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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 28
# Folio 28r, page id 00068241:0055
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satis ex his intelligo extractiorum non tantum pro bino  secundo sed et
quovis gradu puro fieri posse; sed et pro affecto, eadem methodo. Inio haberi
poterit regula generalis pro omnibus aequationibus simul ac semel. Notandum praeterea
ista multis modis variari posse prout litera  pro certo aliquo numero
sumitur, item prout explicatur relatio inter se iuvicem ipsarum literatiam
et p. uno si lubet per alterum explicato, item prout P vel t, est quantilas
fracta vel integra.
eadem methodus valebit et pro radicibus aequa
tionum extahendis verum dificile est rem ita imre u radices rationales
invenianture, quando revera adsunt
X + pX + 9
= 1
ubi X, X+ pX + q7) b, 9 quod si eign aequatio ista rationalis, radicem
bp
habet vel c b  vel 9. ponamus esse b, erit X +pX +Gp q
 b bp
ergo X + pX Y b p. ubi si b p X fiet X  D Y, (P. Ergu
B I, vel 1t  ) et), vel-
XF b. ut suppox
suppo
batum
vel +1, +5, vel ∞1, - s, vel ( vel ∞1, -1, +5,  vel - 1+1 -s
Itaque si ultimus aequationis terminus sit s, poterit radix ejus rationalis esse, +1 vel - 1
vel +5 vel -)
N + px 191
+ P
++Y
X + pX + qX A.
)  S -s0 +58 - sV dsc
1. q. Ex x G p
++V
t2,2tv + V
2
-5
u
Radic aequalis talis est, si per eam dividatur tem
aditatur
terminus ullimus mutato signo
tem Regoluendus quatiens
muli so sign
anferatur _ termini penultimi quantitate cognitae; Residuum, iteram per eam
cognitum penneti
dividatur, et quotiens auferatur sus anfentur addatur cognito autes enultinii, et
ita porro, tandem si in mmo omnia evanescant, seu si in prim seundo quotiens
proveniens sit -1 (quando scilicet primus terminus simplex) Tunc vamia radix erit quam
liles quaesita
Vera methodus pro aaquationibus esse videtur, ut Primum aliquis divisorum
intimi termini substituatur ubiquei deinde si id non procedit, idem ille secumius divisor aliqua
quantitate auctus vel minulus in infinerum et ita simper porro; hac enim ratione
non quaevis ed aliqua tantum radix opparebit. Si non consiteremus diversos
uetrm termini divisores, videtur valor in cignitus aeque aptus cuilibet radici. Netatie
videri videndum quomodo discerni possitit rudices impossibile per series infinitus.
p