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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 99r, page id 00067993:0197
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A serie A. auferatur series  Singuli termini a singulis respondentibus, restabit
series A- B ut si ab 1. auferas Z restabit;. si ab 1. auferas L restabit;.
si ab f anferas; restabit L et ita idque semper futurum esot, ut numeri
ipsius A ordine redeant, generaliter demonstrari potest, adhibita sormula Analytica ad
modum corollarii prop.. (quodut quod in re facili ut verbis parcam, omitto.
Ergo Ergo
Sed
2
  erc. erit A-B.
13 4
 stc est etiam A - 1
Habetur ergo avalitas inter A. _B et A- 1. sive ablato utrinque A, inter AB et 1.
Adeoque et inter it B et 2.
Ergo 2B side tx
sit Tbula
Frncio
Triangulum
Htarmonicum
seucujus numeri
sunt Reciproci
Eto
Propositio...
valet
3 sa q d 120 etc. 
Numeri autem 8. 24. 48. 80 120 sunt ladrati imparium unitate minuti
summa seriet infinita 
1
Et summa seriei iginita sasis 4 i 4803 80 99 teo etc. Bst 3
Numeri autem 3. 8. 15. 34 etc. sunt quadrati Numerorum dam parium, quam
imparium, unitate minuti
Pars prior ita demonstrabitar ad modum sraecedentis, iis dem prope verbis:
se series
ser
80
etc sit A
etc sit A
summa seriei infinitae,  +  +  (10 t 75 + 2, = 20 Eest 2.
3
Numeri autem 1. 3. 6. 10., 15. 21. 28 ∞ et. sunt Triangatares Trgonales,
series
etc  sit A
etc
sit 2B.
3
4
 io
s
erit
etr
io ete valebit 2
Quod erat demonstrandum.
Sc hotium Prop. l.
t
ete enlm
ete
e
lu
un
75
s
.
0
concinuunda longius labata.
er a 3
eruus ,
 
in ad.
5
 L
 E tc. Summae serierum in infinitim productarum
ex aliqua
Imo et in sinitis. Sit sertes quae cunque sini termini quotcunque continui alituius ex serie 
series 5.
ut Trigonatium syramidalium, etc. Reciprocorum sumti ut, e  10  quorum quaritur
summa. Sumatur sumantur ex serie praecedenti termini duo, unus L aeque altus ac : primus assumtus hajus
alter  proxime inferior ipso  no vissime assumto. Horum duorum numerorum  per 2. (mmerum,
seriei infinitae summam exprimentem,) differentia LZ multiplicatorum differentia,  
aequatur summae assumtorum, 3 8 10 ic Et ita ceeri centum si
30 +30 H 30
50  1