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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 34
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caelerum si multiplicatio instituatur alio modo alia veretur productorum repraesentatio,
nempe: Z
(1) Z
 F, Z X p Z2 - ZcZ - 21
2g-c
V.2
22227-3 1
a
L
Z 3C
et hor rursus multiplicando per Z- 4 fiet.
75 - 4 y4
3∞ n + 128
82
1on. +4.
+6 .. -24 Z
3..12..
3
-7a
6
Multa in hac dispositione nmoranda, sed quae omnia ex hoc
capite pendent, quod nimorum orminus cujus libet
Liget ad huc unum calculare, credo vero
uneaae multiplicatus
etsi res forte mereatu. Caeterum inspiriend
vec
appa et hoc calculandi modo non in simmus
fantum, sed e per pantes, idem quod ante provenisse
Caeterum summae iniles fiunt aequationes:
et denique: 1Z
122 43Z~ + 22
- 1074 + 3577 - 507 + 247.
pono semper numeri cuyslibet armitu
inter se juncti uut aequales nihilo, multiplicetur haec formula, per Z - 5, fiet:
seu
= 10Z5 + 3F Z 5023 + 24 72
4. +40. - 140. te.. - 96Z
14Z + 757 1902 1224 Z 496Z
ubi rattu plina te mumas srsusserpec aequaratlo.
seu
= 1075 +35Z4 - 50Z
= 5 n 440.. = 175.. +250 4- 120
152 +85Z7 21573 +2452 1208
Ubi notandum Inductione apparere, quod sempercrescant cognitae terminorum, usque ad
penulti mumi, qui est omnium maxiinusi at  ultimus rursus decrescit. Termitni secundi
sunt numeri triangulares 0. 1. 3. 6. 15. Termini ultimi, 1. 2. 6. 24. 120. sunt producti
nuterorum continui deinceps at unitate, rempe in (1,3 2. (2, d6. (1,2,3, 24, (1, 2, 2, 4, 5,) 120
sed reliquorum dfficilior determinatio, v.g. tertrorum : 2. 11. 35. 85 etc putet tamen eos esse
quodammodo sumntos ex pycamidalibus, 1. 4. 10. 20. 35. 56. 84. quanti sunt 6. 50. 125. esc
qui quomodo ex Triangulo Triangularibus, denventur non da fanile judicatu; t et opus
si est prolixis inductimnibus ad ista indaganda. Si
s in qualibet termino in serem pscorum cognitarum seu numerorum inquiramus, ut: omisto ultimu
lormule
ut, 1. 1.3.  16. 1 1. 1dr 3550.
1.6
5 25
1. 15. 85, 225. 274
11. 70 140 49
46 70 -91
sed his nunc quidem nissis redeumus ad nostras formulas generales:
Esto primula quaelibet:
by + caV a d dae V2 + ea V2 + fat 2
gy +hay2
+Ka y2 aloyE  YZ
5023 A3. B.
quaeratur ejs differentia a. formula quae hoc solo ab ista differat, quod pro y ponatur y4β: ut autem res
2bdi 2 ilcaeque v21 + 5das y +4 e a512) +8 5a gV
+7.
in numeris habeatur et vitetur gerror calculi scribemus:
r SYn
195 gE Antra 5. 121 4,  pa 5 y2  41g la  u3 4 5 mae 5. yi
92
et hoc
per, 2, 2 3, vel bat
1 + 4 multiseita
vel 143, vel 1 +4
eic. multiphenti
dant reriquos, sunt autem:
1. vel KB
ners
net
sequentem, non ergo considrandi nisi qui lineas
incipiunt, hi enim per
122
vel
t
_ 
87474
214+