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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 283, page id 175905688X:0305
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=305
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# Lines: 56 recognised, mean confidence 0.82
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EIICD
ruredo
lacre
esse
lct
ex nd
auIE,
Der lit
domin
e qu
vehoce
amte
I0.
ore
exlelor
COMMENT AREE TA LADRANIII. 283
ee alium S millia amittere. Contravero si damnum sic 22 ini)-
lium, qui hrabuie s millia debet amittere 20 millia, quadruplum
nempe sux pecunia; alius aurem o millia lucrari debet, proprerca
quod d priori sumpleric 2 millia, quae si emendis mercibusim-
venlatuissene, damnum S millium ei actulissent.
Porroradices hae Fal(x non inconrenienter in Geometria ex-
plicantur retrogrediendo, hoc eAt, uE, quae delignantuF Per = ie.
crocedant, licutillae, qua denorantur per L, Progrediuneur. Cu-
jus rei exemplum post ridebitur.
Interrit aucem earum cognitio ad inveniendas reras radices,
quippe, tallis cognitis, aequationes Facile dirilionis opc ad paucio
res dimentiones reducuneur, ex iisque vera cruuntur. Cujus rei
exemplum in sequentibus habebitur.
Accedit _ hoc; quod, poltquam tam fallx quam verae radices
alicujus aequationistuerint inventae, carum beneticio ad plenam
totius quaectionis cognitionem atque lolutionem perducaimur, de
calus nonnullos decegamus, de quibusnobis antea nihilcerricon-
Habat. Cujus rei exemplum sequentia icidem suppeditabunt.
rnde liquido constat, quod squationis summa, quae plures B
radices comtinet, dividi semper possit per binomium, quod com-
posirum est ex quantitate incoenita, minus valore alicujus ex
veris radicibus, quaecunque illa tandem sit, aut plus valore ali-
cujus ex falsis.) Hloc enim ex Aquationis, quae plures radices ad-
micrit, consticucione manilectum est: cum aequatio quaeris pro-
ducatur ex suisradicibus, in se inricem ductis. Ouemadmodum
ab Auchore fuic explicatum. Unde Fc, ut rurtus per illas dividi
PoTuc, cum id, quod mulciplicatione componitur, rurtus dirisio
nerelolratur.
Sic liponatur x ∞it, hoc est, x - a ∞ 0, d ruxIuS X ∞ b, hOC
CA, x - b ∞00, d denique x ∞ c, hoc cAt, x - c∞ 0, acque muI-
tiplicemus X = a ∞ O Per x -b00, e rursus productum per
X = 6∞O: exUTGeE AEquatIO ∞ 3 - a X N -  a b X = a b6∞ O.
6
L bc
 ac
Duae diridi potest per x = a ∞ O, Per X - b ∞O, e Per X = C∞0;
Ced non perx plus vel minus ullâ alia quantitare. Si aurem eadem
xquatio rursus mulciplicetur perx. + d ∞ 0, (suxponendox delig-
B 2
AaLC