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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 113, page id 175905688X:0135
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=135
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 recognised, mean confidence 0.82
# 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.

e
pct
cere
euc
c
I O LA B R E V E S.
13
circulum EIR O L in puncto L, eric quadeatu ex
quale rectansulo RM O. Deinde, quia M D aequalis est
DO,_OD ipSIDR, eric QMO ~
qualis RO. Vnde addica communi
OR, Hiet quoque MR aequalis O.
Ac proinde (i a rectangulo O MI R au-
feracur rectangulum RM Q, hoc eAt,
QuadraTU Cx L M, erit reliquum
aequale quadrato ex O seu M R.
TIInC CUIM R MI SIc ∞ Z, HIL seu
MO ∞ a, _ L. M ∞ b: erit Z ∞ a Z
-bb.
Similiter (I a rectangulOOMIO au-
feratur rectangulum R M Q, hoc est,
QuadraEUI CX LM, eric reliquum a-
quale quadrato ex RO Ieu MO. AC
proinde si M sumatur proz, habe-
bitur Z ∞ aZ - bb.
Jam autem cum linea R O divila sIE
bitariam in D, ac ipsi in directum ad-
jecta QMI, CritreCtanGUIU R NT O, hoc CA, quadraFII ex L M,
una cum quadrato ex DO SCu R D, aquale quAdtaTO CX DMI.
hoc est, ex lemisse ipsius a; ac proinde quadratum ex DO seu
DR aequale quadrato ex D M, minus quadratO ex L M, hoc ett.
aequale = a a = bb. Vnde Siaddamus V = a = b 2, hoc eA, D
seu D R ad D M vel = a habebimus MIR pro Z; si vero illam
ex eadem DM auteramus, obtinebimus quoque (M PrOZ. F
quibus patet, primo calu tieri M R, hoc est, Z∞ = a- L V = a -- b
secundo autem M (, hoc est, Z∞ : a - V = a - b. Ica uthXC
aequatio Z ∞ a Z - b b duashabeat radices, nimirum, M R e
M L, quae, sic ut jam diximus, exprimuntur. Id quod secundo
erat demonstrandum.
Pollune quoque haec omnia, quae de radicibus dicta unE, per
Algebram demonstrari. Si enim in primo exemplo, sicur feci
US, DONaEUT Z ∞ = a- L V = a  + b:: auferendo utrinque = a3
habebitur V = a  F b ∞Z - = a. Acproinde, Si lumaneur ho-
tum quadrata, erit et
 = 4Z. + = a  ∞ + a F b : Fc ablato
uerin.
C. M C2
L.M X
nsit