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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 16
# Folio 4v, page id 00068013:0008
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10X +  =0 20X + 21X 12 = 0. Ex  mulliplicando per 20X. fit 10, 20X L 11. 20X=
et 1 2 muslipilicando per 10 fit 10020X + 1021X +10. 22. Ex Tot 4 fit HO. LIX +.0. 2
Ex het 4 fit +10. 2IX + 10. 22 =0
~ 11. 20.
1820.  1  U
2ox 10 X + HX + 1220 et 20X + 2X +2220. Quaerabur
communis divisor
20 X + 21X + 22)C
- 10.  p = 10. 22
=10. 20, 21
= 10. 21.21 =10,21. 22
(+11. 20 XX + 12. 20
= 10.4 ct - 10. 22
=12. 20. 2DX
1821.
+ X + ZIX +227
uveta
-10. 21 X = 10. 22
epoit
cn
Rem., 11. 20 A + 12. 20
divisio 1
10X + 11X +
20 X + 21X + 22
10, 21N - 102
divisio2
20 sub quotins 1. p AeSId. 1.
+ 20X +4L+ L
+11. 20. 21 X + 11. 202
=10, 21, 21
(+ 1. 20 FR F 12,20]
10.io
- 12. 20.20
+ 10, 20. 2
+ 10. 21. 22
fl. 201X
+ 12. 2C
= 10. 2
b90oti
410. 412
+1I. L0X
-10.2.
10. 25
subquoti2. Resid 2.
+ 11. 20.21
-10. 21. 21
-12, 20. 20
+ 10, 20. 22
+11. 20
10. 21
=120.
+10. 20.
71. 20
=10, 21
L0X +2IX + 22
sub quot. () subR etid. 1
2190X
Resid. seu subsesud
+2213030
2l. 30. 31
Resid.
+20. 31. 3) absolutum
Itaque ab hoc video esse incipiendum ut habeamus catulogos seriem quohentum
et Residuoum simplus simplicum ivrsionum
subquoti  subresid. Y
10 X + 11 10 ensit 21. 20
20X + 21 20
-10. 21
subquot.t ( sub Besa. 1
Zootiens Resict.
AII. 20
R-10. 21
20 Y. 242
ubgu2 subhresi d. 2
10X + 11 X + 127 10X (I. 2OX + 12. 1  Vl. 20 +12, 20. 20
20X + 2)
to. 2.
~ 10.2) - 11. 20, 21
(20X + 211
b90.)
=H. 20. 21
L+10. 21.41
20 +10, 21, 21
subresit.
1. 20X = 1, 20 H,1. 20
10. 21.
20 X + 20 n( 20
(quotiens (Resid.
J 11262521
410464121
(+ 11. 20 (12 20. 20
3-10.21 - 11. 20, 21
08 410 21. 2)
20X + 20.41
subqu. sibre sid. 2
Sabq) tubr.
IOXHIX + IX +13) 1X+1 2O X +n. WOX + 13. 20) + 11. 20 X 11. 20. 20 X + 1. 20. 20) 1ibo 11 3. 202d20
2X+ 21
20X + 21
= 11. 20. 2X
2410. 211.
~H. 20. 21
20 +1021, 21
11. 2d21 iZ. 2C. 20. 21
20 erit quohiens 10X +11. 20X + 122020
Ita habemus progressum
nam quivis quotiens componitu seraetentermi
(410. H. 1 + 11. 28. 21. 21
(20 X + 21 20 - 10. 21. 11. 4
10,2 = 11. 20. 21
20 +10. 21. 21
( 12. 20, 28. 25
 oiri
Riesiduu
C 205 et 113. 20. 2020
212. 20. 20. 21 l: 20X + 20. 21
+ 11. 20. 21.
21. 21. 21
habet cvefficenties terminorum primo inferiorum, eosdem cum residuis omnibus praecedentibus
Residuus autem sit pro X ponendo  2
10x +uX + 1X F 1F Ex B. B  120 X = M. 20X411 10 f e  X. Ars d. 1 10 20
10x + 2 21)
se ternitit
2130 X F n. 307
copendio
dok is
30x+ 31)