Gerhardt: Leibniz über die Determinanten. 421 



Neutrius neinpe ipfius i coefficientes sunt o, 10 — 20, 11 — 21 



seu compendio o , 51 , 52 

 Habemus combinationes cum suis signis debitis et ex iis aequationeni 

 incognitis affunititiis pariter ac litera x carentem 



+ 10.21.C.2 — 10.22.U ubi 12 et 22 = 1 



J -* = o 



— 1 1 .20.52 + 1 2.20.5 1 e t 5 1 == 10 — 20 



et 52 = 1 1 — 2 1 . 



Unde fiet 



+ 10. 1 1 .2 1 — 1 o. 1 0.22 



— 10.2 1 .2 1 + 1 0.20.22 ., . , 



= o , posito si placet 12 et 2 2 = 1 . 

 — 1 1 . 1 1 .20+ 10. 1 2.20 



+ 1 1.20. 21 — 12. 20. 20 



Si 1 o + 1 107+1 ixx + 1 3a; 3 + 1 4X 4 multiplicetur per 30 + 31^ + 3 ixx + 3 3a; 3 



et 20 + 2 i^+2 2^x' + 2 3^ 3 4- 24.C 4 4o + 4ix+42o;^+43^ 3 



ubi 14, 24, 33 = 1 et 43 = — 1, componendo producta in unam aequa- 

 tioneni fiet 



10. 30 + 1 1.30^+1 2. 30x2?+ 1 3.30a? 3 -f- 14.30a; 4 



10.31 11.31 I2 -3i ^-S 1 +14. 31a; 5 



10.32 11-32 12.32 13-32 + 14.32a; 6 



10.33 IJ -33 I2 -33 J 3-33 + 14-33^ 7 



20.40 + 21.40 22.40 23.40 24.40 



20.41 21.41 22.41 23.41 24.41 



20.42 21.42 22.42 23.42 24.42 



20.43 2I -43 22 -43 2 3-43 2 4-43- 



Sunt septem aequationes, quibus tollendae sex literae 30,3 1,32,40,41,42; 

 nam 33 = 1 et 43 = — 1, unde, quia et 14 = 24 = 1, fit 14.33 + 24.43 — ° 

 per se. 



Unitas babet coefficientes o o o 10 — 20 11 — 21 12 — 22 13 — 23 

 seu 3 1 , — 41 seu compendio 000 50 51 52 53 



30 babet coefficientes 101112 13 14 o o 



31 01011 12 13 14 o 



32 0010 11 12 13 14 



40 babet coefficientes 202122 23 24 o o 



41 02021 22 23 24 o 



42 o o 20 21 22 23 24. 



Hinc cum 53 conjungantur omnes seniones ex coefficientibus, demta 

 linea prima et columna ultima, cum 52 omnes seniones ex coefficien- 

 tibus, demta linea 1 et col. penult. etc. Quilibet senio habet tres notas 

 sinistras 1 et tres notas sinistras 2, summa, notarum dextrarum est 9. 



Sitzungsberichte 1891. 39 



