# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/00068207:0051
# Permalink to this reading: https://leibnizlegible.com/page/00068207:0051?run=74
# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 27r, page id 00068207:0051
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068207&page=51
# 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
# Lines: 43 recognised, mean confidence 0.92
# 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: the recognised lines in reading order, one per line.

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