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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 5
# Folio 9r, page id 00068002:0017
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fol. 8
99
4950
Eademque opera apparet  quomodo definitus numerus terminorum
columnae trianguli Harmonici summetur (excepta semper, prima)
summetur. Exempli quaeruntur summ nameri cet quaeritur summa ce
causa
quo fractionum ab L usque ad  se seu Reciprocorum triangularium
que 495o, sumatur propim in
respectioc ponem (vel pro respective ponendo 21, 22, 23, 24, 25 et ab 1 utque ad ab  usque ad F
1
columna ante cedente reciprocorum naturalium, terminus p respondens  (hoc loco i) respondens
nempe I
smatur terminus proxime seque
i
in eadem columna se antecedente
u phespondentem ultimo summandorum hoc loco 4950
siplicata per
101
summa omnium fractionum L +  + = + 1 + L + 1 et c. usque ad 1
+ 10 15
qui est o et 10
21
4950
inclusive. Haec in Gallia olim reserta per occasionem
adjicere non inueile visum est humetsi ab eo tempore per vulgata puter
u cepimMana
Porro ut appareat quomodo formentur po
Sed ad potentias potestates solys nomiorum formandas redeamus,
quibus se quae scilicet indigent binomis. Numeris combinatoriis, ut mox
patebit. consideram constant autem semper ex formis ejus dem gradus,
quibus numeri ex combinatoriis nultiplicando for mati praefiguntur
grud Formam voco terminum com f conf summam membrarum in
quibus ati summam omnium inembrorum in quibus literae ex certo
literarum ne aliquot literis similiter formatorum. Ut a+b
Ita a + b +C, et c est forma primi gradus; at formae secundi gradus
sunt a +b+C, ete et ab + ac +ac et c. et formae tertii gradus
2t
sunt a + b + etc et aet a b + ab + ac +ac  + bc + bc, etc
et formae et abc + abd + bcd etc. Compendit autem, ut jam monui
sic designo ut a mihi significit a vel atb, vel a +b +c, ex vel ete
vel etc.
ab inihi significet  vel ab vel ab + ac +bc, vel ab +ac + ad + bc +bd + cd vel ete
vel etc.
et a erit a vel a + b, vel a rb2C, etc et ab erit ab + ab ab
vel ab + ab + ac + ac + bc + bc, vel a b + ab + a c + aC + ad + ad
+bc + bc + bd + bd + Cd + cd,  vel etc et abc = abc velabe + abd + bid, vel etc
Itaque a(L a itaque ces a + b + c etc = a
+200, id est - 1. itaque in praesenti exemplo vaoros sic stabunt. et  quadrat t a + b +c etc = a + 2ab
= a +3ab +6 abc
cubus
Biquadratum
= a + 4db +6ab + 12 abc + 24 abc d
Ut jam investigemus numeros coefficientes formis praescriptos
considerandum est quot modis ferma prodeat si  quod delut in schemate
patet
dic apparet in cul velut in cubo
nempe tot quol sunt transpoa + b +c 4
a +b+c
sitiones ejus, sic ab
a
vel aab in cubo ab
a + puodit ter nempe
assV
ava
bsaa
 (4950
2tXL