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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 11
# Folio 12v, page id 00068261:0024
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Uti habemus operationem subtrahendi quones liceb
les est divisio, ita datur operatio dividendi quoties licet, 135291: 7=
quae nondum habet nomen
3
291: 7 = 19927 +
56+3 +3
seu 16 135291
15
2 + 7(8. 2.-30
= 394 +3, + E +
19927
y= 62 761 +3
ieu
1Gr+ 3, hoc per 7_ 13
B
+
2
+3
135291.7
(39+ +=+
E
d
tst
dat
+7 (. 14 1p 17
= 135291.,
2 = 2761 + 2, + 2, hocper 7 peu 135291
ul
4 75
+ hoc per 7, seu 135291 = 56+2 +3 + 8 + 2, hoc per 7 seu
14
135291 = 1 + = + t   p
=8 + = + = + 2 + B f 2 hoc per 7, seu
jam Et hic finenda est divitio, quia quotent ultimus 1, amplius per 7 dividi nequit
e
3 + = + 2 =
 + 3
+
0
P
+ 2
B
A
determinandi
3. P+07 +2 + p. 1+97 +2
es
st Ao H.
p
Mumerator integer
2. 74 3.7+07 + 2 . 0+A
s
132
si
p2 +2 =
75
70
At  1740.427137707+2
dB 
ura
76
t
Hic notari debet numerus divisionum, et resudua gradualia et feries quotientum, et
p
rese series resoluorum. Quanquam ultimus quotiens cum serie resituorum
sufficiat ad omnia
pe
eud a
70
summa refiduonum, t 1 + 0 + 2 +3 +0+ 2,) semper est minor ultimo divisore (velut
I
e
t
quivis residuns est minor divisore primosem sinetale et dimnes quodsi fingerentur ei
aequales, res rediret ad depressionem, et fecet + + L +   D Comnes numeratores
et
y inde a p seu
potentiae ipsius,
e
Cum enim queves minor sit suo divitore
essent unitates omnesque nominatores essent
 et ascenderetur ad
 interiorem ultimo divisore. Porro summa
+
4 +
sit harum fractionum est progressignis Geometricae 1. Ergo reddito 1.
ide ab 1. Et fiecet 1 +  + p3
potentiam ipsulo
ek quod est majus est
+e   et sit minas initate. Etiam hac summa
est minor unitate. Ergo cum
q
ticucta ad numerat communem denomina
torem, dabit numeroram infe minorem communi denominatore:
summa resi ductem
dinatid7
crat minor lenitate.
C
taq
adeoque dia residuum di
itionis ipsius numeri iitio dati per
 divisorem maximum.
Et ita si numerus datus 135291 dividatur per 7 quoties fieri poest
summa fractionum singularum divisionum est
aequalis fractioni altimae diccisionis, et proinde reductae sngutae
fuctiones reduect divasionum onnium redactae ad communem deno-
76
seu dividatur per
minatolem,  dant numeroratirem aequalem resituo divisonis
totalis e seu nimeri dabi per maximam dolentiam ippus
numita dato proxime cuferiorem.