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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 177v, page id 00068201:0354
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optium ratio tollendi literas
sit 1m + 21 = 5
+1. 12m ff2. 12n= (. 12
=2. H1B 2. 121) = - 2. 15
1m + 2n + 3 = 5
Um + 1Zn + 13p = 15
2 m + 22n +23p = 25
+ 2. 2, H1. 21
+ 1. 1. 1X. 22
= 1. 2. 12. 21
- 1. 2 11. 22
iI m 4 12 = 15. Protollenda.
M = 45. 12,1.12
=215 -2.11
+2. EIn =
= 1. 2. 15. 21
= 1. 5. 1. 22
4 1. 1. 15. 22
C1
1m + 2n + 3p =, 5
1 in + 127 + 13 p = 15
21 im + 22p + 23 p = 23
+ia m + 2an + zapsa.
+ 1b m + 1bn + 1364 5b
=21C m F22cn, +23Cp  (25C
1 a + 1b 421C =0
una
CB 2n   5. 11
1. 121
-1. 22n
4 ∞z. 5. 11. 21
en
=1815
+5. 21
- 1. 25
protollendis
literis dua
bus, datis aequatioibus
tribus. Tres aequatione
propositae 1. 2. 7. multi
plicantur per abbitrarias
a, b, c. brientur tres
aequationes nova 4,b
1 ex illis composita in qua
ut tollacau quos termines, m et
(b2a+126422C =0 orientur duae aequationes sine m et n’ou
a21(C, fit Hii2 12a + 2. 12G = 2. 12. 21C r o
ollenda est una litera
sit +1. 12 a = 2C, 12. 21 c nempe agg. 5 et 6.
= 2. 11 a
Ergo a =
n La
= 11. 22
+ 12. 21
quarum ope tollendo unum
literam a habetur valor
= alterius b (adeoque et ipsius
=+C. 22 C manente c arbitraria. ita subtatio
duarum literarum reducta est ad theorema
=2. 11 aptea inventum pro sublatione uniqus, et
+1. 12
ita porro
Im + 2n =5
Y1 m + 12n = 15
+ 1m + 2n + 3p = 5
+DM + 1ZN + 13p = 15
= 2 1 m + 22n + 23 p = 25
sit 2.11 b = +2. 21c
= 1. 22
ita sublatio duarum m n, reducitur
1. 12.
fit (12. 11 n + 5. 11
ad sublationem duius a
si ergo C= 1. 12 = 2. 11
= 1. 12
1a FHOD 2IC()
el
c. 15
2. 11 = 1.
12. 21= 1122C
abq
1. 12 = 2. 11
42. 11.2)
fiet a = 12. 21 - 11. 22
Ergo P = 5, 1221 -, 11. 22 + F 1. 15. 22-2. 15. 215=1. 2.2F
b = 1. 22 = 2, 2]
3, 12, 21- 3. 11. 224 1. 13. 22 =2.19. 21 42. 11. 2511225
12
pro5 scribamus 49; pro 15, - 14 pro 25 sculmu 244
 P: 9= 4. 12. 21 4 4. (11. 22 ol. 14. 22102147150, 1147
03. 12. 21-0311. 39101. (3. L1 -02. 15, 21+02, 13 - 01. 12. 23
ms
nominatire O, 1,2
fiet
0 posteriores semper in nneralore 1. 2. A compo
1+ a nant  in numpralore vel
utcunque transpositi, quia in nominatores 1. 2. 3 ulcunque
in et n remoti
est pro p, quiade nominator mulliplicat p
ccanspositi, quia 1,2 sunt met
40 proq quia minerator mulliplicat a
osit
Hint methodus generalis pro ntollendis
habent
ampertigua i i in quibus Jum
lit 
rodisferi
out 4. .2 et
ndifferum
sct a 4ve
1
4 est pu
2a +12b422C
atet
 c