# Leibniz Legible — https://leibnizlegible.com
# Piece: https://leibnizlegible.com/api/records/55429/text
# Catalogue record: 55429 — [Overbeck]: Calculus Analyticus pro Aeqvationibus se mutuo explicantibus a²y²....
# Incipit: Sit ⊙ = 2h/a z-h
# Date: 1716-04
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=55429&katnr=36920
# Work: https://leibnizlegible.com/work/DE-611-HS-861255
# Title: LBr. 705 · Overbeck
# Folios: Bl. 111 (from the shelfmark LBr 705 Bl. 111): 2 pages, canvases 221–222, page ids DE-611-HS-861255:0221 to DE-611-HS-861255:0222
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-861255&page=221
# Lines: 53 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 111r — DE-611-HS-861255:0221
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000221.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
Calculus Analyticus pro Aequationibus se mutuo explicantibus
ay=bx tacx + a fx + ahh
Sit O = 2hZ-h D - fz+ hv,: a
a
a 8D2
(2
b0 +c8O+ f820 +h Xo
a E
E= f +v Compendium sit Z-h = X
Facit f+n (f2 + hv) = 8b(X  cff+v 4 2 H Lnx + h (f +v)
a.
aL
seu 2 = X+h
Multiplico totum perc
fit fto (2 schv+lo) = 8bh X (ce 2s +f00) 2hx +k β13k foxhiso  tissi
it AE ffehor f ffiviselioo-solx talicat tghexe tf hxraffonx tehxfo xti olios otiso i
Ex Compendio collantur 2fZhv - 2 fKhv +2fkhv manet ergo
fsezho+ fh + fE +kv= 8blex: a +4kfx +4hx +2f.tx tafolxthf 13lv fo
Tollantur denuo utrinque K2fv + h V3 fiet
2
(232feho +v - 8bl X. a l fx + 4li xv + 2hxfet effvtx + hf3 +3lexf2
fiet
Ex Copendio 2hxf = 2h2f3- 2hhf3
f22 12f7h0 + f2Zv = 8bkX: a + ahe cfx +ahcvx
addo -2hZ F3 +hhf3
Afnhx = 4foh Z - qf vhh
+2hZf + qffohZ- fuhh - f3kh
-2h2f3+h + hhf3
E
fit fZ  2hZf3+ hf3 +2fhv + fZv = 8bh X: a + glcfx ralicox + 4ffvhZ. fnkh
Pono 72 - 2hZ + h = X2
h =X
fit XC+ Effoht + fu  = BbhX: a + gh fx +4hC vx 1afvhF- x vh ffotit
Effoht utrinque tollantur Fiet
Xf, fnt - 8bh X: a +4hc fx + ah cnx + fnht. fuhx fuhh
Aet
 Subtrato
=h = X
Y3f 2- 8bh x: a +gh. fx + 4henx n Eh Essett  ohZ + Hoh
fen
e
rectat
e
= Bbhx: a + 4hec fx +4ACV
L.
c
fnth + fuxti
Totu divido pX2
fit f. = 8bhx: a + ahcf: a + ah.cv:  Muttips per a
fit a f3 = 8bhx + 4ach + 4 a cvti
Ergo V = e a f - 8ba X - qucs
Aach

## Folio 111v — DE-611-HS-861255:0222
# Source image: https://digitale-sammlungen.gwlb.de/content/DE-611-HS-861255/jpgs/default/00000222.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 1 line, status machine
e