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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 293v, page id 00068201:0586
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Numeus Terminorum inqualibet forma specimon est artis Combinatori
sed usum praeterea debet
formae refficiende
1. (1.
30) et.
Im (l BI) c.
em (Bm. 131)
Iun (lnir. (m 3 3)
l’nn emin. 1m
Bmin (mn. nn)
C
Imno (ek).... . 0
Imino .......
lano. ......
reece ea ec
Bmno (P mino  no). 0
Uneno
maeximum ad
15
se
1
20 35
multiplicationes formatum in se invicem compendio faciendas.
2E
56
60 165 16E
120 20.
15 35 70
84
10 A. Numliis literarum teu Naturales
54
108
120
252 360
B. Numeri Combinationum seu rangulares
2B. .. . . . . .. dupli B. Nam 1n) dabit 
vuns
nen mu
Numeri Conhuationum seu Pyramidales
3C.---- -tripli C. nam lnn dat l’orn. ln. lnn
2BC.... . . -- Nam varietates, 13nin. fiunt ex varie.
126 210C
60 10... ..-
.90 210.
180
C
latibus lmn. hoc modo. Quolibet hujus
formaeterminus, ut l’nn dat duos seim
nos prioris formae, ut l’n del lmn,
aa 1m
Ad.... - lmno. Io. lmnc. lmno ex imno
3,4D.-- - (1igo (lnno (1nno ex l’mino.) ubi pates terminum PNno bis prodire
-34d
producendae formae ut
(M) no. Ino. mno ex Imno eodem modo et reliquos omnep.
 Ergo ad habendum numetum terminorum formae lmino ex fea nino
debet variatione unius termini in forma lehuno, debent variationes pro
venientes dimidiari.
Bm n0. lmno. Pmno ex l’nno.: Nec metuendum hic, ut si caeteros
formae variandae  (1hano) terminos, ut Impo varies rede at aliquis terminus nn Imo. Imno ectmno. ratio est quia nunquam iterum
redibit 13. Quod sasecus erat in prodiuenda forma l’mno. ubi 1 duobus modis prodire potessat, uno ex forma varianda, altero ex variatione.
Imnop...
l Mnop..
lmnop.
0
3
2
24
120 360... . . . . . ..
.. . 2, 3,1. D.... . .. . . - l4 M 3p20. 14m3nO ex l m n0
Vm2no. 13otno
 BB no
 26 5b 126 22 E........ Numeri Consnationum seu Trangulo. Pytam idales
30. . . . . ... . .  . ..sE.....-
Imnop. Im nop. lmn op. Imn6 p. Imnop ex imnop
60... 560......... 45E......... (Om nop. (Omnop. (1) mnop. Omnopre l’nnop
nnop Iop. (m nop. L(n) noB. (m nOP
Unde patet. Nunerum formae emnop esse 45E. Nam si nulli repeterentur etermini variatione producti foret numerus 45E. idem aptera terminus
non nisi sene l vedit, quod jamtum praescire possumus, quia 4, 5, seu 26 non potest dividi per 3,  sed per 2. Nam so  non posse manifestum est
Nam quater aut quinquies prodire non posse, manifestum est.
20
120.. . . . . . . . .. 4,5E.. . . . . .. lm nop. Bnnop. Bm.no p. Pmnop ex l’mnop
180
-
3,4, 5E
CNam numerus terminorum hujus formae, fit ex 4, 5, E numero terminorum praecedentis formae, multiplicando eum per 3. Cujus rei ratio est, quod
omisso (3, quia per variationem non producitur, perinde est ac si ex mnop. per voriationem produceremus m ox. sive si ex lmno prodneremus
d
vaciando cujus numerus erat 4D, produceremus em no cujus numerus est 3= D. quod fit numerum formae variandae multiplicando per 3
60 360... . . . . . . .
120 720..
... 3, 4, 5E.
21 4,5 C.....
28 84 210 F....... Nameri Conbnationum seu Sestarido pystamidales
6 42. 168.504 1360 bF
15 185. 240... .
30.210....
 280
e
120 840
60420
-
SB. F . . . . . .. brevius, quod sex rermu combinationes 15
5,6,F
15,b F
d
456F
BhCF
e
(mnopus 1Imnoxqu Imnopq. minopu ex minopas bierius,
 a
lmaopus hnc p mnopus unop ex Vm opq
eninopus lmnopus min opus minops ex l opus
245,6Fsa. . . .. fit ex lmnopg. quia q recumnopq. sex sunt
combinationes omnem duae
qualibet ad cubm possunt altolli
30
d
12nD13
Mnop.
linop
Imnopq
lmnopq
lmnopq......
Pmnopu
lmn opg.
le
.
a
lnnopus ......
lmopus
nnopqus
e
.0
0
0
op (o ).
0
accu
2mno
lmino
Imno
emnor
o. 10. 117))no
)no m o
1 130
m Ini
1mju l) enile) hnon b)
go(2