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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 241v, page id 00068196:0478
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Ut litrras _t 1, 13; 31, 33; 12, 22  irveniamus ope denominatum 123, 223; 11, 213; 112, 112
Incipiamus ab 11 et 33 per denominatores 3 et  pumum et ultimum
00. 223 + (00- 13) 32
Ex denom. 1 33 = 00 (123 +2 + 13) - 13. 32, : 12 = 00 (2231 321 33) 33. 32, gE 00 (223 132) 1332, :, 12 -00 nom. 2
Unde fit 13 f00 31) 13 = 00. 12. 223 00. 123  00. 12. PE 0000.
, 12. 13. 23Foao2 u, Unde fit B3 00 213 00 12. 123 F 00, 137. 32 - 00. 12. 123 - 00. 12. 12 400. 00. 123, 00. dv 12; 00. 32
v0. 1b. 131 399
A = 10 1331 seu 13= 0d cc 12 + (16) 123 (03:, 1n E 1092 (0)00. 
seu 13 =
seu 13Z 1( 12
 nde 100, 22512 + 00. 32. 12C 13. 32, 2. 3. 721. 12)
=12 + 08: 123 00. 123. 12 +00. 12. 12 +00. 13. 12  69. 125. 00 - 00. 12.00 - 0d. 1700
4223 +22)4 e
vgo, Teg3
F13. 32.00
Exralore 13 fit valsr 33 permutando t. e3. itm t0. et 2..
Ex valore 13 fit valor 33 per mutando 10 et 30 item 10r et 20.
3212Z F12) +00. 223
Ero siet 33 =
Ulli ex 123, 223 duximus 13 et 33, ita ex 112, 212 ducemus 11 et 31, permutando  1D et, 3a
fita ee
(= 22 132) +00. 112
2 (+ 112 + 12) +00. 212
valores inventos quantitatum 13, 33, U, 31 substituere oportet in valoribus ipsorum 113, 213
fit 11 =
Sed hoc ut possit commode fieri expripendi sunt compendiose + 223 - 123 +32- 12 400 = 1312
ubi nota oa yHE bis 00 = 1312+3121
32+ 12E = B 82 8
= 2112+ 1321
32, 12 = 42 32t 12 = dt2
1I = 12. 3112 +00. 112,:42
13 = 32. 3121 +00. 123:42
122 - 227 +12-32 400 = 3121
312- 112 + 32 - 12 +00 = 31 12
112 = 212 +12 - 32 +00 = 1321
31 = 32. 1321 +9a212, iq HS valores substituamus in voloribus 113, 213
33 = 12. 1312 +C0023,42
firt 9042. 42. 113 = 12. 12. 3112. 1312+ 00. 12. 223. 3112+00,00. 112. 223
400. 12 112. 1312
3232. 3121.1321 + 00. 32. 42. 3121 +00100. 113. 212
Et 00. 42. 42. 213 =
00. 37, 123. 1321
-00. 42. 12. 3112-00.00. 42. 112
00. 42 323121 =00. 00. 42 123
= 00. 42. 32.131 = 00.00. 42. 712
- 00. 42. 121312 = 00. 00. 42 223
92.  (13- 21) = +1 2519 12 4 32 ( 317 + 0092 22, 4 00G21 
1   a
ineur 
+ 32(+112 421
unde fit
L - 212 = 123
216(o3 1223+2.
+21325+ 12 + 13 (+M fu2Ipu + 0 ( 00 (5 400 (1215
= 123l+ 31)
V.11252325
Itio si faceremus 12 +32 0 fieret 223 = t23
Haec aequatio eadem manet, si permutas 1. et 2. item 100 et 2..
-11357+32