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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 175r, page id 00068196:0347
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BAB videtur hic
una mechoius prohis Demonstratio et amplifieatio
interpolassiogabus e
emonstratoru  Arithmeticae infinitorum
 martii 1656 scheda 2.
pe -1
e-1 a Wwallisianae
repiehusa  CA aa-X, = ex a A. a- X + e. R. A- X , du
Sed faciendo ax proportionales ipsis X seu X Geometricae progressionis,
qeti c-1
fiet: W. A
a- X
e Cd
+ C. X. a - X
Ergo generaliter
si potentia si gradus si detur factum ex dignitate abscissae
t refidai dignitate residui: et factum ex dignitate abscissae
unitate aucta, e refidui unitute minum quae sit uno gradu
altior, et dignitate residui, quae sit unilata in serio
C
vel contra
tradu inferior ex se invicem pendent.
C
uno
Et achus
generalius quia dx possunt fieri proportionales ipsi
W
qetoao
seu . pX, fiet d X. a -X = Co  X. a - X +
et cum β3 sit constans, utique patet generaliter
s
et a X mulcipticata per aea
h-  n+I
as
x
a
s
ha
0
e- 1+ V
(3 X
pendere,
a
ex A. a-x
a
u 10-1
X. a - X
ex se invicem
multipticata per b C
et per
a sei sed nihil hinc novi, et omnia eodem
v
o
cedeunt, et licet facias dx= constanti tamen semper
idem prodibit thecrema
A
SX. E X Si- X A redantur ad 1 - x. Si - X seu ad L - si -x
eX
Sx
ex
Xe
pendet ex, 1X. 1 -X Similiter Et porro reducitu
quia bantur
1- 2X + X, L1 -X,: _ et X 1X. Ergo Mecim etum
Ergo quia dantur: eet S1- X et +X. YI X dabitur et Y.
1
s
L ad
+
IXA
d1-X
Xe
Et ita porro, et hinc tandem generalis habetur demonstratio FEeoremat
XVX
Wallisianorum. adeoque progrussus Tabula condi poterit generatis
si id tres sint et fiet
e co
e
d
x d +mX n nApX. qu
d abc = ab dc + ac db + bc da D)
l+mX. HA PX. BCK V. rXC-
10-1
+mx. G+X. ppCd. EX
ea
v
+
+ n+ pX. g+rX. e inc