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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 4
# Folio 11v, page id 00068217:0022
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Unde conjungendo aequationes 43. 46. ete tolli poterit
litera, et per crucem multiplicando habebimus
HeKEt
(47)
R. 2hkp + h4q- teY,  Kp hp ttipe -k9 aequ. K  ch Xpatike. lis p hpia tips tes
Si jam per  aequ. 31. 32. 33. explicare vellemus literas h. R. p. utique
satis protixus oriretur calculus, satio ergo est compendis causa relictis e. f. G.
18)
tollere 4. r. s. fiet enim 4 aequ.
eth.
Quos valores substituendo in aequi 47. fiet.
(51)
f ragu f AK sau rp
R. Enaip +HMBHHtis (tiA. 2K. p. h p t tepe tig aequ. K ihiteip HteKC. Hf  Dk p. hp + ti pe (ti p  h 9(h p)
SX+S
quae est aequatio identica, quae interim calculum probum esse confirmat
(52)
(3)- Kp +he  hepotts yo ∞
iet ergo X aequ. k p + hp ph petKG. vel Xaqu.
per aequ. 43. X -atkp +tete hf peraque R3 2h Kp +tKqt Y  aqu.)
6.
Ex quibus posteriorem sraefero, quia q. r. s. explicatione non indigent ut e. f. 9.
ed ut tolli possit X una adhuc aequatio quaerenda est, qua reperiatur ipsa
X ad nullam potentiam assurgens. Quod ita fiet, aequatio 43. multiplicetur
perhix. fier: hDX (hO X aqu. 0 et aqu. 34 multiplicetur per D. fiet.
66)
hDX +KDX + pD. aqu. 0. Ergo + HDX + pD aequ. 0. et X aeqo 
+ho.
hO+KD
et per 13, ernt Xagu B. Epo +pY +h O + KDO agu. 0. d est explicando -
D et C fiet:
A V
HI
VuI 18
Qua p rttipq  p7 ( ati K Peak N eq (Kpr oteMeq. (diipra sixr
2  +tK K t p -ite pus + 2H  ps, atp - t p 9s B, v
vi
 IH   q
phi K pgt ti X pB (+HK rteK B + h. KP (. h KpV,  (60)
e
ChiKG
pe
VI 1X
q(HK pq hkpqV
WKas C 2hEK D + heK 45 = h. X 7s
+siht -rs tK
+ p4
ca su
(55)
(7)
2295t3p
+r 1Bp
r K3p
29 h p3
aequ. 0
seu destructis destruendis, omnibusque divisis per h, fet
fiet ordinando
+ 95kK _- quh Kp
+ q. K2p +3r hkp
+ghrprashkp
+y...
(62)
61)
aequ. 0
Quod et pereple du Quod est generale
duabus aequationibus absoutis seu genem,
libus quarti gradus 1. 24
(63)
(65)
sed in nustro bi si faciamus H aequ o. idest per 31. Y aequ f seu Zaequ  per 21
fiet: ssit = 29sh + qetep C66)
+p =29h3 tis tesi aequ. 0
Idem brevius sic investigabimus: si K aqu. 0. per 62. fier per sB. Oagu testi
(67F- p + ghp sh
O aequ  X aequ.
6a
quap t oti pastiv
et D agu. rti rursus si K aequ. 0. fit X aqu S per aqu. 34. Ergo
11
fiet-  + DS. B aqu0 Unde patet p et h. signis contraris intime
es
esse affecta debere fiet antens p. ahp + st + rh Y p aqu. 0.
vel
quia ambigna solutio est, fiet p - gh p + sh - rh L. ph Eequ. 0 quas duos vatores
seu aequationes ut se 72. 73. velut radices aequationis 56 in se itvicemi ducendo
prodibit aequatio 66 quam subtilitatem qui non animadvertet, nunquam poterit
conciliare aequationem 72 cum aequ. 66. nam si pro aequ. 72. scrilae scribat
p2- ghp + sM aqu. = rh Y- ph. ut utrinque quadret, non prodibit aequatio
66. Sed alia in eo differens ab aequ. 66 quod pror h p reperietur - rh3p.
quod et me attonitum habuit, frustraque errorem in calculo quaesivi donec
rationem perspexi
+he
eX
t
p
t
+