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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 9
# Folio 11r, page id 00068104:0021
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Ostendi semper eo reduci posse
posito dy proquisionis aritimetice
seu adus = 0 ut sit habeatur
relatio inter X, dx, dax dddx
et  habebitur valor ipsius dddx
jam in iogeti considerande sege
Hom. pro infinitis, negliamus legea
Hom. ordinariam, et sunt homro-
genea X, et dicar e 
Et sunt Homogsenea.
Lat (dx X Z
et se 
RA. SKIX, Sspax Xa
 etc
dx, (ax ddx, (saxdax xd
dx, X ddx. Sed hoc considerato
non potest negligi lex homemadina
eiis uud dx hom. Xdx dax
expouens ipsius dx sit e, ipsius dax
sit f fiet += 2C - 1. quod si
jam faciumus exponentes quantitatum
seu 1 se
unde
aX,  dx, ddx, esse progressi
e
onis Atrithmeticae, 
sunt, seu est 1+ f = 2C Quod
si seriei hujus 1, C, f, etC risfe.
rentiam constantem ponamus esse co
fiet C= 1=cd et f = 1 - 2W)
et ita poreo qud si quatimus
et 9 = 1-3c0, se sin retine
amus C; fiet f = 2C =1 et 9= 3C-2
prnum vatpincio dedae debet
X es ex dex addx
20-1
3C- 2
cum ergo semper habeamus valorem
dudx per X, dx, ddx, ideo si ponumu
esserieinem rationatem, fiet
dacux hx: X + ax + bb
+n ddx: dx et. Ubi
notandum si summabilis estaequad
summa tricem ore ab uno latere habi-
turam esse Adx, ab altero tantum
opositum ex Xe et dx, abioqui enim
in Tuure dexho aequationis ad
debnisset etiam reperiri dddx
verte