# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/28629/text
# Catalogue record: 28629 — für (?) Overbeck: Mathematische Aufzeichnungen
# Incipit: ay = [Wurzel](ax_3 + a_3x) hoc reddendum extrahibile, fiat
# Date: 1715-01
# Sender: Leibniz — Addressee: Overbeck
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=28629&katnr=56079
# 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. 116 (from the shelfmark LBr 705 Bl. 116): 2 pages, canvases 231–232, page ids DE-611-HS-861255:0231 to DE-611-HS-861255:0232
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=231
# Lines: 84 recognised on 2 of 2 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 116r — DE-611-HS-861255:0231
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000231.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 82 lines, status machine
a1) = V(ax + ax) hoc reddendum extrahibile, tsiat
y = 107 + 200 + 12a et X = 507 +60D + 56a
O
40v
a
400
40 140ZV + 5 1oN coroaZ VV Y 3. 10+V. 20. 40a 7V
100 n. D0 aas.
1 10 201404 + 210. 20.1. 404a B, 10ror ab
40D ayy ~ - 10 4047 v D2. 10. 20. 4a Z vV - 20. 40 av - 2. 10. n. 40 aZV - 2. 20. 1 40 a axv - n. 12. 40av
ta∞ ~ 502 + 3. 5060 Z (V+ 3. 5o 60. 60 a ZB+ 0. ap3  (1 50. 60. b a 2V + 3. 60. 5b au WV +3. B. 56. aV 150 5b 1350 56 a
+40va~
+50. 40 a7v +od. 1. av.
(-2. 1. 20
+56.40 aa
ob ZVy. 50. 40. 401 3. 50. 60.60 - 2. 1. 20 30 =0 1b avv; se. 4o. to B. 16. 6a 
ut destruantur termini , V, ZVP, ave, fiet
(unde ex aeq. 2 fiet 50: 10 = 2. 20. 40, : 4040 + 3. 60. 60 = 56: 12 Restat inveniendus valor ipsiis 60. Ne mpe
ot V, obV; 60 +60. 40. 40 - 20. 20. 40 0
ob aequ. est 40. 40. 60.60  = 20. 20. 40. 60 + L20 = 420 -60 40 = Y (4 20 -60) +  20: 60
si esset ed 68 = 0 fieret 40-  20, 160 seu 40 = 201:  60 seu 40 - 260t 14 60 en 46- 60:2
seu den 40- 160. 12, seu qu 402 20 ,  20 V se 10- 20 M seu 402 20de et
vel denique 20= 40:)2 et 60. = 40 +2. it applicemus ad aequationem 1
452 (2  40 t = 40 YZ  si esjet  20+ -60 = 0, fieret
- -. 60. et 29-60(2
A~- 2,00. 3:60
 40= (60  seu 40-  seu 460 = 40 et 20 = 2. 40 fiet 20 = 4012
iga exaeq.. fiet: 440 7 40 = 2. 40 Ergo F ~ + et firt 60 = 40, et 20 = 40 12
50: 10 seu 56: 12 = 2. 4012 : 40. 40 + 3. 40. 40 seu 50 : 10 = 12: 2 = 56: 12 = 1: 12
etqiet y = 10Z  40V + 12a et X - 15G Z+ 40V + 120. 40V  quid non licet
Si esset 10 =2 = 12  20 fieret y = EA pA y = Z + ~+ a. pet X - a Z Se t 1 A 2,: 2
40 v: a
seu X- g
PM2
Et fit y= 10Z+ 4oV Y2 + nagictova et X -
d rgo paciamat redeundo ad equationem 40 = ( 20 -68) +  2088:60
faciamns 20 =1 et 60  , fiet 40 = C  = 16) + Z : = seu 40 = 2, (+ - 4) 4 :se
A = C  L. 3 + 1. Unde ex aeq. 1. fist  + L (1+ 3 + 13) = L 13 + 1 seu 2 + + 2 + 2 13 = L +3 + 1
quod succedit Erit  50 : 10 = 56: 12 = 13 + 29:, 4 + 1 + 13 = BA 2+ 13,:, = + 13
si q si 20 esset 2 et 1660 esset 1 fieret 20 = + ( 13 +2.
=  = 4, 2+ 13.:, 7+ 13
603 + 60. 40 40 - 20. 20. 40 =0 pultiplietur per 60 fit G460. 40 = 20. 40.60 = - 60
under eqisent: 1 +7 +213, = 8 +
seu 60. 46 - 20. 60 40 + =. 20 = 2 20 - 60 seu 60. 40 -  20 =  (1, 20 -60
seu denique 40 = 1 (920 60) + = 26,: 60 sit 60 = 1 et 20 = 2, fiest
seu 43 +2 =40. Tentemus aequationem 1. fieret
7 + 413 = 4 + A13 recte. Hinc 50: 10 = 66. 12 = 2. 2(7+ 4 (3)., ,  (2+ (13):, 7+4 (3 +3
40 = Y(15 - 1) + 2 _: X
V2
Zaer a 2 B2 +a et y- a, zivta
t
si xd - 50z + 40 V + sba, 140Y et y: a 50Z2.
pa
c
1+
seu d 50:10 = 4 +2(3, :, 5+213 = 56: 12
( + 2 13) (7+ 413) + 3. (4 + 2 13) = 2 (5+ 2 1) (2+ 3). divitatum haec aequatio per 2 F s3, fiet
20.90
1 10 = 5+2(3- 12
50 = 4 +213 = 56
2(7+4 (3) +6 = 4 (5+213) seu 184 e4 14 +6 -20 = 4. 213 = 2. 413 =0 quod succedit
60 + 50. 40
nempe ex 42. sit
Hade Esto ergo ay Nunc ergo calculum dis ex inventis instruamus.
AcZ + Zv + ) a et X-
ag = L (ax3+ a X) fiat  d =
(2+ (3) V
(5 +2(3)Z + 2V + (5+ 213) a et X =-  : (2+ 1) Z
gt- (37+ 2 5 4
121813
y. L(3 2 27 eB X(1t2. 90 a 
xaos
v + 2(2+ a Et  
exmp=C
)+ (74 + 40 s) a Z + (1or + () av + (3tcrisaa, (11 4t3) vv
Cit + 20ld9 a 4 eo ye
(2+
(2+ 13)
+0v
400
e
50 = 8, 813

## Folio 116v — DE-611-HS-861255:0232
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000232.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 2 lines, status machine
B
nsee aves