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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 354, page id 175905688X:0376
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=376
# Source image: https://digitale-sammlungen.gwlb.de/content/175905688X/jpgs/default/00000376.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 43 lines, status machine
# Lines: 43 recognised, mean confidence 0.88
# 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: the recognised lines in reading order, one per line.

A PPE NDTZE. DE C UBTC ARUM
L R O B L F M A.
in sericirculo sapra mnum A D descripto quadrila-
terokBCD, demta sint tria ejus latera AB, BC, e C. D:
Oporteatque in venire diametrum (eu quarium latus AD.
ElD AB ∞ a, B C ∞b, C D ∞6, diaetCF VerO A D ∞ X; du-
cacurque recta BD, acque in B C productam perpendicularis
dCMIEFAEUEDP
per 3. Ouia itaque triangulum A B D est rectangulum, ideoque
terrii Elem. = QuadraTuM A D X quale duobus quadratis AB, B D: S1 d qua-
per 47
deato AD ∞ a x subducatur quadratum AP ∞ aa, relinquetur
primi Elem.
quadratum BD ∞ x x = aa. Porro quoniam obculansulum eA
per 12 se- triangulum BD C, at que 3quadratum B D majus quadratis BC,
cunai Elem. C. D Cimul sumpris, duplo rectansulo B C F; (i d quadrato BD D
N x -a a subducamus agcregatum quadratorum BC, C D ∞ bb
Fcc, reltabie duplumre.
ctanoulum BC F D X V -
a a -- b b = c c. Denique
cum Cumilia sine criangula
ABD _EC F D, Ciquidem
ipla rectangula sunE, ac an.
SUIOS PTRTETCA AQDCF
aequales habent: erit ut
D A ad A B, ita DC ad
CF. Unde cum A D Sit ∞ _, AB ∞ a e D C ∞C: CrIEC F ∞ =
Oux si ducatur in duplam B C ∞ =b, fiet duplum rectangulum
a bc
BCF∞ -.. Aquandum propterea duple rectanguloB CF
ANEC iNVeNEO D X X = a a -- bb = c6. Ouarc
1b0
ae quabitur
Xx - a a - bb - cc. TIOc eA ordinata aequalitate, crit
∞3. ∞   a a X  2 a b6.
-bb
C6
+ per 22
terrii ee 13
primi le.
nde cum hxc aegnatio sit cubica secunda tormulae, vigen.
dum deinceps an quadratum lemistis ultimi termini sIE imajus Cu-
bocrientis quancicaris cogniex penulcimi, an rero ipli aequale, an