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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 284r, page id 00068201:0567
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nota autem quod penultius tenulius aequationis reciprocae func erit
3.  Xa
1 lt + a l Gu
-3c ha
  hi cgaet, 
∞3C + ht
sive
, + pa + p
-95 + 3h,  Ca sine 1a l+ 1 etetart
1t
C3 = h)C + ae l (2)
9cHc
Ch-HC+ atl
quodifi jam ponamustam c quam im esse quantilates affirmativas
sive h. p. 3C, tunc si possemus efficere, hunc terminum ultimum majorem
quadrab i penultimo
si eveniret ut radix daret ipsam m quo casu
e rellimu
et najorem fieri tripto quadrato triente quadrati a  tertis
quod ut compendiatius faciamus ct (h aequa quadnb
et fiet hys +3C+G
ergo  = 3C A
9e- 9h2 +ga
gnt a
pradic ert. + +69
F13
imo dinuric debet 2, 13, S.  c +B
faciendum ergo prim
acclue
X( n  -3c
C - h=C + aet
h. sit najor quam 3C. et ut differentia
sit lo major quam i 3.
praeteream opus est ut quantitas
nominator C3 = hC + al sit quantitas affirmativa, quod nullo
fit negotio, ponendo l. esse affirmativam, c. esse negativam
sine ulla nova ipsius c artitrariae determinatione
Resumatur calculus in numeris.  y3 X - 1 Y + 1 r0.  pone yp Z + C. fiet
12
+3c27
+ c3
-12 -1c 71.
+ 12.
+ m
24 13c 3 13c7 203
anc
me fimc. an
+m 1. 4nc.. +3c
et ponendo Z e
C94
=12 m. -1cm
+um
ut iam tollatur terminus penultimus aequationisqe
 fiet: Aquatio Recipira:
fiat:  m,, c3 - 12c + 12
et fiet:
2
4 +3C
vel
+encM.
12
22
+5c28- nc + 12.
=9c+ 12
-3C +12
-38 + 12
10
=3C+ 12
X +e ne +n B
+cneu. ZeC, O nct2
nc3.12C+12.
+(2, c - nC + 12,
23C4 12
y3 23C
3e2+n
+I
-3C2+12
X (- 1) 3C21  (+ 30, -3c412 Cd
+3C, C=- nC+12
3c+12
quae per compendium cum certesio ita enuntiata
a
C  pCd + qed eY B dabit Tubicam tans
F2PV + p v - q70 cujus aequationis
Terminus focandus, constat quod provenientis aequationus
cubicae si rursus tollatur
tar cerminus tertius comporiatur ex
tertio hujus demto triente quadrati a secundo hujus, id est crit terminus tertius aequationi
provendentis: P+ 4r-2
ne itaque ut  tertius terminus provenientis sit affirmation
opus est non tantum Ar esse quantitatem attirmativam sed et majorem quam pr.
sive 213, Vr p P. sive 2 13, f-3c +1
C3- 12C + 12
1t4 sive . 213, 1-3C2 + 1
ponatur pis faciemus autem compendii eam
c
eteeti
o
p.
= (2) 3C - 1, +3c, 8. 82 et 12
BcI, _ (() c3 - 12C + 12
13- 12C+12
quod fieri redo innostra potestate est,
S+(4 e quadrato, faciendo : er.   4 fd + (4) et erit Cn +
=d2
 imo simpliciter si ponamus CF ut habebimus interrum
posito erit mon  Est A h. fct 1 im Z H33, 8   er 203 f. 3e v e st d3 sis
a 3.f, 6p   ais s
u
7 A 91 2,  ) 2t -+ mutule
1
3
+. h
C - h.c + al, 17
aquationg recipisae
num esse affirmativum
com
intr
+3C
Polen
atari subrrae cartesii ex
X + C - 12C 7 12