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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 10
# Folio 5r, page id 00068007:0009
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teroie
Detture ct frletoe potuar 1.
Pro 10x+1 =0 et 20X + 21 = 0 fit aequatio litera liberata: 10. 21 - 11. 20 = 0. Hinc jam continualis
explicationibus sit aequatio tellens literam ex duabus proxime altioribus paribus 10Xnao et poa ruta
Et inde natam aequationem litera X carentem) rursus explicando fit aequatiotoldens  literam ex ad huc proxime
altioribus 10X + ax +2X + 1320 et 20X + uX +2X + 23 =0. Et ita porro continuando. Cipsa autem
lex aequationis est Lexautem explicationis hoc est dt p fiat
(10) +10. 21 1, L L 0. 22 (13) 250 23 (9. 1192. etc.
(20) - H0 2n (2 HB En (21) - 11. 2n 23 - +101
=I. A =in. 27
inpota ahais pe
l
1A2 - IR. 2
si aeggue. datae sint 10x +ux ec mo et 20X + 21X et c tunc
in Resultatohibus per tatem caxplicationem aequationibus reperietur semper crestim crescere
ia
equatio pro
in est 13 et 2n est 2
ut multiplicatione numerum membrolum  in progressione ad
aqualio cubus inabus x, habet termins 27 pro A, habet  pro X Eoilidsbipro ,  es genule er
pro tollendia litera X, ex duabus aequationibus 1e 10X + 11X et =0 et 20X - 21X et 20 fit aequatio nov
term
nongl. Sed tamen dabitur modis compendiosiis enuntiandi. Tentemus
actu ipso in primis a , X, N, nam in X aperi cietur ad terminos numero 1024
libera ab X, cujus termini sunt
Ex 10X + n =0 et 20X + 2 =0 fit = 19. 21 =0
11. 2.2
11. 205- 12.21
+ 10 2b 1h 12. 21 F
DE
. 21. 22 - 19. 10 212 =0
+ 10. 1
12. 21. 21
e a v. L = P21. 20.0
+ 10.212(16.
23
(+12. 23
() +102315
1. 2
G20pBHEI X, UX+ 920 + p. 15) E119 20) l- 5. 205 1 413. 21 1. 0
12. 2
+ 10215 12 23) 1X1 8. 26E +1322
11. 2051- 13.
r l dh- 13i
1eere, 18. 12 F1I. 2012 + 12. 20
et =101. ~. 22 - 11 12. 2021
=10. 11. 21. 22
litetes  + 1oilti
A usis catul potilluus saet ad investiganium quae figurae sut quadrables ex communi Geometua. sit aequatio 10y + H = 0 . ui  X otert in 0,
ta dy= C
d0
+10du