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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 54v, page id 00068255:0108
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ex hoc jam taem facili pt. pene identico Theorem ate
denul
praeclara et universalis Methodis exurgit notas summarum dyadicas
inveniendi diffributas  colamnas, quandocunque termini addendi sunt
dgadici d+, Hmbent nemne a+b - al, a addatur
obi addatur
o a ei ubisuppano e non s et, nisi totm su 0, bnon ssini   sit
 a +b+ C. Ad columnam primam addatur C o nempe ad d A fiet in colomna prima
ngum n inde nata
inde n Hidem inde na inde naca p) te
fit aabim Cau
nea
leq bd. Et in columur secunda
C(-a+b) + =, a -b+c et in cot 2da inde nata
et si smbae tunc b esse 0. db
sit o dam esse  A dannus jam C et quaeramus a+ b+c, ponendo
si una ex notis sit O ea ee tunc d esse 0, si dua ex notis sint b
tanc b esse o, et tres ex notis sit e tuncc esse 0. i quia
igiter C addi dibet ad apr a + b, ideo addant ad rtolumnam
primami, nempe ab: sunt igitur dus notae dyadicae in unum
daddendae, 5a +b, qua est d psa C in ex quibus et quia C non est o
dusti altera ex nisi d et bs.nt b, hino c non est 0, nisi a et b
et Cb non nisi et a sit o, hinc c non est o, nisi - a +b sit 0, it
seu nisi ambae =a + b) et c sint (4. hinc in addendis simul his
relocum
duabus notis quarum una est -a +b, altera est c, hab
theorena praecedens t sint, 6+ a 1b +q = La +b e_-( a+6) +C
loco ponendo = a +b et loco b ponendo c, et fiet
a +b  Cn
 a+B. I. = (dea +b) dc seu a + b +c a +b s.btt a - b + c
da ut ana
sed colure Habaimus atib A Cm
et a rb +C = =a +b  + a- b+ c. Erho Hit inadn 6
_ a + b+C = a .) a - b + C C= Cb) a = b+ c m
6  a + b
quod verum esse etiam demonstrari ex eo potest quod b. ( - b = b
Ergo b sa -b +c = va + b+c sed opera pretium fuit derivasse
ex theoremate additionis  trinomii additionem ex theoremate additionis
binomii
pergamus ad a + b + c + d,
a +b+C + d = b a -b +c +d
a -bic
a+c
na +b -c + d
seu si bnonsito
noia sit 0
ortine praevalen
erun collocatae
atera a, b
et 1, b1 a
si C pravaliat, ipsi
b et ipsi a, e
praevaleat ipsi a
Paivalentem vaco
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Lat
sed aub non sempamitas eft matua
Ita prodit
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Onis
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cando, et ater
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arbictorer2.
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 b +c-d +R
a +b =ctd - et
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