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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 26
# Folio 10r, page id 00068239:0019
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6
12
24 2
4872 9
In sola dispositione p 12
2
15
2 17
19
16 14 6
25
30
36 55 5
49 91 105 77
64 10 196 182 112 4
Si 204 336 278 294 150
10 385540 214672 45c
2 21
1
34
1.2. 3 3.4.5
3.45 V 1. 2
1.2. 3 1.. 6
4. 5. 1.7
5.6.7
Hinc reciproci figurntirum
seu fractiones eorum
summari possunt,
nam generalite
ex. c. si reciprocimu
triangulo triangum
aliquonsque sumtorum?.
summa motisti pers
aequatut differentiae
duorum pyramidalium E.
extremorum; seu
disse rentiae suocum
extremorum aliquo
Cmmodo multiplscalorum
ut focle delem
potest
ut si sit ex Tabula imparium replicatorum
series H cujus summa est +E 6. ea multi
plicata per 16, nempe quartam polentiam
ipsius 2, dabit K. serdem post hanc
quartam, quae facit 96. Unde putet
has summas, esse terminos progiessionis
Geometricae duptae multiplicatos per ternarium
Et ita semper. sumna habem
potest quilies prima totumna sonisiorsi
est ex quantitatit, aequalibus; vartons
in aliis non procedit, quia q primus
terminus prioris serici, fit etiam primus
terminus senei posterious
Haecnethodus utilis est noque solum ad
ea
summas ordinum seutrausversatium,
sed et ad summas extumnarium seu
perpenidicalarium linearum in veniendas
quod si series non possit revocari
eua nesconte
e differentras aequales tandem tamen revocabitur
ad trancendentes valdes patum a se differentes
sive valde parras; et hac supponendo pro veris, potest
quaeri summa.
In Harmonica progressione et ejus
differentus illud memorabile, quod ordines
1. 2. 8
coincidunt columnis. Nam 1. L 1. 2. 3. 1. 15,9
coincrdunt cum:
Hinc utalit Quia summari possunt reliqui
ordines poteit reciprocorum triangularium
poterit methodus haec
pyramidatium
erc:
ad summandum vidinem primum ipsorum Har
pro
tionis
s
monicorum, saltem per appropingrationem
adhiberi, si si scilicet differentiae rout
muentur donec fiant salis parrae, ut
negligi possint. bamque idem fieri possit
constanti ratione accuratius semper atque
acturatius haberi poterit progressio appro-
piuquationum pro progressione Harmonica
Moo (73 16 1c
edem et in aliis
Nota obiter: 2 + 4 11 +
E. + 49  36H 5
4.9
9. i6t 9us H 194 H 18
10
1
28
16.25 16. 25 1400 40
2536t 25. 36I 900r170
5(36. 49 16 ag 1 6 H 136
49. 64 49. 5451361 196
62
75
81
Naturalium
Reciproci
2. 9
.10
2.9
9. 16
5 12
1. 6. 18. 2
n 10 13
1.6, 18, 20. 35. 67 8 144 mint poressio 28 32
16
5. 12. 2. 15 28 35
94
47
29(11
7 10 13 B 7 1
64
2bosst
8
3136
19