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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 141r, page id 00068195:0281
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si A+ B+ C p abC. Ergo si A et B et C sint aequales
sitque tunc a + B + C p _BC etiam erunt in casus
inaequalitatis, sit enim a maxima sequens, b, tertra c, et
fal l +m +n=a m+ n = b et n = C adeoque fier
13 + 3l mp + 6bun + m +  + 3 mn +  n siplum + nn 
seu nam omissis  jam allimus limes quo in casu aequalitatis
est non minor a +b+C3 ipso p abc, est cum p est 3
fil ergo l’+m +3lm +6 lun + n +b mod p. (3 lmo) Aeminoma)
Ergo
Ergo patet in 2un si casus altimitiuntis, quo in casu
aequalitatis non nin est a nec e abc, eoessi
es transferatur ad casum inaequalitatis, fore
_ a ppabe. Ergo generaliter est ultimius limt
shectem aticqus neque dici posse generaliter diar
casum, quo theorema, quod enunciet a p B abc
posito p en quam 3 nam in casu aequalitatis
reperietur falsum. Et haec methodus videtur
ootinere proalus omnibus.
Nempe quaeritu
de quae quaeritur ultimus limes theorematicus, hocu est
osotur og est q
ritur splctit omnium possibilium maxima itet
e non possit asseri, quibuscunque existentibus a, b, c noapossit fieri
Efiliud treorema,  a p m+n abc. sumatur si jam demon-
frari potest posites a, b, c aequalibus, et existente tunc e p mabe
detiam sequi ut in casu noqualialis sit a+ b34Cp mabe  et sit
in limes theorematicus in casu aequalitatis, erit et limes
theorematicus in universum.
si A p si A p B certo
eF si A majus B certo prodo tractato a sit enim a +b + C mnabc
bimes maximus, t thectematicus ert et in casu aequalitatis verus
sed hoc falsum est ex hypothesi quia nm casu aequalitatis si
E s assumamus coefficientem majore, quam m non amplius est
verum Est o autem
consequentiam sic probote
p polito a  a p m abc in casu aequalitatis erit in abe
leu
t incasa aequali aoquimatis per demonstrationem positam. Est ergo
 incas aequalit inaequatibnem est maxium coefficiens phectematicus
sed
pui casu aequalitatis. Ergo et absolute quia tun in casu specipli.
FM. coefficiens theorematicus.
c
et locm Ergo adcn
univer
qualdalis
ad
li
in
uo