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# Title: Leibniz-Handschriften zur Philosophie LH 4, 7B, 2
# Folio 68r, page id 00068646:0135
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TAt 
TH EOR.
1V
Contentum contenti est contentum continentis
seu si id cui aliud inest, inset tertio, id quod ei inest eidem tertio
inerit vel si A est in B et B est in C, etiam A erit in C.
Nam A est in B, (ex hyp.) Ergo A + L ∞ B (per def. 3. et charact 3)
Ergo est aliquod L tale, ut sit A+ L ∞ B (per def. 3. t vel
charact. 3) similiter quia B est in C (ex hyp) erit B+ M ∞ C
in qua assertione pro B ponendo A + L (quae coincidere ostendimus)
fiet A+ L + M ∞ C. Jam pro L+ M ponendo N (per postul. 1)
fiet A + N ∞ C Ergo A est in C (per def. 3) Q. E. Dem.
TH EOR. V.
cui singula insunt etiam ex ipsis constitutum in est
tiam
si M est Si A est in C et B est in C, erit A + B nC (constitutum ex A et Bdes. 4) erit in C
possit fieri
Nam quia A est in C erit aliquod M tale, ut A +M ∞ C (per def. 3)
similiter quia B est in C erit poterit d fieri B+ N ∞ C
quae conjungendo (per coroll. Theorematis 3) fiet A+ M +B+ N ∞ et C
Ergo jam C+ C ∞ C (per AXiom+) Ergo A + M + B + N ∞ C
a
Et proinde A+ (per def. 3.) A+ B  est in C. Q. E. Dem.
THEOR. VI
Constitutum ex contentis inest constituto ex continentibus
Si A est in M et B est in N erit A+ B in M + N.
Nam A est in M (ex hyp.) et M est in M + N (per def. 3.)
Ergo A est in M+ N (per theor. 4) similiter B est in N (ex hyp.)
et N est in M + N (per def. 3) Ergo B est in M + N. (per th. 4)
jam si A est in M + N, et B est in M + N, etiam (per th. 5.)
A +B erit erit A + B in M + N. Q. E. Dem.
THEOR. VII. pa.
siBerit si qu
si quid additur ei cui inest, nil constituitur novi
seu si B est in A erit A +B ∞ A. Nam si B est in A potest fieri
+C∞ BFC∞A (def. 3.). Ergo A+B ∞ A+ Ergo (per th. 3) B+B+C
B+ C + B ∞ A+ B ergo A+B ∞ B+ C+ B, ∞ B + C (per axiomius
proris praecedentis
t per dicta hic) Q. E. Dem. Par 2,
 conversam
Si quid addendo alteri nit constituitur novi, ipsum alteri inest
EORemalI
 A  conversum T)
Si A+ B ∞ A tunc B erit in A, nam B est in A + B (def. 3.) et A+ B∞A
Cex hyp) Ergo B est in A.  q. E. dem.
cui nomen
imponemus 
intermscendus
familians simo
cui juncendae
 demonstra
hoves
expressione
propositionum
smitiares
illustrande
exemplis
+ (per insertum
inter th. 2 et)