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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 68r, page id 00068201:0135
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sire rmaginaliis
incognita pujus
De transformationibus aquationum, (adhibitis duabus incognitis ad praeparationem.
quadrato quadraticam
stusis in Aralysi Mesolabi aquationem propositam quam libet:
()
4 2
x Ex,  bpX t
ita resoloit in duar X X 9y et 4y + bngy - b X + b aX p b H- B pX
ex
a (+)
no
Jam faciamus X  E Z + d.  et Y A e V + f
ab
X + rCd qe 1S a BE V  2f Y 
jam ex 2fer aequae redque +d = Z - bd p equ + af sive v⊓ 7. Z
V
94  Cd 32 Cgo + 4 cd3q + d+
bit
= 2c3d.
Q- Ba - b d pv. pone b p 4C, for
a  C - XCd sive a 
tantum modo ponatur b, seu 3d
seu CH (3-el
13-  
2d
CV
p2
seu C+l, 2C N13 quod fit ponendo ex lvel
si velmius lc ut a sit assrmativn sufficit
o
2
nct.
-2∞9F..
q ed.
=a ed..
- 4 cd..
acdut
- 2cd..
+2 cbd.
+2c45.
- 203b
- 289f
+bd
- 26395
+qu
utor hic praeformane per duas
incognitas, quae etsi non vet alias
superneomerarias dat tamen alias
expressione, quam praeformatio
per unam
redque + d. et
V2 - bd
c p =4)
Hac
id ac quidem recte sed utilius deprehendo immutare calculum, neque secundi termini cognitam b, sumere
ese 12 er e 8. et 1p et  
G+ c.
eut a pro danitate, fieri enim potest, ut secundi termini cognita absit, quo casu b nihilo aequalis. praeterea
esto c
eum calculus sit magni momenti, utile est adhibere numeros
tertius
6aa brabat juleru videndum in aequatione cubica trium formularum, ac pimum cum secundus terminus
18. 14
est affin tou extrat potest radio videamus cum est negatious
s 4 aH ba b d. 0. unde aequationes duae: be a, et da + a pe. nt da= be
Eigo b pd
(11)
ponntur e n L3 + m, et ap  V a + P
11
P s + almy +N, a p n V + anpB + p
Nam ex aqualine sir Amalogia.  at 3 mendo bessa.
e
a
 ca p V, fier: 
ac ab + db
ace
iumet ea  at e , ast
na,  b, a a, c.
t b ad a ita
+
Unde ob aeq. 1., erit  ly + mb 1 2 v + 2np V + p et per 2 fet: d2 v + d ps  d F 2m t m - lymtil
ande ex  fer (9P (+ 1m D B uil yV = anplvys + p 1y lmy. Et valorem ipsius  substitient
62
in aeq. 7. puo ipo fer. C) du V + dp p t l yr = inpl vy + p l y (- 1m . 3lim y + m -ly mb
b
enpen F
= mb3
12
lv + nplv + P
+ mb
l. m. n, P ipsam l omnino evanuisse
 b
5d
+im
ob + 2npor. +b, et facta multi plicatione
tollendae fractionis causa:
bdu B + dp (n b m b) (F mb) (undon
Ubi notabile est ex quatuor arbitrariis,
Unde
b D) er dpB +b
1)
b4
pro y sabstituendo ejus valorem  d  +dp - m + nb  y, tumfier ex cq. 6. frei
huvr dot nibe ub
0) 1is
quy
s
n v + 4 ne pb V + 2n s V + anpb V  p
+ rupbv.) - b+ no2
(+ in b3C nv
a
absdu. + dp ( +nV + pb
+4n pb..
+ p2b2
+ 2npbr
+prb
frei )V (4) X + bdeZ H  ab et aequabiter a radici quadrato quadratica ex
bae +  b da
ba
a
Esto (14)
facimus jam n. V + ib rpB + ban F
quopu +
+ d  g faciamus bd nV + db p,  o. sive pnV
Ergo 910. Quod est absurdum, quia qa.
restabit n Vr
Elia ita ex i bn +2bn pP + bEx n BE + anpbV + 6n paC2 B
aup BP + p+B+
15) 1a
Sq
 3 = b dn . =b dp
Ponamus . 6)  p3   b d u erit XPB 1Dbd, et env bdp
sive (9) +nV ( b6) bd. et ex 15 fier.  bnV +Bp nv = anpb D + b. Video ergo rem non
procedere hoc modo, firei enim aequato itoditas, quia a n confderane vetat mna iesgnta itiaue posita neb quia mlis s 
Ab ad a, ita aedeceade
Tentaturan fri posit ad epressionem
Geometricam omnium radicum crbicatum
et de Radicibus cubicis