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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 14
# Folio 1r, page id 00068263:0001
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major terriario. Demonstro: yZy. ternarius, ut ostendi D C numero jactuu
Onnis quadratus est aut ternarius aut unitate
Eergo Si Y ∞ est ternarius erit N21 Trnarius. Ergo
et ternarium excedit unitate. Sin Y ternarius per se patea
Omnis quodrato quadrato aut quinarius aut unitate
mujor quinario. Pribatur eodem modo, quia VY
quinarius. Eodem modo infnita alique condiue fereienus exempla–
Omnis quadratus impar unitate maja seralio aut ternan
omnis guaorato quadratus terminatur per 1. 5. aut 6.
ans unitte major separ
et quivarius aut major quin ario unitile
Y+ denaru.
Ern est a3 4 37+b 2lidur
Ergo omnis cubus Jam
est cubus qu quilibet Ergo potu
latu est Y   major unitate
nitelligi potest y41. Ergo cubus quolibet
latere miantus est senarius. Hoc certisse
yrammide da nmbre  y F 39 + 2y
128 -2p26
(12 - 21, 510
2 -2 ternarius
quinarius 2400d 12
seplenarius 92 13
exemplum elegans inductionis deceptricis
Ratio exceationis, quod tunc accidde ipsum
512 seu 63 dividi posse per .
Ergo 23- non potest dividi per 9
 Ap
exoientis polestatum et pur. Et omnisquin unus par
differentia surde solici et lateris est denarius.
156, ep1 12
1(4) 1+ 3a
tinc aliud thcorema elegans:
ultimus character suidesolidi aequatur
sem per ultimo characteri radicis.At
quia disferenta rads surdetolidi pt
rudicis terminatur per O. Et vero si
exacte in spicia B est quidam periodus i
inmeris prygrestiois Geometricae, qui semper
nonie redit. Hinc poterimus circa alias quoqu
offerentias etemu ratiocinari
a periobicem suthracti relti quendenarius
Dispositio ruanguli Arithmetici pro
combinationibus: Par exempe
2A. dans 4 B. se combine sC fois
c’est adire il y a 6 con3naisons
dans  4.
Aia Theoremata haberi poterunt si datus
numems ponatur y - 1. proxime superivo Y
y + 7. Trianglo du prochainemat plas pand: mens dan le
postanids du prodaiemat plus quand=
Triangulo - tangundet yt 469 ax 119 46y)
ggnnesiu
Ubi mirum solum Novenarium dissentire
l1. 6. 15 20 15. b. 1
Hunsqus Nibus, Madres yt  Ex. 1)
niam Nu
estpri
y +35 +3y +,
+3 +6 +3
X2 + 284 1
+ 1Y + 1
(43y+2
y3+ 6Y+ 11y +6
esse y +h 11Y. denarium. Ergod Y HN 13Y = , senarius. Ergo y y senarius hrne
+ Y. nnte y ty bindrtus ea Ergo y +2y - y. binarius Ergo y - y binatius.
y. X 3⊓2 = 2y H 6navio. Ergo et ternario. Ergo Y +3y+ 3y - y ternarius. Ergo V- y ternarius
vopium ytn vinarius e y y ternarius
his in se duoris etim hinc pates esse yy, senarium
VEr ternatis, 1o N +3V. est par V + As - y par. Ergo y3- y par
Multa hcuc aeitam ercoremata poterunt londi facile
Ergo Y + 19V. est ouinarius. Ergo Y- y. Erit quinarius
3S e
habemus ergo teorema perelegans. Potestatem quinti gradus
datore minutam esse ouinarium. Unde crediderim si continneti
hanc progressionem prodituram Y - y. (id est 0) unitarius
N- prindris
3. quamus V y seplerconus
Jannar. 1676.
tessetis. Proposuit
9 180
ot 63
non tamen 23-2
Pursus ut D paltti rursus omnis cubus,
re et auunde
nitantus est par–
e minutus est
termarius, ut 1)  demonstravi 
be dconniscubus latere minutus est senarius Eddem modo
demonstrabituru omnem sundesolitum latere in inulum esse
omns enic
Terminari
p est quaus rit hemonmaoi. At omnis dipterenitis
est denarts. Eis e
tatis differentius
ex meis demonstrari potest; omnis cnbus latere
Est autem haec fonnula integur sempt, hinc patet
+ 4V 6. y XAy + 11
+. vpl 18 e + 18∞ 40
1) +224 + 11
32 102410
5 10 10