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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 283v, page id 00068201:0566
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nisi ponamus Pp0. adeoque tantum opus est, ut habeatur aequatio
quadrato qua dratica termino secundo carens, cujus e tertius terminus
sit affirmativus.
sit ergo aequatio
43 + 3C Z2 + 35
+m 1.
V3 + - h V + ael 50
4 c3
- h2. p-hc
+3Cm .
+ atl
+m
H C
+
hc
+ 3Cm.
=tom.
e C3 m
= h c m
+arl m
Si ponac 3C + n. pjo. sublato hoc modo secundo
termino non fiet tertius affirmativus, tollatur
ergo penultimus, erit mp c-hc rael et
- 3c2+ ht
tiet terminus ultimus p C3 - kC + 2 l, ()
L3C+ h
ot tertius erit; 3c - h + c3- hE + a  3C
-3C + h2
sive  tic  h  tic 2a tc
-3c+ h2
quae quantitas videndum est an reddi possit
affirmativa, sit. si sit affirmatuva
quod si volumue ut haec qua Ac primum
si sit 3c major quam h. tunc debet
9c4 - 3h2C + L4, L3C - 3a lc esse
quantitas affirmatira quod esset in dubicum
si -3c4 =3ac esse t quantitas affirmativa
id est si lesset major quam c3. id est
si l’ W
Sa t9r
id est si   quad ratum ab l. mujus triente cubi ab h
Dividatur tertius per ultimum, fiet;
-g1 43ke - h+, + GC 13 a lc
C ahc + El, F2).
Qui erit seunu terminus aequationis recipidiae
certius
secundo termino carensis. Cuius nominator
jam tum est affirmativus requiritur ego
et ut numerator sit affirmatious sive
et _C2 + halc sit major quadrato a 
differentia inter 3c et h2. quod semper
in potest ate est, quia ipsa c. arbitraria est
cum vel solu 3C major reddi possit quam
hujus differentiae quadratum et quantitas 3a2IC
semper sit affirmativa, modo demus ipsis idem
esse signum.
ibere
sit y p ZtC pec
sive Eppih +lig
sive cpi n 
Unum tantum cavendum est, ne radix
quae postea extrahetur, sit ipsa
M, id enim nihil conduceret ad
resolutionem aequationis (ubi cae
propositae. Quod videtur impediri
poste quia  ipsius m. Signum 10000
in potestate est
onda
100
9964
29984
1s