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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 5
# Folio 13r, page id 00068002:0025
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fol. 7
triragulo
Nempe basis in Arithmetico sunt naturales se numeri progressionis Arithmeticae
1,2, 3, et4, 5, 6, etc;  ita basis in Triangulo Harmonico
sunt reciproci naturalium, qui sunt progressionis Harmunicae, ut
nempe , 21 314. =, = etc.  Hi enim sunt reciproce ut
scilicet
Narmonici sunt  versd 2 ad  ut 8 ad et tamavi generatit
parmonicisuas reciproqe numerorum trianguli Arichimetici.m Dico, ut
porr porro, ut Triangulares dant summam naturalium dant triangulares,
ut aritimati
et puramidales summam triangularium dant pyramidales, et
2
t ita porro. Ita contra reciprocesnaturalium seu harmonicos dare
dant summam reciprocorum triangularium, et reciprocostriangularium
datsma date summam reciprocorum pyramidalium,
et ita porro.
12
5
ii 56 hb 25-
e
10
+ 10 20 355
15 35 7012
6
10 
6 21 50 26250
ft
ut constat,
Modu summae autem (ex hibentur modo sequenti pro Numeris quidem
trianguli Arithmetici hoc modo: quaenitur nun summa numerorum
in columna quadam inde ab initio usque ad terminum datun umatur inclusive
numerus columnae proxime sequentis, termino cato respondens,  erit
summa quaesita. Ita omnes naturales ab tad 6 inclusive initio ad 6
sunt 21, omnes triangulares ab initio ad 21 sunt 56, et omnes pyrami-
dales ab 1 ad 56 sunt 126. Et ita porro. P sin summas velis columnae ab aliquo termine
summandorum
us ub aliquo usque ad aliam, sam ter alium velis, tantum a termino
ut u in columna triangularium a 6 ad 21 detrahendus est terminus columnae
sumenda est differentia inter columnum terminum, ultimum columnae sequentis ultimo hadncus
sequentis ultimo respondentem, et terminu kolurae sequentis primum summandorum
antecedenten den 36 a er 20t10t 16+n