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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 88r, page id 00068201:0175
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Haec in scheda isla coepta atque affecta demum
in scheda 12 jannar. 1684 absolvi
i  caebcet
Ad tollendas ex aequationibus literas incognitas Methodum inveni generalem, in qua
stane pene omnis calculi algebraici viscontinetur, incipiemus a pluribus aequationibus sed
simplicibus, plurium literarum; utque in s datis ordinem aliquem observemus
quo scilicet in quaesitis, ubi inventa erunt propessio appareat, ideo omnes coeffi
pieutes primo aequationis sunt denarie supra denari secundae supra
in vicenarium, tertiae supra tri enarium; rursus litera a coefsicientes suo denario
vel vicenario vel tricenario addant unitatem, literae b coefficientes
binarium et ita porro. Et ila stabunt aequationes
20 + 21 a + 22b ae qu. 0.
10+ 11 a + 12 b  aequ. 0.
ambae inneliplicentur per arbitrarias et componentur, tolli poterit litera una a
et stubit 10l + 11 l a + 12lb aequ. 0. 20m + 21ma + 22 m b 49. 0. Quas duas
equationes componendo,  aeq 2fer +10 l + 11 l a + 121b 1
 1 m  um a 6, 2 2m b5
et proinde, ut tollatur , fiet ul aequ et 22m
g. 0.
13
et faciendo laeqo 22
et m aequ. 12 salis factum est. et fier: + - 10. 22 ∞, 11. 22a aeg. 0.
+ 11. IR +12. 21.
Hinc jam habetur Methodus tollendi eandem literam in duabus aequationibus repertam
multiplicatione scilicet per cucem Nempe sit  quationes 10+ 11a + 12b 49. 0.
et 20+21 a+22b a9. 0. Multiplicetur aequ. 1. b per 22, et aequ. 2 per 12 et
subtrahatur una ab altera, sublata erit litera b. nempe stabit:
+ 10. 22 + 11. 22a aeq. 0.
- 20. 12 D21. 12 a
sint jam tres literae: aequationes et literae: 10 + 11 a + 12b + 13C690 et 20 + 21a rub 2 )
et 30 + 31 a + 32b +33C aeq.0. prima multiplicatione per crucem tolli possete
sed quia ea bis institui posset, satis est simul plures conjungere adEibitis
literis arbitrariis, et fiel: 10l + ula 42lb + 13lc . )
eut 131 + 23m + 33n aeq. d
20mtuma tum b + 23mC 4 ∞7. 0.
30n +31na +32n b +33n C
et 12l + 22m + 32n Eg. 0 et
Ed quia ita calculus aeque propemodum difficilis ac primus ideo salius erit resumere
muthiplicatio nem per cuicem, et fe + 10. 23 + 11. 23 a + r4 3 b aeg. 0. 10. 351 1. 35 +12. 32b
e et +20. 33+4. 33c
c30.23- 3123 a
+10, 12. 25. 33
- 10. 13. 23, 32
- 12. 13. 20.337
4 13. 13. 20, 3E
=10. 12. 23. 33
+ 1. 13 22. 23
+ 12. 1323. 30
= 13. 13, 22. 30.
sed ita nondum
homveoptotice.
.23b
1
L 1I. 13. 23. 32
(= 12. 13. 21. 33
=13, 13. 21.32
=20. 13 - 21. 134 - 22. 4 b
Ergo + 10. 28 0 1133
3. 13 - 91. 13a - 32. N67
+ +y. 23 9+2. 33
-20. 13 32.0 C.
= 1.33 ,12. 83
430. 13 - 22. 13
= C+ n 23
+31 - 22. B
=13, l+23. 3em K7) Ex 5 et 6
= 12. 33l - 22. 37M.
290
et fiat  l aego - 23. 31 et Magot 13. 52
110
+ 22. 33
Et habebimus: n aequ. + 13. 23. 32 - +3. 23. 32
13. 22. 37 = 12. 23. 383
Ergi ex aez 4. fier: - 10. 23. 32. 95
apparet modus hactandi
+. 10. 22- 33.33
+ 13. 20.32.33
C 12. 20. 33.33
literas  omnes
seu
= H. 12. 335
M0