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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 13
# Folio 16r, page id 00067974:0031
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probanda est hoc therrema culculi
situs. Ex his tribus propositionibus ABC est unic
AL MN est unic et BCLM est unic. admissis
duabus, tertia admmittenda est. seu ex
duabus prioribus sequitur tertici, et ex alt una
priorum B tertia vicissim sequitur altera
priorum
ABC unic idem est quod Si ABC
~ (A) BC, erit A ∞ (A)
ABC ~  (A) BC nes idem est
quod AB ~ (AB et AC~ AC (A) C
Itaque A. B. C unic. in haec resolvitur.
Si A. B ~ (A). B et A. C ~ (A). C erit
(A) ∞ A
vel
Ex quibus sequitur etiam si B. A~ (B). A
et B. C ~ (B) C erit B ∞ (B)
vel Si C∞ A C. A ~ (C). A et
C. B ~ (C). B erit C ∞ (C)
Itaque ex uno horum trium sequuntur
reliqua
si A sit suae relationis unicum
ad B, et B sit sua relationis
unieum ad C, erit A suae relationis
unicum ad c videamus an
hoc demonstrari possit. Si A sit suae
relationis unicum ad B erit et sit A∞si
Aed A B ~ (A). C
si A sit suae relationis unicum ad B
enit verum erit si A. B ~ (A). B fore A∞ B
si A sit suae relationis unicum ad B
erit B suae relationis unicum ad A
Itaque harum duarum consequen-
Fiarum una ex alta sequitur
(fore
Si posito A. B ~ (A). B sequitur A∞(A)
etiam nositio B. A ~ (B) A sequitur fore B ∞ (B)
Si posito A sit unic ad B et B sit Ex 4 et 6 se quod (B) ∞ ((B))
unie ad C, habebimus propositiones sequentes
(1) posito A. B = (A) B sequitur  A ∞ (A)
posito B. A ~ (B). A sequilut B ∞ (B)
posito B. C ~ (B) C. sequitur B ∞ CB)
4() posito C. B ~ (C) B saportu d. C ∞ (C)
(5) Ex his sequitur (B) ∞ (B)
ostendenda esset alterutra ex his propositionibus
et
Bosito A. C ∞ (AD. Z. erit A ∞ (A)
potto C. AC IICD) A erit C 00 (C)
3
5
Ex 1, 5, 9 sequitur (10) A. B (~ A. BB). C
seu ex A unic ad P et ex B mic ad C