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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 358, page id 175905688X:0380
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=380
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# Lines: 35 recognised, mean confidence 0.89
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APPEHDLX DE CUBLC A RHM
Ouia itaque demissis ad hoc perpendicularibus BF, DR, in
triangulo rectansulo ABI, quadratum ex A I∞ = xx subductum
per 47 pri- a quadrato ex A B D aa, relinquit quadracum ex BI 2: erit qua
miElem. dratum ex B ID a a = = X N.
Fodem modo, in triangulo rectangulo C DK, quadrato ex
CK ∞ = b b subducto d quadrato ex C D D aa, relinguetuFAA-
=bb, Pro quadrato ex DR.
Porro quoniam, propcer limilicudinem triangulorum ABI d
per 4Sexri AD K , AI est ad IB, LICUL A I ad RD: erit quoque ut L X
eteriso
Quad. Cx AL, ad a a - = X X, Quad. ex IB; SIC X N F b ~ + = bb,
quad. Cx AR, ad a a -- = bb, quad. Cx R D. UInde mulciplicando
extrema, inrenietur produetum = a a X X - 1 b b x X X qualE AAXV
 a a b X F = a a b b = = ∞ = = = b x 3 = = b b x x, producto sub
mediis. Iloc est, demptis uerinque aqualibus, de terminis omni.
busper 4 ductis, si ipsi deinde ad unam partem transferantur, ho
bebituF~ + F b ∞ 3 =3a AX X = = a ab x - a abb ∞ 0. Oux suM-
ina Si DOrrO per x L b ∞0 diridatur, obtinebitur a quatiOx 3
aa X = a a b ∞ O, Teu x 3∞ X +- 3 a a X.  a a b. Cadem nempe
quae superior pag. 350, in qua cubus crientis quantitatis cogniex
penulcimi cermini exce dic quadratum semissis uleimi termini, cu.
jusque aequationis rera radix illic per rectam FL, hic aurem per
rectam AC delignatur.
per 5 pri. Caeterum quod angulus secundi crianguli DC F, qui est ad
miElem. balin, criplus lic anguli A, qui est ad balin primi, ita patet: A. qua-
per 32 les enim sunt anguli A e BC A 3, propter aequalia crura AB,
primi Elem. BC.; ec ob id + externus C B D alcerurrius hujus duplus. FA
per 5 pri-
mi Flem.
per 32
aurem hic C B D aequalis ipsiC DB 5, propter aequalitatem li
nearum C B, C D. Ouare _ C DB, id est, C D A ipsius A du-
erimi Elem. Plus est. Atqui binis hisce A _ C D A aqualis est externus
DCF