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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 5
# Folio 13v, page id 00068002:0026
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At pro numeris trianguli Harmonici summandis contrariae
insistendum est viae. Nam Summae columnae sequentis continentur
in antecedente; et praeterea summantur ne
columna
ente
in
aut termini omnes feriei, non ab initio sumti, sed sumti a
finc id est infiniti. Sillud tamen
interest accedi quod series columna continet summas sequentis non
simpliciter sed constanti numero multiplicatas. Nempe columna
reciprocorum naturalium continet summas reciprocorum triangularium
multiplicatas per 2, et columna reci horum continet rursus
continet summas reciprocorum pystamidalium sed multipliatas per 3,
et denique columna horum rursus Et columna reciprocorum triangula
rium continet summas reciprocorum pyramidalium Multi
Tolumna reciprocorum atralicontinet reciprecorum
reciproco naturalibus
friangularibus
pyramidalibus
summas
divisas
multiplicatas
triangularibus
pyramidalibus
bitriangularibus
ex
Itaque si velis summam columnae secundae in serie Haraom Triangul
in triangulo harmonico deflescentem in infinitum seu usque ad o
ab inde ab aliquo termino
praecedentis eumque
sume terminum respondentem columna
divide pulva si divide multi plica
si sit in columna
mulisilica per
n
4 et
etc
et habebis quaesitum. sic si velis in unum addere columnam
secta summare columnam secundam ab 1 infinitum; sume erit
terminus primus l, cui in columna praecedente respondet1, qui multi,
plicatus per 2 dat 2 summam clumnam quaesitam itaque
2+  + et in infinitum
1 ++ 20 +  etc 
e3 a + etae
+ 1 L + L +L etc in infini
+8F
+ etc
=+  + 3 +  + = etc in infinitum L
24  + 1 4  + ete Cerlt letl = i.
Z+ = +  += et
L + ~ + L etc
t  + 1  t etc
10 +2 +5 etC
+ + 4+ etc
70+ 20 +35 etc
L +  + L + = etc
+
35
is + 5F = YC
 is lieoit
 2.
=
in finito
ppondentem
 primo termit
summandorum