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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 25v, page id 00067993:0050
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in infinitum decrescentium
summae. 6 +
Demonstrabitur ad modum propositionis praecedentis, nam
 quemadmodum ostendimus  4 3 + L + +  etc. esse 2.
ita demonstrabitur  + 1 + 24 = dsc esse 2.
Nans)   io fH, d. sit A
et
X+ (+ 1) + Rc. siu B ses pmme
semper scilicet series praxime praece
Nam
Nam series proxime praecedens  + L + L + L + +, 8c. sit A
et series proposita s
Ergo
4 + 1 + L + 2 + + &c sit 2B
2+ 2+ 2 + ∞+ 2 dc ent B
Auferantur a singulis quantitatibus seriei A, singulae respondentes seriei B;  residui
1
30 60 10
erunt termini sequentes ejusdem seriei A, ut 2- 2 dat L, et  - = dat , et  -2 dat-
et ita porro quod semper futurum generaliter ostendere non difficile est. Er
Et Ergo. + + L + L + , + + etc. erit A - B
At
3 + L + L + + + 2 dsc est etiam A- 1
go aequabuntur A- B et A- 1. sive B et 1. et 3 B id est series L + L + L + L, + L etc. erit 3
idem in caeteris fieri et generaliter eventurum demonstrari non difficulter potest
Habetur ergo aequalitas inters A- B, et A- 1, sivae inter B et 1.
inter 2. B et Z; Ergo 2B sive  +  +  + 4 e dc. valebit 2.
SR0 P051710 X L
Sit Triangulum Harmonicum, sive cujus numeri sint reciproci numerorum Trianguli
Arithmetici a Pascalio editi
Triangusum
Harmontum
sive
TRIANGULUM ARITNMETICUM
UtUM HARMONICUM
Ee
E
0
Trianus
Anct
i
AA
runt de
serierum trianguli- Harmonie
riangulum
Harmonicu
Triangulm
Hagmonia