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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 B 5
# Folio 31r, page id 00068255:0061
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 32v); this page is its right half.
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 98 lines, status machine
# Lines: 98 recognised, mean confidence 0.84
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

A
sa
Et
+1 1+a F
al -al
= al =at e
ndi
paritu
e
la jc P
il Ita
al -al
+al + a
-al + a
-2al
a
plici ut ante
El
a
Divisio dyarithmica
ice
Notatu diguum
1ceseetb et
Si a = 0 et l = 0 fit X = 1 si
sie a = 1 et l = O fit X = 1 sit
sin a = 1 et L = 1 fib X - 1
Si a = 0 et l = 1 fit X =0
sit X= 410, 2a + 1l + 13 al 
si a et b 20 fit = 10 = C
si a a = ,  e C e = 0 fit X = 1 + 11 = 1. Erp
si a = c et l = 1 fit X = 1 + 12 = 0. Ergo 12 = -
Denique si a = 1 et l = 1 fit X = 1 - 1 + 13 = 1. Ergo 13= 1
Et  tandem genicaliter X = 1 -. L + al
sit y = 10 + na +   13b + 13 l + 14 alri5 B l+ 16 ab + 17 ac
Si a = 0 et b = 0 et l=0 fit y = 0 ergo 10 =0
si l= 0 et a = 1 et b = 0 fit y = 1 = 11. sin a = Det b = 1 fCy 20
Nin a = 1 et b - i fit y =  1 = v + 16 fit1 b e
Si l = 1 et a = 0 e b =0 fit y = 1 = 13 sin a = l et b -0 fit g
fit y = 0 =  12
fit 9 -0 = 1 + 1  + 14 et 14 = = 2. sin a = 0 et b-
fit y = 1 = 1 + 15 et 15 =0 sin a= 1 et b = fit y-0
= , + 1 = 2 + 17. Ergo 17 =0 et tundem erit
generaliter y =  a + l - 2al
e
si a = 1 fit X - 1
si a = 0 et b = 0 sit X20
el
-al
si a = O et b = 1 et C = 1 fit X =1
fit X = atb -ab- b + ab + abl + bc ( abe si A = 0 et b = 1 et c = 0 et la0 fi1 X - 1
si a =0 et b = 1 et C = 0 et l = 1 filXe 2
X = 10 + 1a + 2b+ BC+ 14 L+ 15 ab+ I6aC + 1 7bC + 18 al+ iu bl + 20 clt 2t abeF
+ 7 abc + 2 ab l + 23 acl+ 24 bcl + 25 abcl
120 si omnia 0, nempe a, b, C, l, fit X =0. Ergo 10 =0
si a = 0 et b = 0 fit x = 0. si  C = 0 et l = 1 fit X = 0 = 14 sin C= 1 et 1=0
fit X ~0 = 13. si C = O et C =) et l = 1 fit X = 0= 20
si a = 0 et b = 1 et c = 0 et = 0 fil X = 1 = 12, siy c = 1 et lc0 fil X = 1
= 11 + 17 Ergo 17 =0 sin C= D et l = 1 fit X =  = 14 19 et 19 = - 1
sin C = 1 et l = 1 fit X = 1 = 1 H - 1 + 24 fit 24=1
sit si a = 1 et b = d et c = 0 et l = 0 fit X = 1  - 1 
si C sin  l = 1 fit X = 1 = 1 + 18. Ergo 18 = 0. sin c = 1 rt (=0
fit x = 1 =  1 + 16 fit 16 =0 sin C- 1 et 1 = 1, fiet X - 1
1 +6+ a  23, seu 16+ + 23 -0 seu 23 - - 16
= 1 + 23 Ergo 23=0 si  a = 1 et b = 1 et C = 0 et l-0 fit x1
X = 1 = 1 + 1 + 15 et 15 = -1 sin C = 0 et 1 = 1 fit X = 1
1+ 1 = 1 = 1 + 22 fit 22 = 1. sin C= 1 et l = 0 fit X~I
fit X = 1 = 1 + 1 = 1 + 21 Et 21 = 0. sin C = 1 et l=1 fit X = 1
(fit X = 1 - l + al ut aute
11114 1 - 2 Et tandem X = a + b - ab - bl + abe tabl + bel- 2afel. Hine si pro a ponamus opro b, F, , )
= 1 + 1 - 1 = 1 + 1 + 1 + 1 + 25 et 25 = -2
si = sit  = A + B - AB - BL + ABC + ABB + BCL - 2ABCL
sit aL A = l- al B = a - al
= + l = al 
+ a = A + abl
+Dabl
+al, e
+al
ab
C =b. et et L=l
+d - 2al b ut ante
pivi damus ... a)b).
si a = 1 et h - 1 fit X = 1 si d = 1 et h = 0 et b 0 fit x = 0 si a = 0 et h = D fit A-
= +l te
sit X = 10 + ua rih. per. hl
sed a = 0 et h = 0 incommodum est quod possunt satis facere tam c quam
et fit X - 1 =9 et X =0 =0 Ergo XX = 1 X + 1. 0 = 0 seu X - x =0
seu X = sese o,t sit  si a= 1 et h = 0 fit X = 0,l + 11 = 0 seu
Ergo 11 = = 0,l sit si a = 0 et h = 1 fit X = 0 A = 01 + 12 et 12 = -0, 1
denique si a = l et h = 1 fit X = 1= 0,t F - 0, bt = 0, 1 quod est
impossibile, itaque non licet relinquere in divisore generali ellaquere
primam incertam
licebit dividere per
ipsi ergo non licet dividere per h, multo mmus
sid si
Generaliori adhuc calculo opus
non per 1) l
sore dividendo per h
sed video rem non procedere