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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 118r, page id 00068194:0235
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= b +c+ d.
obea
+C
+
b+c + d
bc + bd + cd.=
+d
d
c. + bd. + cd
bet vatell. bea
bcd
bc. + bd. + c0
id
bvera
 + c d
Hypotn.
bac = - ca d
m, est excess.
bc. + bd. + cd) = = 2r bcd. + b + c. + d)
b + c + d
b + c + d
6 + c + 3)
Demonserat. Synth.
bc. + bd + cd
b + c + d = = 81 aaa F 243 maa
27 bcd. + b + c. + d
21omma 1 sammm
b + c + d = = B1aaa + 243 maa
b+c+ d FZi6mma + 54 mmm)
bc. + bd + cd)= - 27 bcd F b + c + d
+ C + d
Consectar. 1.
6 + c L d
b + c + d
+ C +d
b F C. + d
Consectav. 2.
Consectar. 3.
bc. + bd + cd = - - 3bcd
hMh = D
Demonstrat. Synth.
 m = n -- t B. (∞)
X3mN
2mmn = 3mnn
. 2mnm = 2nnn
Lmmm. FEmmn = 3mnn 1 Znnn
oladathomaa tgomma remmn
 81 naa F gomna +24mmn
+Ionna + 9 mnn.- commun. addend.
 dinaa 1 gomna + 27 mmn
+ 18nna 1 omnn
FBlaaa. F 16= maa 1 gomma + 1Emmm
+ Bi naa tgomnargmmn
+ ronna tIEmnn
+ Znnn
+ BI naat gomna t2 minn
+ ionna 1 omun
quod el.- Blaaa F 162 maa F gomma F 16mmon
bc + bd. + cd) bc + bd + cd) = bcd + b. + C. + d
d Lc + d
+c + d
b+c + d
388
L + Sed .. BIaaa + 16Z maa. + gomma + 18mmm
erat
demonstrandu.
bc + bd L cds = - bcd + b. + c. +d
.+ C F d
2
t 8inaa + gomna i zammn
+ 18 nna + 12mnn-- 27 bcd 1
+ 2nnn
bc + bd + cd) 2, bcd + b + c + d
b + c + a
+c + a
quod
evat demonserandum
Propos. 3.
h 3f Bhhh
82
B = 3f2
Propos. 1
a, a 1 m, a 1 2 m
am a+mtn
Hypoth.
a
bac Lcad
BIaaa L 162 maa 1 gomma + 1ommm.
+ c -+ d
am, a  m 1n
Hypoth.
 cn d
M. de, sic excess.
m Ln
bc + bd. L cd
=35
bc + bd+ cd
+ b.
+c1
27bca F6 tcF a
6+c d
t
m, n, sut extessi
m = n
 bc. + bd + cd)
+c
+c
+ d
Bemontis
a; = a + =, M.
i 2a, a -+ 15 LM...
27bcd
a
Hujus theorematis demonstratio, eadem est cum pra
cedenti, nisi quod magnitadines, quae ibi maioves
scent, hec contra minores esse debeant.
d