Full text: [Allgemeine Analysis] Theoria combinationis observationum erroribus minimis obnoxiae (3. Band)

282 
NACHLASS. 
2lcos^-i-|-2i' cos f cosf¿-j- etc. 
-|-$sin4-i-|-35'sin|4-f-i8"sin|-i--f- etc. 
Quamobrem pro hoc casu viam aliam ingredi oportebit. 
Multiplicetur X per cos (-|-#-{-&), proditque, si termini ultimi in X sta 
tuuntur a m cos9W<2?-|-6 m sin moc 
acos(£ £ a'cos (•!#-}-&)+£ a" cos (f oc-\-k)-\- .... 
+icr COS((fW-j-£)<0-h^) 
-f-^-a'cos(|-ic— ^)+l«"cos(|-#— yt)4-4-a'"cos(|-<r—k)-\- .... 
-f- a m cos ((m—-f) x — 
-f sin sin (f <*?+&) + 
-f- £ t> m sin ((m -f- 4-) x-\-k) 
-|-£i)'sin[\x—^)-f-^"sin(|-a?—k^j —(— y$sin— &)+• •• • 
-f-\ t) m sin ((m — \)oc — k) 
lam si in hac expressione pro x successive substituitur a, b, c, d... .t, quod 
inde provenit resp. per 
, \ 
1 
sin f (a — 6) sin£(a — c) sin £ {a — d).... sin a (a — t) 
1 
sin£(6 — a) sin 1(6 — c) sin-£(6 — d).... sin£ (6 — t) 
1 
sin a (c — a) sin % (c — 6) sin a. (c — d) .... sin a- (c — t) 
1 
sin£(d — a)sinA.(d— 6) sin-J-{d—c) .... sin-|-(i2—t) 
etc. 
i 
sin 4- [t — a) sin -J- (i — 6) sin £ (£ — c) sin £ {t — d) . . . . 
multiplicatur, productorumque aggregatum == W ponitur: ex iis, quae in art. 2, 
(in casu priori, ubi m idem erat, quod hic est tradidimus, facile sequi 
tur, haberi 
W = ^[%if m a m cos(\[a-\-b-{-c-\-d-{- . . . —#) —j— Ar) 
T(2i) 2w b w1 sin(^-(a-f-&-|-c-(-^-}- . . . 
Ex altera vero parte erit
	        
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