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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 122, page id 175906937X:0146
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=146
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# Lines: 36 recognised, mean confidence 0.86
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D E L T N L F L B U S
PrOD. 3. X X - lX = M M ∞ O.
Per transpolitionem habebimus X x L. lx∞ mm, de per conse.
mm
quens = majus erit quam x. Rursus exiltente a x- L l~DMM.
eriemminajus quam ex, e mnajor quaimx, ac proinde mema-
juS quam Xx. AEqui habemus ∞ x L l ∞ ∞ m m. FrCO M X L. LX
majus erit quam mm. Flinc dirisd ueraque parte pet m. L. l, Aetx
mm
Major quaim-
m. Quare invenca eAt x radix XquationIS PrOPO
mm
mm
litx major quam,. J m aE minor quam , ee M.
C A P I F TI.
Delimiribus Aquarionum Cubicarum seu trium dimensio-
num, secundo termino carentium.
Prop. T. X3 X = M M X + 1 3 ∞ O.
DEr transpolitionem habebimus x3 ∞ L m M X -n3, erieque
Lmmx majus quamn3. Unde diri (OUErOqUe FeFIINO DEEMM,
erit x major quam-. Deinde per transpolitionem critmmx
MM
x3 ∞n3, aC PeT COnTEQUeNS M M IMajuS quaIM X X, _ M Major
quam x. Ouareinrenta est urraque radix a aequationis propolita
de minor quam M.
Prop. 2. X3 X - M M X = n3 ∞O.
Per Campeoeadebimus X3 = M M X ∞N3, CFIEGUC XX
majus quam mm, ec x major quam m. F. rit quoque X3- n Cmm,
ideoque x3 major quamn3, _ x major quainn, ac proinde nnv
majus quam n3. Aequi per transpolitionem propolitionis habe
ImUS MM X + 13 ∞ X3. QUaTC MM X + BN X INajUS CrIE quam X3;
ee dirisd utraque parte per x, erit mm. Lnn majus quam xx; ideo-
que x minor quam V mm-Lnn. Inventa ergo est x radix aequa-
tionis propolicae major quam mden, ac minor quam Vmm. L n.
Requeliquet, ad cricandam extractionem radicis cubica ipLIUS N.
quod loconn in rinculo allumi possit quantitas aliqua, gux non