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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 207r, page id 00068196:0409
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paginae sequines nqe paru sunt coonganoe, ut patet
exsparia sova libito Aerglico inferta
10X + na = 0
20X + 2 a = Cd +10. 20X + 11. 20a = 0 velt v. 21 X + 11 21 a utroque 10 21. 
10XX FeaX + 12 aa =0 (F 10 20 XX) 1120 ax F 12. 20aa7
20XK +21 ax + 24 a = 0- 10. 20XX) - 10. 21 aX 10. Va a )
=10. 20X = 10. 21a
=11. 20X -H1. 21a modo
20 +10, 22∞) + 1. 22 ax (F 12. 2a a - 0
1720 = 12.31- 12. 22)
(CID2, A. 20 aX) + 10. 2, 12D aa =0 +11. 20, 11. 22 ax (+ 12. 20, 11. 2 aa = 0 fit
∞. 22. 11. 204X) - 11. 2, 21. 204a
=1022. 12, 20 ax (= 11. 12, 12. 20 aa)
 et explicando H1. 20 in HIL. 22 = 10. 22 in H12. 2
- 10. 2 -12. 4 + 12. 20 -18. 2
Noca sinictrs sunt semper eed eaedem eodem ordine 1, 1; 2, 2
11. 20, 1122 - 10. 22, 2. 20 =8
compendro trogr.  25 -0
= 10. 11. 21, 22 4 12. 12. 20, 20
20. 22
_1C
+10. 12. 21. 21, 19 l2 . oo. 22. tt  194. 1. 2 o 2. EE
Notae dextrae simul componunt 4. Et pars continet amnes possibiles transpo sitiones, homni quatior 0, t, 1, 2
altero. continet omnes possibiles transpositiones ipsorum 3, 0, 2, 2, ubi evenit ut 02, 0,2, et
208 Sed ea lege ut viter ab. a.M vel 2, 2. nulla transpositio habet locum, e quivalea
at, a= et a2 a1, seu av. am et aa sed investiganda superest re gula plus semel
Occurrentium, ut 10. 12. 20. 22
quod signa atinet, patet eadem habere signa transpositiones
seque paria, nempe abam. bnbp et anapblbm sed diversa signa habere alam bs bp aplen
velea
vero nutaturi
pota dinistra in pa resenta parti pariatione relenetur alter
in hac caumsinandi ratione observatur oupex institiae exuna
nntu spavile
ut notae unius aequationis originalis, eodem modo tractentur ac nitae altetius aequa
tionis originalis; s iaterse permenteret, ita ut Pro 10, 11, substituendo respectine 20, 2C
predeat idem. Altera lex justitia ut coefficientes ipsius X, neo eodem modo tractenti
ut seispondentes coefficientes ipsius a; et proinde pro 10 et 20, substituendo I1 et LI
respective, prodeat idem. Itaqu sive notae sinistrae Nohae autem dextrae cor
respondentes habentur, quae sibi complemento sunt summum aequ ad exponentem
summi gradus in aequatione
calcu
s etiam
tie.
m enim qua eodem modo tractentur in modo
011.7.2 ato10.  
1OX FMaX X + craax + 13 a3=0 410. 20X) + H DAXK +a0 a aX + 13. 20a
Ed
ic es EL. 21  + 229
+1023C3+ 1. 2an +12 25a 715I
20X. + 21 axX L MaaX + 23 a3 =0 - 10 20X3 = 10. LIAxX  10 22 aax = 10. - 3a 0 - 17, 10X3 - 13, 1 qVX - 13, 21 2X 13. 134
(+ 1220, 10. 2 XX + n. 20, 1023 aX + 13. 20, 10. 13)
=1120, 10.23 = 11. 28, 14. 23 aX - 11. 20, 123
+11. 20, 12. 23XX + 12. 20, 12. 13aX (F 13. 20, 12 23 aa (3
= 18. 2, 23,. 20xx = 11.23, 13. 20 q = 12. 23, 1 2004
B) orL(t1O. 23. 12.20 =19. 23. 19,2.2-18. 29)12. 20 + 13,20. 10. 22) X  10,23. 13. 26 - 19. 29. 19. 29 -13,. 20. 12. 20+.13,20. 10. 2)
Expricte vel 0 = - 11. 20, 11. 23+ 11. 20. 13. 21 4 10. 21. 11 25 - 10. 21. 13. 2i1
vel 10 +0, 21123 x + 10. 18. 23. 23a =o
1 =B. FB 3 F 1L EQ 1 et 1Z et 1 Zu1G. 21. 15. 2
=11. 28.  23 + V. 20. 13, 22 410. 2. 12.2 3. 104 32
Exposepore  (+12. 23. 11. 20 = 12. 23. 10. 21 - 13,22. 11. 20 =13. 12. 1021 X-1(+ 12. 23, 12. 20 - 12. 25. 1B22 = 13. c. L riy 1 13) a
+10. 1. 2 23 + coM 21. 23
-13. 28. 10. 23 +13, 20, 13. 20 + (0 23. 10. 23  10. 23. 13. 26
vel 1s. 12 2t. 23 4
4 1B. 10. 43. 23 d.
Opdinando (- 10. 10. 22. 23
+. 10, 12, 20, 22
f 10. 13. 29.22
=10. 12, 21., 23
= 10. 13. 21. 22
+ 11. 12. 20. 27
= 11. 13. 20.22
de est 10. 11, 22. 23
10. I. 22. 2.7   l
+ 10. 10. 23. 23
=- 10. 13, 20. 23
=13, 13. 20. 28
Resumamus 10 X + NAXX + 12a a X + 13a =0
20 X + 2 a xX + 22a aX +23a3 = 0
itaque notas sinistras permutuliima
dextras conservabimus
+10. 23) XX) (4 l2. 20 in + l0. 23 (1X
(+ Il. 20 in +12. 23) XX)
-21. 1B - 22. 13
22.10 =20. 13
12. .  1 131019 2 p 3 1t3 .9.21
Ordinrandio expria
-10. 10. 2273 +10. 10. 23. 23
(+ 11. 23 in ∞l1. 20 ) eX
1 18302
A - 10 11- 3. 3. 23
f 12. 10 in 212, 73) a) ((t 17. 30 in 212 23 )aa
+ 12 13. 20. 22
+13. B. 20. 2)
A (= 10, V2. 12. 27
+ 18. 13, 22. 22
+ 12. 12. 20.23
= 12. 13, 20. 21
(+10. 20 X2+ 1. 2c a XX + 12. 20ax + 13. 20a 4 = 1
= 20. 10 X3 2. 1Ca r. x = 22 10adX 22.10a
+10 23X3+ 11. 23aXX + (2. 23a aX (+ B. 23a= 0
= 20. 13X - 21. 13aXX = 22. 13aaX  23. 13a)
+ 12. 20. 10. 43 X 4 13. 20. 10.25
= 11. 23. 11.20
ubi pro erolutione in uno quoque
pari membri manelum dextrae transam
nentur simissiae; it
sitiare differun sugmo, quae duabus cquenint
+.11. 29. 12. 234X +2. ~. 11 2310
1. 23, 13. 20) =11. 23 13. 20)
in notis sinistris, usi respectu Xest 0. 1. 2. 3
parspecto a rpt 3.2. 1.0