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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 302v, page id 00068194:0604
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3
+
eE
)
et nt
s
Hoc jam artificiam saine pulcherrimum, et generalisuum
et totam Methodum diosanteam mire illustraturum
applicemus ad formulam datam X, etc. et
sit H formula haac: X X +CCX + bcC  Traisformanda
depossite ex traubilem, seu cujus factor sit extrahibilis, quantum satis est
fiat X =h, Vy + ly +mm,: yy+ 2ny+ nn, ubi facio denom natore
 extrahibilem, quia. trasfer in formulis non negligendus
est nominator, e si in aequationibus negligatur
S.
 pro X sonendo b, fiet b = h, gytlyt mm,:, yy+ 2ny+ nn,
in th gy + hl y + hmm = , quae ut habect
 -b..
=2bn = b nn
yy + hC - 2bn  + hmm -bun - 0. et de
s
b
p - b
seu
debet esse
2ftmm -bun = hl - 2bn, seut himmabui hab = hblli quibu ab
dtium quia hoc modo, pro una sola roidice ipsius X res efficeretur, seu solum
 itm unum detur par radicum aequalium pro y, deo praestat assumere
et divellendis
fiet.
e
nonsst
XX + bx + CC = 0 fiet XX + bX + 4bb = Zbb cc et X = - 2 b + Y  bb -cC
uod in aeq. D substituamus pro b, et fiet:
ani - Lbun D + nn F Abb cc, h - L b + Si bb -cc =  hl. + nb - p sibb 
pot tum = Zbbn. h- 2b + nn 4bb- cc = ht  hl - nb +un  bb - cc
idem
 hum - Lbnn + R. h - =6 un = - hL + nb, 4n ut evanescat irratinall,
brevius fieri sit n = 0 et fiit hum, et h b = + fiit utique
M = 2 et h: h b = 1 4 seu 4h h. b seu h ab seu b - 
fnimbun faret 4m
t fintmm, h. 2b = sll, et hmni- 0 sed hoc absurdum, ergo
et  pro 2 1.
si volumus sollere n, retinenda  irrationatis, et fiet.
l
4 b S bb- cc h+ 4 bribb -cc
2 Fhae ei Em 1.
det
seu fiet
m.H h + 2b_S= bb -cC = hhHl. sit iet mn = A Hl
11
4n + 2b-2Y. tec
sit  Et idem est ac si voluissemus Xx +bX + cc facere exhahibilem
assumendo X = h, yjs + ly + mm: yy, fieret utiqre h
A GAhh l 3 chhrin gu + 
+ hh U. + 2hhlmmys + hhm: t
+b t +hlb B. Fhamb yy
Ubi numerator
potest reddi extrahibilis, es
debel repercti tem succe dere modo
fiat nim = hll 2, 4h. + 2b - 2 vbb- tc
patet etiam hinc egregrum sane compendium quod etiam ab cartu
noolim debuisset in measem venire. Nam si velimus extrahibile
eddere factum ex X frmulam Nm EEE. de quae fH ex 
XF XX + bX + ce ducta in X + sufficit reddi extrahibile
XX +bx + CC ope X =hgh, yyt ly +mm, :gy ita enim
X. +  x +f fiit +hyu +hly + hmm,: yy, et Yx 1S fuit Asgus Agatum
et X+5 fiit =L Y 1+ Fyy + ly+ mm
 si mn = ut dxinus. fiet _ X h, 3 + lytl
X = siht 2bh - rh Sb. ac  gy 4+ ly. + htill 8E t
+h + 2b - 2b166 -4cc, yy
ubi l, et h manenti arbilrarict
et video si faciamus
l:  (L +( fih) = 2M: ( (l.: ( s. 2
eti seu (=amml: C1(. h))
in
(a +h LH: (41 + 2b - 2V 66. 4cc)
aequ. l+ (f: h), etiam stfyu tluem
tuii
ei b
X A bXXH CX
AX+ bX+CC
= bxx) abbX +bet
eet
+ 1
3
e
Ea
=_c et