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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 34
# Folio 3r, page id 00068247:0005
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pevus t. schediasmatis de foimulis omnium dimensionum
27- 7
dunensionom
ista assumtio c ipsius Z. hunc habet usum, ut  isse peu exponers aeqtionis pro artitrio sumi, et ita
problemat alioquio insolubilia forte solvi possint. Hac enim ratione efficitur, ut exponeus dimensionis
in grediatur ipsas quantitates. Vresdiamu itaque in quont formulam, cujus differentia sit
sit ea vee 
,1 25, 2 +B Z 2
+. t-
.  1 t- Z b.
05. 224+ Z a5
Z-34
: Z. 41..
Z4
273
Lt
=2
e
2 bi
Z4
24
6
1
Zt12
91 35
3
sust.
ma
et
Lt. L
2o Z Z
i
2
_. L
liquam
in Nominatore seu _ L exponens non sit
eveniant destructiones, oprae fretium tanen exd
113 et po delxpea X7B
 ea 17
omne, destructiones, si scilicet
ut in numera sore seu S.
ifficere praeteren possumus, ut cessent d .
Ita enim si aliquae
verum alius, vius M.
eas dissimulare, et sine destructione
al
iu relinguere; de cum duae rea in quolber differentiae gu Termini quantitate
cognita habeantur sedis, una pendens abZ altera ab B. et una quaeque valde regularis
et simplex, pendens a numeris combinatoriis
videamus quomodo X +B multiplicari possit in se secundum exponentem 13 sane
si secundu ces uta quandam generotem bicrimiorum scribas, ut supra; continuanda eut in infinitum
operatio nam facrendo y - 1 9- 2 7- 3. etc. Patet jam Z 2 esse H quam Z adeoque
exponentes fiet nihilo minores; exponentes autem nihilo minores significant divisiones loco
multiplicationum; poterit ergo in infirutum contranati progressio; et vicissim serem
tunus infinitae summa erit binvini potentia secundum exponentem, Z. Itaque si in non sit numerus
rationalis, explicatio, subtrahendo ab exponente, unitates fiet semper infinita Et ecie novam
accessionem ad oodtanam de summa seriem infuatarum.
sed quid si ipsam 7 hoc loco s3
d 1. 3
8
Nota si sit exponens,
dividas in partes aequales pro abimo, b. L, seu qsi aut si numerum partium
aequatum da su desinre mas muto;
ser crimi 3 2  2 red etc. et B eut mndrus laturas