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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 37
# Folio 2r, page id 00068250:0003
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epe duarum aequationum ejusdem aterae tollere literam, etlissea per
anonem Generalem res utilissima foret. Cui oanis rationitus jam accessi venit et in mentem
simplex duarum datarum multiplicatio per formuras arbitrarias ad tolledos
omnes terminos suffecturas. Suit ergo Ita enim res omnis reducitur ad solas
Aequationes simplicese multiliteras, quae a me jam sunt ad sanonem perfectum recctae.
Sit _ 1D + 10X = 0 et 21 + 20X = 0. Multiplicetur illa per 31 haec per 41
et  C X 1I  et producta identificentur, fiat 02 11. 31 + 10. 31X  21. 41 +20. 21X
n ve n urro  it 1B + IBX + 10XX = 0
pe. bo
100 sin _ 2, Huc e 
4131= 10: 2
et 22 + 21 X + 20X+ =0
(31 +30X et per haec per 41440X fiet 12. 31 + 113IX + 10. 3IX X
et 22. 41 + 21. 41X + 20. 41 X
+22. 40X +21.40 20.40 X = 0
aa aequationes 3 et 4 fiet
 ia 
mult plicentur elap
+ 13.30. + 11. 30.. 4 1030X
20 e 411 et u
sunt tollendi termini tees, et identificando
+ee
0=
h
2. H- 2240- 20. 4, - 21 10 20
habemut aequationes quatuor, literas si tossendas  quatuor, sed in effecta tres
L10. X. 20 31 + 11 AE. 2030)  nomo ron L0
Ex aq. 7. fib - H2. 2020 - 1B. 1. 21 1
et fit
= 1B. NC2 - H. 2020 1. 12. 30 - 12. 20 41
roda
fil: 10rt2 E1 10. 11. X. 2736. 21 - 10. 1. 17. 28. 21. 21 - 1. 1 LN. 20.20 +11. 1I. 15. 20, 30. 21
fit +10. 10. 22
H. 12. 2d
unde denique
10. 10. 1. 12. 20. 22 = 10. 1X. 12. 28. 20. 22 = 10. 12. 12, 20. 20 + . p. 13, 30. 20. 20
Est error snto nam 10 et 2 A 10, 1, H se debent habere ut 12, 11, 10
21. 20. 22 31 + 11. 20. 2 30(
41 12. 31: 42. 40 = 10. 30. 20. 3t ex aeg. 6. fit an. 2B. 2 .  10. M 2.  =0
it ex aeq. 7. fit +10. 20. 36 31 + 11. 20, 22 30
-10. 21. 22..
(13) Ex aegus. 1 et n
11. 26,22 6, 11. 20. 2 (3 4 10. 2V. 2) 312.20. 
0
b= 12.30. 21
seu actu ipso multiplicando C. E 10. 11. 21. 22 + 10. 12. 21. 21 g, i1. 1L. 20. 2 - 11. 12. 20. 2)
= 10. 10. 24,32 4 10. 12.20, 22 + 10. 12. 20, 22 = 1c. 12. 20. 20
- 12. 20.20.
seu A10. 10. 22. 22 (1 5) R10. 11. 21. 22
612, 12. 20. 20 = l10. 12. 25, 22
810. 12. 21. 21 a f11. 12. 20.21
11. 11. 20. 22 A10. 12, 20. 22
H
10. lo. 22. 22
10 1 21 22
12 l2 2020 ag. lo l2 20 27
10 12 2121
11 l 20 2
1, 11 2022 b0 12 20 22
Hinc sc Ubi sequentia notanda occurrunt:
(1) Aequatio ultima seu in qua bin Litera est sublata conate mambtis
ita formata est ejusdem Cllrae  coefficientes unius aequationis datae, se
habeant eodem modo, ut coeficientes alterius aequationis datae
(2) item Ex eadem aequatione coefficientes termini primi secundi tertii etc. se habent
eadem modeo ut aequationes coefficientes termini ultimi, penultimi ante penultimi etc.
(9) In omni membro si coefficientes ejusdem aequationis pro Capitalibus assumantur
ascendet Capitale ad tot gradus, quot unitatem est exponens maximi gradus
Et haec quidem praevidentur certa demonstratione, et ex serimento praesenti verificantur
in aequatione altera
(4) Hini etiam judicari potest quot oefficientium sit quadis terminue menorum, nempe
dimensionum
tot quol uitates sunt in summa ex exponentibus maximis ambarum aequationum
(5) Si per notas numerales si coefficientes per notas numerales exprimamus seu
per numerum constantem ex ncta aequationali et graduali et rem Actamust
et dige et ordinemus secundum graduales, patet in omni membro notas gradutles fore
easdem nempe hic 11 2. 2.
et notas sequationsales hrarscloni o,
(6) At notuse o notas aeqationale, hoc loco variantur tum eo quod dum
grad
eo quod aliae atque aliae assumuntur tum quod eadem transponuntur, sunt autem
considera conbinationes ad hibendae quae faciunt summam dimensionum aequale summae exponentium
habemus
Et ex. 0, 1, 2 hoc  componendo 4 partes
maximorum, hoc loco 2 +2
212+ oro s ote 2 +2 seu B+ 9+ 8 + 2 seu 0
1+1 (10+ 2
v +08 +2+2
Opt (It 2 +0,2 ber2
vel transponendo
1+2(+0+) 0+2(0+2
0+2) + 1+1
2+2 (0t0
Nec pluribus modis variari pt. Et quavis conbinatio unam  comblansi patitur
transpositionem. Cam sit bimebe pliores duas notas habens  exaeqst posterures
hote
ex eq. data 2. Unde inter priores  Un inter ipsas autem quae sunt et ejusdem
laequationis nul fit transpositio, quia cum eadem adsit et nota aeppationalis
a
ninit mutaretur
fine el utue
tom nt eadei a  ptta in sunis cenia edet
tionis sunt eodem, nam cmispositio noe srius imenbrum reddit b
1. 20.21
E.B 2
ane
lo. 21. 2
+12. 20.20
l1. 20. 21)
a+630-
31C + 30d
bE- ad
Sta + 30