fit ya = 5+213, + 16: (43 -5)
Maltiplicetur, 5+253
explicite 413 -5
mv
fit 4W? V 4 4W: vn +N: m D + BW: mv + AW: m p + 4: m =B w J. v. + 12W. Nm +6W. mB + 1. m + ZWI: v + 1: M
e
Aufero utrinque aequalia ad Litera 4. 8: mv + A: mv=
1br +8B3ro Aequatione 2.
1V2- 5
de
2. Et eximendo quaedam ex V.
Aufero qu2. vm
Restituantur Aequatio 2. d3
fit y = (5+213) N. + 16N
fit X = 413-5
a
qui Valor voc
 =13, - =Y
4013
64 a
5
a
Br3

## Folio 115v — DE-611-HS-861255:0230
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000230.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 4 lines, status machine
Monseigneur
on cergneur
d Leibniz
bien humblement