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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 137, page id 175905688X:0159
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=159
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.78
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# After the first blank line: the recognised lines in reading order, one per line.

uation
uM
et
10, e
Omne
eTITUT.
Fet
qui
sulin
Xqual
ention
ellio
sumpe
I5 b ene
arUI
Itera
tam le
CaM.
0
11
Ol
N. O F A B R E Y F 5.
tocum per 27, Orietur y3 = = cy7 L 3 d dy . - b3∞0. OUX
aquatio quoque inrenietur, liprocedamus juxca hujus Geome-
erix Mechodum: Subrogando nimirumr in xe quatione proxolica,
quadratum ejusyy, ee iplius cubum y 3, in locum x, quadratix, de
Cubix3: _ diridendo deinde sCCundUIM TerINUI PerZ, terrium
perhujus quadracum 9, e quartum per iplius cubum 27. Fadem
demonstratio locum obtinet, li in ae quatione radix incognica plu-
res dimentionestrabuerit.
AD P ACL N AM 79, ee sequentes.
D ROPONAtIEK+ X L P ~2 F qX- r ~ O, dE SuPPOnatuF juXLZ
 Pexe Ccripeu hujuS GCOICETIK X ? f y X  E y + =P-
,  O, ericquex = ; yy = =P3 2 = y x, ac proinde quadra-
cum unius partis aequale quadrato parris alterius, hoc est, x +:
7Y X X F =y +  pX  +  pyy = = PB∞
472 = 9V  y y X de
consequenter x + +  y + + P x  + = Pyy + = PP + 4 ∞
Exr. ∞0. Ex qua aquatione (i collatur priima X + X - = p X X - = 9X
r∞o, relinquetur = y+ F = P9 + pp. + r - 2 ∞0. Vn-
demulciplicando torum per +y7, exlursetys L py t. L p2
9900. Ouod erat demonstrandum.
F. Ar 73
Fadem rarione demonstratio het secundum omnes rariationes
lignorum  ee =, atque obserrationes in hac Geometria expo-
lcas. In cujus rei exemplum duorum adhuc lequentium casuum
demonstrationem subjiciemus.
Sit aequatio propolita x + X = p X  - F q X = Y ∞ 0. Si er3O
juxcatiane Geomeeriam luppoluerimus v + y x f = y - =p
∞0, habebimus x 2 -  Lyy - = P∞ 2 = y x. Vnde d qua
dratum unius partis aequale erit quadrato alterius partis, hoc eAt,
∞E f 99 N + =gt - px - = py y - + = PP ∞ Q - 4V - + y9 ∞ X
Ec per consequens n + - Lg +  P X X - = P y y + =pp. + 9V
2
30. E. qua si auteratur prima x + + = P X N L qN = Y ∞0.
relin-