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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 3 (shelfmark LH35, 3 B 3)
# Folio 12r, page id 00068253:0023
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1-1
RM = a
na art liansf. ab.
2ab
Ex Regula nea generali in veriundi quotientes fractonum periodas
cujus Numenatar
 ivedeter  id est 7) t per eum sividendus est nu
doncc prodeat periodus. Sed ne opus sit dvi
sione actuali, regulam hanc inveni. Ad numerum datum addatur 1 fit 1000 ei
111I11I
dimidium 100, erit multlicalor perpetuus. jam qu periodi quaesitae quotias ultim
est semper In sposito scilicet, ut semper assumi potest. Numerum cujus fractio qaertur
esse imparem). Is ducatur in multiplicatorem fit, 100, scribe 0 vet ne +0. Hoc
dic in multiplicatorem fit 200 scribe scriptu habes quotientem rum retine 10
transs abtac -abe
Quobentem novum duc in multiplicatirm, adde retentum fit _ic, scribe o pro
apotiente tertio retine I_. quotientem dertium duc in 100 adde retentum fit1
scribe 1 retine 0. Et ita habetur periodus.
1860000 f0100 100 100 eM.
demultiplicatus per primi
sit numerus
D.D Ct acstr  
firbus a ax
comprobabimus operando acto
n r l
quotientem 1 dabit  ddHat
retri
idem esse ac si eadeba multiplices per deeunt et productum
et, abr bh. bh. am, quod adde ad ddu
semper dabit periodum quae sitam, multi si multiplices per 10, et addas1. fit periodus
manifestum e
Et patet nvera
debet 1 vel l.
ergo bl + am dabil b+ a = Pab+n lenn- btanab
quaesita, cujus ratio patet quia ascubu
et ab + ab
eum et  bm t an = C + ba Hinc fit p= in p sit et + bm = an + ab,  saq u de
e de b. a L mult
ab quod transferetu
musferctur in locum sequentem, et de vel restabit da aliab adeoque sit p= C+ a - 2ac
a
anferetur ab ii locumse quentem
eut c + a 4
idem esse ac si
poro m. a ad m-
et + ab + ab  aa -2 ab + a b
ub quod patet, non posse ire ultra 1
eta = cta + hac seu ata = eta -rac
pux quo scribru 2 ab + c+ a ad
labi
et set P alt ab c a
ambsi ambo 1, nompe, a et t
c
et et a - 2ac + ab = p+ ab. + aB= 4 bC
 est in lrane
aa + bl = 2 ab vel aarbb. 
aate
p estin el + db + an = cl t abl + a + abb - 2 aab
M= al =a n  + 2.. = bl + am = bl + aa = b + a =aan h
fiet a + 2 ab = a a + bb et n= aa + bb -2ab, et ab transferetur
= 1
el + ab taa
pat
et ale c+ a + ab jam  a + c = aat   at
in columnam sequentem.
+ ab = 2ab + ab =
entransferetur XC-
rabit quatto qu
en sequent nlis est erat quadzacio, qui
tab
rac
2a+
len
iic
ipt 2ab (ad +cc- 2ac) + a + c+ 4aacc
b - 2 abcc +4aabC, adeoque
ransferendo ab + ab (aa +CC - 2aC) in sequentem, fiet p= a +C + 6aacc 
2a
a + C
a
= 4aC - 4ac + aabb = 2a b - 2abcc + 2a a bc
seu fiet
p = a + c (+ 6ac) - (8 aC (F ab, - (2 ab =2 abC) + 9 abC) seu p  a +6 nb- ab
 conjungendo primum.
la et ab, et post addendo c. Nempe p+2... = c abt a + ab + C
x (1 uab rati) seu PF a + b - 2ac + 2abc
seuqu au ab tabet
et paosn
100
00
quotientem n quem scribe et reliqua retine, ita apparet et ila porro, s
= A Xb-ab rab i (+ 2aacC = 4aC L 4 dc + aqusibe a
reliae
H3.a
00
ux additis bl et am, habebis tertium
quod deb Multiplica a
pocier
+d (uib. ab acrabus absolvi debet a
ad esemp
nnib
tau
in
e Multiplicator, id est dati unitate aucti dimidius
FY1Y 1
NA.
scribe a restat
)= a+  a) b (14) aCaEd ( an bo ab. ac tab.
nayf. ac- abc
Hac +ab
pnttum
Mhi
2a
paginae 18 ascripta est, oritur haec pro dgadicis. Sis numerus , vel 111 dyadice
numerus inde finitus:
Paob resa ab)
anab reab
P2
queab
e
fit
Aliter idem
at atab = a  ab. jam . addi debet c, fietque a + ab - 2 ab + a b
+ ec = 2ac + 2abc + 2ac = 2abc, et reservando ab + a c - abc
ut ante
in sequendem col. ifiet P = a (F ab, - D ab + C = 2aC + 2abc, 
 q+2... = dl + Cm =bn Z ap + ab + ac = ab c = d + hc s Ab) + b - (2 1b. A
 a( ab F ac= (2n9 + (2abC (+ ab + ac) = abD = a + b - ( + ac - abc +
a+ b  a tb 2ab + b ob aub reservetur sb, manet atb. 2ab primum atb
et atc- abc etiam ergo erit erit q gubfab +2ab
= 2ab = 2ab, + ac + abc - 2 abc 2. (a + b- ab) (ac - abc) et in sequente honsferetur
(a F b = ab) (aC - abc) adeoque Gia +b - fcb + (aC = abc) - (2 aC + (2 abc(- 2abC -+ 2 ab c 4 2ebc. 2 a l1
ab non excedit 1
+b-ab attabe) + acuabctab0 ab 
ravond eo tet aedi ala at anerare uti seri  ae  steatari
ervetur
ed cb a
in it d H. al
eudnea bu an
euda eu luan
Apepuap.
eu
n h l
f11C
15)
1ab, per bxo