Altera Plückeri theorematis demonstratio. [185] 35 
‘ ‘ 
e ste. AM! n P . . sBeis . 
His praemissis „. et 7 quolienles ita eligantur, ut aequationis (d) ea coefliciens, 
quae ad dignitatem .r? pertinet, in nihilum abeat: prodit aequatio conditionalis 
2, en a 
0321 12/ vl 2101 0310 
r 5 F A m n 
et demonstrandum est transformationem per formulas (27) realem esse sive —. et 7. valo- 
res reales sumere, quibus adhibitis aequationi (28) satis fiat. Ponamus igitur 
M—= uam" + 3«@ m*m" + 3a m'm'? + a m“?, 
30 2] 12 03 
N= «n*" + 3a nn" - 3a n'n"? En an", 
30 21 12 03 
unde derivationes 
MM. ME 
N, N, N 
yapyz Wr: > ua Lt 
rite ducantur: tum fit 
>30 03 
a= Mn" + Mn" = Nm? -L 2N mm" 4 N m", 
al E y” ya x? 
a= Mn?’ 2M nn" Mn? =NmW+N m“, 
12 yar ya = Yy x 
a=aem + uam", 
10 10 01 
a=an tan 
01 10 vl 
et calculo longo quidem, tamen minime difhieili eruuntur formulae in theoria aflınium curvarum 
tertii ordinis gravissimae: 
ra aa % — MM, (mn mn’)? 
21 3012 ya y° 22) 
=\(0 — ao u + | @aa-—aa|mm" — r — a@ a \ m"? (m'n' — m''n‘)? 
‚ı2l 3012) a EZ 3003 12 0321 \ 
aa—aa=ı? (a — ax a, mn — rn @ — a@ \ !(m'n" + m'n‘) 
Sa 12) 2112 3003) 
+2 BE ar man (3% — m’'n' \? 
12 0321) | E 
—aa=/N’— NN (m’n — m’'n')? 
12 0321 | yx y> 22) 
(29) wR 1! 
a NE N I 
‚laı \ 
3012, 2112 3003 
a? — a a \ n"?) (min — m'n‘)?, 
12 0321 \ 
u 2 — aa 
(2112 3005) 21 3012) lı2 0321 
= (au — oe —& En — a !a Me — a @\) (mn! —m'n)$, 
!\2112 3003) 21 3012) 12 0321) ) 
aa—aa= [Ma —Me\ (min — mn‘), 
3001 2110 Äyor 10) 
aa—ıı= Br — Na\ (min — mn‘). 
1201 v310 (yo 210) 
[e)1 
