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# Title: Leibniz-Handschriften zur Philosophie LH 4, 2, 11
# Folio 5v, page id 00068571:0010
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per  rationalibus
Aequationum numeralium resolutionem eo reduxi, ut
quaeratur saltem modus inveniendi divibres numeri dati. Hoc
t
 ergo jam attentabimus. Sit numerus
E ut 2X +3HF
238656. Concipiatur
Quod si posset fingi aequatio omnes habens terminos signo + plus
affectos, quae esset divisibilis, si numerus datus esset dosvisibilis,
postemne videtur mihi quaesitum ex jam tunc invensei haberi posse
sed huc non est in potestate
ex pressus dyadice
videtur vera methodus esse, ut tentimus omnes combinationes
X produri potest ex X et X, item x et X; utrumque tentemus
X +bX + cx + dXtC
x+m
CTonXIt CmxxtdmX + em
4 + Ex bs
x +SX
+2XX +ZX.
gn
e
ponamus nmeros omnes notas esse dixadicas
nempe dvel l
X significat 2
quia B est em, itaque pro e et in sumendi
divisores psiqus D, eritque utrumus = ipsi D
B =1, sed si 6 -0 erit vel e vel m,
vel utrumque 20
quadsi B20 fit f = Z
et eltom =3 quod si
praestat sem si B =0 sumere pro numero
ato ejus dimidium, ut habeatur impar, seu D = 1
jam l= 1 ergo
itaque e=1 = m
fit el = et dia Ergo si Z =.
dm = 0 ergo d-0. Ergo CM = E
ergo C =E et fit b = d E, quod si BB minor E, fit absucdum nec opus progredi
pet non procedit, nec opus progudi. si Z
Ergo vet H si
q= 0 fit d =1; sin Z =1 sit d =d
Sad 8 = 1- f. ergo G = 8
d
itaque 3 d = _ 1. 3 = f-h
1FC = 23 +9
1-3 + c= Z+g.
etd = qu a 1b = a tb + 2ab
= et d - 2ed = Z. sed C = 1 ergo d = E
addantur in unum d+ c + ed sit Lrct od red seu 1 - 3 + c + e - ez, sed e = 1
sid e= 1 fit 1+ d - 2d = Z seu d = 1 - 3
b (arb- ab)
fit 2 +C= 28 = LZ + lZ +C considero ut tres quantitates, quarum quaelibet nota
(a +b =
a+ b = ata ( ab addatur C sit a+b- rab - rac- 2bc + habe ssak + be u gc - 2abe abc + abc
dyadica sed a +b +C = a - 2ab + 4 abc
atbrc = ea 1. ab
-2ab - 2abc
tgabe
Hoc calculo non funsset oru
D+ C+ ed = d+ 198 2 2d +C
Ergo 1.3+ 1. 3tC
dabit
fit C = E, trans fertur ad A ( in seqsit d.
prodit C + b + d = E+ b + 1 - 3
seu E+b +1-Z. 2 (E) +E- E( + b - b3)
hn E+b+1-2
i
= 2. 1-3
4 (1 Z
+ 4abc
+4 (1.3)
1- 23
+2 (1-3)
-2c(17
158
Ergo
=
bci -2abC
b
2abc
+ab habe tabe
et fit tandem E = C
et jam in unum addenda
c+ b + 1g+
sit _E+ b + 1-g =
= 2abc
 +1-Z+ e+ b
= S_
+2EE, 3+S
52 +5 + 2E7+2E3
e -2, C. 62. + b -bz + Eb
E+ b - 2E +  2EZ -2b + 2b3 - 2Eb + 4Eb - 4E8 25Z, 31E- 3 +E + 2E3t259
-2Eb - 2E+2536, 2b + 268 +4bE- 46EZ =d
+4(bE - bEZ) F
1
+4 Eb (1-8
+2bE+ 262 + 2Z -4 b13 - 5 = = fu. 1. 31 E18)
Et b = 18 + Z + - 2EZ ,  = 1i 8E, F3E+ 75) L 13- 8 -2. big G
seu 1 - E - E - b + 223 + 2b3 + 2Eb - 4 Eb2 = d
=+ 1 -Z- E- b (E+ 3- 2E8
l = 8- 143+E - 2C3
b- 541136E + 2h7
fit
=(4 2(2
s transferendum
continuato ita calculo, oportet ut ubi finitur ultimae aequationes determinent
4(3 +E- 2E8)
seu b = 1 - 5 + 72.013 - 1 - 6f8E F 230, - 225 8 - 2E38
=B
(2tEY)
in sequeatem
13+E. 2EG quid possibile. Et itqe pro quolibet gradu fere Calculo instituto semper
+28E+ 8Z- 28E2
P. 2 (2tZ - 228)
6= (3 +C 23) (g1)
i
Fillet degnire stitum quando numerus produci possit ex dxte et lxam deinde quando
i ob hneri quaesitum Tabulaeque edo possent
ex CXX+ dx +e in lx+m, deinde quando ex bxtcxatdxte, in lx+ m, et ita porro
2.E+2
Hinc corsitligi pl quando numerus pruducipt in ex (XX+ mXtn in et dxtCxX, vel in e+ DXFCKC+ X vel
nost
in C+  + Cx + a dignotiend
.. sic pervemetur ad regulas generales pro
X+ ClZ +dLXt elX
X)
ct a
a
a
n +
alX3+b
+ar
EAXCZ
∞BX+)