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# Title: Ps. 2 (shelfmarks Leibn. Marg. 178, Stück 2; Leibn. Marg. 178)
# Folio 115, page id 175906937X:0139
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175906937X&page=139
# Source image: https://digitale-sammlungen.gwlb.de/content/175906937X/jpgs/default/00000139.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 69 lines, status machine
# Lines: 69 recognised, mean confidence 0.78
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
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# After the first blank line: the recognised lines in reading order, one per line.

u aqui
u, Bonpol
pi
racim
sit a.
 quio
reperitu
3- - bX
ovserant.
LlXr
10, uo
CioruI
ICetUEI
PX +
aeia
=1
1III. Set
ilia,
113d C0
lhicP
N alia
1D
aparation
do duletta
Fret
si
A O U A F I O N I N.
Exempli gratia, si dentur hae aequationes X x  b x - CC∞0
 X X = b X -  d d - b b ∞ 0, habebimus X X = b X ∞6C, 8
X e  b x ∞  bb = d, er90cc∞ bb = d ebo
Venio jam ad alrmmetrias seu irrationales quantitates, pro
quibuscollendis, oportec tantum supponere literas aequales lin-
fulis terminis alpminetris aquationis propolita. Oua quidem ra-
tione non tantum obtinebimus aequationem propolicam, in qua
omnestra licera lune substituta; led etiam tor alias, quotliterx
Fuerunt suppolita. Unde collaris ordine omnibus hisce equatio-
nibus, derenietur ad aequationem, ubi nulla licerarum invenitur
ac per conlequens nullum signum radicale.
Exemplioratia, proponatur xquatioc- L VC. bbx = V dX ∞O.
Ad collendas isitur ejus alzmmetrias, PonamuS R ∞ V C. b b 
_ Z ∞ V dx. Quibus in aequatione proposica substicuris, hobe-
BimuS c. LR- 2 ∞O; aeque ex reliquis supposicionibus erie
R3 ∞bbx, d ZZ ∞ dx. Primo, ad collendum R, habebimus
R∞ Z 63 IdeOGuC R3 ∞ Z3  36R Z - L 36CZ i c3. REqui eAt
quoque R3 ∞ bb x. OUare CrIt Z3 --- 36ZZ  3CCZ =- 63
b b x ∞ O, de per consequens 23 ∞ -  3 CZ Z = 3CCZ -
63bbx. Sed li mulciplicetur superius propolica aquatio 2 L
∞ d x per Z3 habebitur etiam 23 ∞ d X Z. Ergo erie
3622 = 3662 c3 ∞0, de substicuto d x loco Z Z, habebi-
=dx  bbx
MuS 36 d X  3662-  c3 ∞0, hoc CA, 366Z ∞ 36d X - bbx,
eu = ∞
LL X
n dX  bbx
Cdx = bbX - L C3
3C6 + d X
36C- dX
dX
Oux si mulciplicetur per Z, Aet
XZ F bb X Z = C32
.Sed est quoque Z Z ∞ d N. I9i-
Tux habebiius 3 cdXZ L b b X Z -  C3Z ∞ 3CC e X - p. 1b ct X X.
det ab
3CCd X - L c d X X
BC d X + bb X F c3
3Cd X = b b x L c3
366= A X
D 2. Invenca dutem est
Duare habebimus tandem