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# Piece: https://leibnizlegible.com/api/records/9678/text
# Catalogue record: 9678 — Leibniz an Rudolf Christian von Bodenhausen: Aufzeichnung zur Quadratur der Lunulae Hippocratis
# Incipit: Arcus circulares ADD, AEE, BC=AB, lunulae portio ADEA, huius qvaeritur
# Date: 1694-06-09 (94-05-30)
# Sender: Leibniz — Addressee: Bodenhausen, R.C.
# Akademie-Ausgabe: AA III,6 N. 041
# Record in the Leibniz-Katalog: https://leibniz-katalog.bbaw.de/de/extended-search?id=9678&katnr=35607
# AA III,6: 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-6
# In the Akademie-Ausgabe: AA III,6, p. 184 (PDF, Repositorium des Leibniz-Archivs, CC BY-NC 4.0): https://www.gwlb.de/fileadmin/Leibniz/repositorium-des-leibniz-archivs/III6A.pdf#page=184
# Work: https://leibnizlegible.com/work/00068207
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folios: Bl. 27 (from the shelfmark LH 35, 15, 5 Bl. 27): 2 pages, canvases 51–52, page ids 00068207:0051 to 00068207:0052
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=51
# Lines: 52 recognised on 2 of 2 pages, mean confidence 0.89
# 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.
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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 27r — 00068207:0051
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000051.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
Arcus circulares Add, AEE
BC = AB
lanulae portio ADEA, hujus quaritur mensum
quaeratur ejus elementum Ed (D) E) id est quaratur
a Trrangulo CD(D) subtrahatur triang. cEE)
restabit Ed(d))
sit ABsC BCHa, AG.X. Gd, y IFZ EF, v.
D): dx: : a: y seu D(D) = dx a: y,
CE- paa
jam CT= a+y (=DH)
nam ducatur BL paraleela adeoque aequalis ipsi jam CT in LDD
ait trianus. CDD). est autem CTC a+y (seu VH), nam ducta BL
aeq. et parall. ipsi DF (quia BD et CT sunt parallelae) erit tranus.
BLC congruum criangulo Nam BC et DG parallelae, eundem angulumm
faciunt ad parallelas CT et DB ergo anus BCL aeq. angulo, BDC. ergo
lrongula hoec rectanus uta BGD, BLC sunt similia, et ob hypotenusas
aequales BD, BC, congrua Ergo CL = DG (et BL seu DT = BG.) Ergo
CT id est BD + CL est a +y. Ergo cd (D) = atyalxy. Est
autem X = a - saa -gy. Ergo dx = ydy: saa-yu et CXD)- a dy fatys,: a- y i2
quaeramus jam et CEE trianus. CEE) quod prodit ducta E(E) in LCE. est
autem EE) = dZ Vraa: v. Ergo CE6) = dZe  aZ acc: v. quaeramus ergo
Z et V per y. Nempe ob triangula similia DHF, DHC et EFC
fiet _ EF seu V: VH:: CE sendhaa: cd, est autem cd = DH seu arrayty + CH sin a y
fiet cd = 12aa +2ay. Ergo fit vX. atue, taa: 12aa+2ay =  taaray
jam on VD+ CF = 2aa ergo aa tay + CF = 2aa seu CF = Vaa -ay = raa 
ergo dque = adue: saa-ay (v: DH:: L F: CH saeu V = Aty, chea - WP: saa- gu
vvaa - veyue vra (=vvi = 2 = 2a - avv + 2a0y (- y yV;
seu seu v = Saatag, ut aute ) Ergo CE(C) seu de aa: v =
adu: 2Yaaagu = CEE). et fit CDD) - CEE) = idy (ryCa:, saa-gys
= eD (D(E) quod elementum cum sciamus esse summabile natet hoc mudo quamvis
portionem Lunulae quadrari. Nempe CAG, =ADEA
scilicet
 poro Criangulum BC in LAG =+ ax cujus elementum est = a dx
id est =Ydy: Taa -yu = c D (D) = CE(E) id est ED(D)E).
nempe
Itaque succedit theorema propositum, quod triangulum
CAG aequatur portioni lunulae portioni ADEA
quod est specimen elegaas Methodi nostrae, quae
docet calculo invenire veritatem
demonstrationes theorematum in curva
ubique succedentium, etiamsi contineant
quadraturas vel aliquid ejusmodi quod Cartescus
sua Geometria exclusit

## Folio 27v — 00068207:0052
# Source image: https://digitale-sammlungen.gwlb.de/content/00068207/jpgs/default/00000052.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 9 lines, status machine
siadhibeatur a loco y. summatio
per se apparet, nam frt  ay dy: 21aa-y
a
= agdy: 20 -24. Sed y = VaX -XX
s
et dy = a = X: Frax - xX. Ergo fiet
Ergu y dy = a = x. Ergo aydy: 2a - 2X 
e
adx. Ee = B ED() (E) = CG(G)