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# Piece: https://leibnizlegible.com/api/records/59452/text
# Catalogue record: 59452 — Leibniz an Rudolf Christian von Bodenhausen
# Incipit: (Math. Ausdr. & Fig.) Demonstrandum est ADEA = CAF. Ergo CF(F)
# Date: 1692-10-05 (92-09-25)
# Sender: Leibniz — Addressee: Bodenhausen, R.C.
# Akademie-Ausgabe: AA III,5 N. 108
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=59452&katnr=86619
# AA III,5: the volume in the Repositorium des Leibniz-Archivs (CC BY-NC 4.0): https://www.gwlb.de/leibniz/digitale-ressourcen/repositorium-des-leibniz-archivs/laa-bd-iii-5
# In the Akademie-Ausgabe: AA III,5, p. 18 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/III5B.pdf#page=18
# Work: https://leibnizlegible.com/work/00068207
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folios: Bl. 24v (from the shelfmark LH 35, 15, 5 Bl. 24v°): 1 page, canvas 46, page ids 00068207:0046 to 00068207:0046
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=46
# Lines: 80 recognised on 1 of 1 pages, mean confidence 0.74
# 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.
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# 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 24v — 00068207:0046
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 23r); this page is its left half.
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000046.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 80 lines, status machine
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Fires 44: Agort. 92.
Ergo fiet Xdx + ydy3 : l = dl
 Vaa = 2ax +XX + yu = M. Ergo dm = Xdx rydy. - a dx,: M
bb - 2bX +XX +gy = n Ergo du = Xdx + ydy - bdX,: n
= U+ m +n. Ergo
o = xdx +yd) + X AX + y AY =a ax + Xdx + yay - bax
Ergo  dy: dx = _B - X: I
+a - x : m + b- X : n 3: y: l + yem + y: n
FE,y AE, X; BB AB, a
AF
et
AC, b
BF in CFn
BE a =X CE = b = x
Ergo TE = _  x: l + a = X,: m + b - X, : n
seu TE
(: l + 1: m + I: n
AE: AF + BE: BF + CE: CF
I: AF+ I: BF + 1: C
(D)(D). C jam DG tangens in D occurat id an verum
sit calculo invenire licet, ens sed compendium praebet meum
theorema olim circa quadratura circuli communicatum Nemp
ducatur DG. Tungens in D. sit ipsi eq aequalis Y
evit LCMHL
9. d4
 dupl. LCDL. et proinde. H(H M) Na C D (D) dupl
1(P). jam F(F) (M M
ag. dupl CFF). Ergo (per 1 et 4) erit F(F) MIM ay dupl. DE(E()D
Ha auu
cap
et proinde F (per 5 et 3) erit H(HH) F i q. dupl. C E(E) quod
Esecet AB in P. Erit e ducatur Eq tangens ine
circuli ser angulo ad CErecto dibet  Cin et seti et. ER sit intervaleum ordi
natarum ex E E) in AB sucendarum . Frit 2Q in ER g. C2). Ergo  per 6 et 7. fet
o.
B
lev. oba
demonstrandum est ADEA = CAF
Ergo CFF)
vic
e
a an sit vera.
Ergo CQ: 5G.
CQ in ER aq. HF in F(F) seu SG in F(F).