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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 24
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(2. Novembi. 1677.
scheda priore
Logistica decimalis Scheda 2.
Inveni supa omnem fractionem ad logis docimalem hoc modo
reduri posse, sit fractio =. cujus numerator n. sit potentia denarii
ipso n si placet proxime major, d. et divisa potentia per n, seu
si placet ipso n’a d. quoties lubet substracto, sit  quotiens
seu numerus substractionum, q. residuus vero
demonstravi fore.
= aequ. = 3 1 + r +
+
12
.
His ita praeparratis
+ L,YB. ubi posita d majore quamr
n d .
utique  negligi potest
Hinc jam innumera oriuntur compendia. Nam cum d pro arbitrio sumi potest,
nempe 10. vel 100. vel 1000 assomatur autem talis, ut Y fiat quam minima
qam quanto major erit d. et quanto minor V tanto facilia est calculus producitur
quod si aliquando contingat r esse 1. non est opus calculum uetra produci. Sed
x et ex datisjam inferioribus ractionibus vernaliter expressis, superiores invinire.
licebit hoc modus si faciamus ut + sit fractio, aliqua ex prioribus, et sit
unitas. Exempli gratia
b + c
aequ.
Ergo aequ
 d-r
1000.
211
de
equ
211,4, 1000 -
1 aequ seu  aequ. 1 +
-r
D-Y
2u
der
1000-156
F
+1
12
sit L aequ . erit de r aequ. bn. seu sumantur numeri d et Y tales, ut summa
d
ex ipsis dividi possit per n. uotiens erit d. Quod facile erit dum d seu pobentia
1
denarii continue dividitur et farum deest, quo minus possimus accurate dividere
sublet supplebimus illud quicquid est. Utilis erit haec praxis cum inter dividendum
communis more magni nimis sunt residui, ut: Cum 156 major sit quam dimidim
6300f47
A 211 ideo poterimus sic procedere  aequ. 
1000+55
211
156
55
2u
ono fier: 71 1 - 7 + r - r3 + r4 dec quod celerius appropinquabit
et faciendo 4 aequ. 5. 1000 aequ. d. et 55 aequ. Y.
34
rests
ric
quod si velimus producere divisionem, donec commodior fiat progressio sic agemus:
fier = aequ.
211
4734 - 1+
4734
21b aequ.
100000
100000+14
qui modus transformandi etiam valde
notabilis nempe
n aqu
erit aequ seu si L aequ  eris
imo adnon est
d +Y
+r
continus tes uini eosales, sed tan tum hic
1
aequ=
00000
10079000000d014734