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# Title: Leibniz-Handschriften zur Mathematik LH 35, 8, 27
# Folio 1v, page id 00068121:0002
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Origo inventionis.
Trianguld Harmonici
Anno 1672 Hugenius
mihi proposuerat sumnam
Cinoen
Fractionum triangularium
quam particulari sed valde
memorabili solutione i
deprehenderat. Cum ergo in
ea essem meditatione forte notavi
esa si exponatur
AH+ 
B1
1
1 3 6, 10
15
Et si dimiclii termini B addantur
terminiis ex A per lineas quas
vides punctis, reddi terminos
ex A trminis ex B superscri-
plos. Quod in mentem primum
venerit quod vidciem pri–
nempe ne
mna terminum iptius B, dimi-
diatum, additum juncto per
lineam ex A, nempe  facere
1.  seu primum ex A.
item quod nominatores ex pro-
ximi ex A in se ducti, faciunt
semper segtim numeratorum
ex B. dedios duplos, ut
1,2  2. 2316. 3,M
3
A Quod autem in caeteris
suriebus sumenda sint Z C:
2 D, erc. Ita facile di-
vinavi, quia  primi ter.
mini ex C seue ntis
 et 3 primi trmini ex D,
id est semper unitatis
termino
addita secundo seriei
praecedentis, faciunt sem per
unitatem. Unde patet
quomodo simplicium auxilio
saepe composita divinemus
Ex hocm autem Theorenate
inductione deprehenso, summas
elegunti satis Ratiocinio
inveni e it ex dhis  exstrxi um
a
1
fhinetico mina consensus. de