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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 31r, page id 00068207:0059
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Eurerit mensuratio portionis Lunule ADEA. Quod ut fiat
quaercndum ett ejus elementum, ac summandum Id Elomentum
e ED (∞) (C), id ett Triang. CD (D) = triang. CE (E). Est autem
CD(∞) =D (D) in =CT. AG tit X; GD, y; 1F, 2; FE, v.
AB seu BC seu BD, a. CE, fraa. D(∞) = dxa: y. sit BL
parallela et aequal. DF; pat et triangula BL C et BGD congrua
etse seu aequalia et similia, nam ang. BeL aq. angulo BDG;
comprehendunt enim parallelis; itaque triangula BLC et
BGD sunt similia, sed hypotenutae BC et AD sunt aequales; Ergo et tirangula simi-
lin et aequalia. Itaji C = DG. Itaq CT = a + y. (=DH). Ergo CD (8) = a Fy, adx: 27;
sed X = a - Van gy. Ergo da = ydy: Taayy, et CD() = ady 1a +y,: ay: 2.
quaeramus jam et Ce(C) = E (C) in =CC. Et autem E(C) = dz fraa: v. Ergo
CE(C) = dz aa: v. quaeramus ergo Z et v per y. Nempo ob triangula similia
HC et EFC fiit EF un v: OH un ady:: CE uu fraa: CD. Ert autem CD=
OH LCH, seu = a + ray +yy +aa-yy. Ergo CD = Fran +2ag. Ergo fit v=
laatag. Jam Wv + CF= 2aa (seu FE +CF= CE) seu an tay +CF= raa.
Ergo CF = Jan -ag. Ergo Q (Bia - CF) = Fraa Jaa-ay, et hinc
aZ = ady: 2 Paa = ay. Ergo CE (E) seu duan: γ = audy: 2 aa yy. Ergo
CD (D) = CE(E) = aa tay dy = andy,: 2V ar- yy = aydy: 27 aa yy =
=ED (D) (E). Sed sum. ED(D) (C) = ADCA, et s, aydy: 2laa yy =
ra, a Vaa- yy = 2 ax = Triang. CAG; Ergo CAG = AD EA, ut erat
propositum. Si omnia fuissent explicata por Xe Ploco y) faclior fuiset
sumatio; nam aydy: raa yus dat ada, adeoque ED (D) (E) aeq. triang. CG (G).
Haqe propositum thcoroma succedit, nempo quod triangulum CAG aequatum
lanulae portioni Adcit, quod et peuimen Methoti nottra g.