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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 229r, page id 00068201:0457
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a ta B H. (5) 25a + Y 968F side LB H  p + exemplum est scholeni in Additamento ad
Commentarius in Cartesium. Vocemus S3) 25 +0968, D P b. fiet. a s8 )  b - a. sine 87, b=- 2ba +a
Aiplicationem non per b. sed per B multiplicemus, fiet: 7 a b b -a 2ba. itaque ex prma a
(2 1 b - 7a b 1 b+ - 2b a et pro b poncndo ejus intorem: 25 + 196, fiet.
+ 7, 25 a + 7a ( 968 1 43 a b + 2, 25a b + 2a 1968 b, sive bp (112 + 1a 968
jam utrumque hujus aequationis latus cubando f debet, destini radio 96s. 99a + 2aY968
+ 4 .. . . . + 4.......
25a +a 1968H 25’ a + 11 a 968 1968 +  3, 27. 1 a 1968 + 3, 275 1 d968
Quod si non cules ob b. sed quadres ob 1968. nihilominus tamen taemtaemen si habebis
non tantum b. sed et B2. quod a ut tollas, et solum residuum habeas b rursus veuies ad B
seu ad V968. itaque si uuna irrationalis
in ultra simul e extra, incipiendum semper
Itaque quando radix cubica aequalis est cuidam quadaticae
et numero, estque ipsa quadiatiea radix in cubica, non poterio (regulanter) Tolli quadratica pesidua
a tollenda includente regulariter.
sola (ubica. Nec proinoe sequetur absurdum, quod scilicet ita radio cubica aequetur cuidam
numero incommensurabile ommensurabili
la + sca Y SD  aed tas ae Unde cubando: b + 3b sca. + 3bca + carca p ad + a rae
+ pZ + agZ + Y n
et Z H
d X3 + 3d 2agX + 3da) X  agr
pd... + 2pdaus .. + pag
+ p Dd.. + 2pb dgs.
agd ... 12 agd b..
+a90g.. +2a9490.
Pbag
ar... +3a rb.. + 3arb. +arb
ope hujus explicationis fieri potest, ut sit
be rerim en n  ergo f.
Mapt Fng X + 2o h
dXt 00
benim sit aequatio
IXjt
2 + 1.  a ec
ab a mtr -am.am 
Xah + h3
X + hX
X3 + (hX + alX
n. + hn. + nal.
X3 fB X + a) X + aed
Ergo h B-n. et alp Bn+ n + a7.
et de - Bn + n3 + ayn.
se nE-en  + aVn = a rS 0
Notu si ope tot arbitrariarum fieri possis, ut factus ex secunto et tertro
termino equetur quarto problema erit planum in
ductu, vidcamus quomado rulcam. A, nempe 99 
Bat Z + anZe + an  t E
Dividendo utrumque per Z + e. fient aequationes duae, prior:
posterior.
allo autem
+ au 32 + aq
+al + am. + aen
C3- al e + an e - a n p0.
+ aq
ar tan ro
24 +ac +
0pet 2
b
=ap h alh) + al
anhitan (tant)e n. sive e
sive  + aqh
+al.- am. +a
0. tam
etr + h)
titoqu s _ e
agti -aemh - alph + aet
=am. tan
ergo ab a
q+ phaen-at m + a rhaque
= alphan tastn
aphan
am.. +am 1---
=aghalph +ag a12
tam ... - am...
Caerhaemh-aertralph ta rhael
Halitaena phaetu = anagn + an aemh +an alph - anal
phanh +ph a imphi
ph am taghaquh a agh a intr
+ ph- al
Ut prolixitas calculi evitetur, itile ent generaliter calculos inire, quomod. datis duabus aequationibus
aillatur incognita, sunto aequationes duae: e + Bpo et C + c 70. fiet Cr - b.  - c. et bp C. seu (b -C50
sint jam aequationes duae: e + bo et e + de + a C,j0. erit e - b. et Cr, - be. fiet - be + ac. et es C  -
adeoque (ac + b - bd 10) sit jam e + de + ac 10. et e +fe + ab po. unde de Faci, fe + ab. seu er, ab = ac e - de - ac
H. fe. ab. seu ab ac e p de + fde - dac + fac seu epi d ac + fac
ab - ac at reducend:
ab - ac + d - fd1
ut ab abeo a ac n dab u si ai 90t at. sac 10 d i Fatus cntemvi spoqpi egnadei calertus e