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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 38v, page id 00068196:0076
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Cum series expressa relative potest obtiner
absolute magno id commodo est. Ee
Relativam voco expressionem, cum terminus
sequens habetur per quosdam praecedentes
Absolutam, cum unusquisque terminus ex dato
solo loco ordinis sui haberi potest. sic
arheb etsi Arithmeticae propr progressionis proprie
abaaec tas relativa est, quod dimimedietas summae extre
morum aequatur modio, seu quod teitius aequatur
terminus aequatur differentiae inter duplum proxime prae-
cedentis et simplum antoriorem sed di eadem
vorum est si locus ordinis x, terminum quomvis esse
bX +C.
In Geometrica exponentes sunt
progressionis Arithmeticae.
In Harmonica
quoque ris juccedit, ut Nam sint termini ab, ce
constat esse 2ac = b. Hinc 2aC = bc = ab seu C= a
V
a+C
it uem quaitus deremus dA
 pari modo d=.
babi) 2a-b
bac
2a -b
ubi,
2ab3a- 2ab2b-ab2a tabb: 2a-sdae
uni modo _C = = = aabb +12a-b, 3a 2
cad
 al
262a = 2bb -ab, , 2a-b 3a- 2b
pro C ponendo valorem fit d
ab
b
 cumergo sint D:
ab
1
C= ab  b25
a. 2b
2d-1b
1a -00
patet Terminos progressionis Htarmonice habere 2C a = a
seu e
es
3
S0
0a +B
4a - 3b
numeratorem constantem et nominatorem
Notabile etiam cum prorsum
et quod libet recta nyulum haberi progsent
progressionis prithmplicae
Xvicimu hateu pro constante
optrorsumzue iri posse