THEORIA INTERPOLATIONIS METHODO NOVA TRACTATA.
285
repositi
lantitas
n = 0
absque
: expli-
M = 0
iompre-
ccessive
vicibus
ur, tan-
)
in * (c—6)^
icet sta-
A =
B
sinf(a — 6) 1 sin^(6 — o)
t» A cos % (a — c) | B cos % (b —- c)
+
sin [a — 6)sini(a — c) 1 sin|-(6 — a) sin ¿(6— c) 1 sini (c — a)sin |(c—6)
+
U
sin^(a — 6)sin* (a —c)sin|-(a — d) 1 sin|(è — a)sini(6 — c)sin£(6 — d)
-1 I T . J)
1 sinA(c — a) sin *- (e — b) sin \ (c — d) 1 sin -*- (d—a) sin * (d — l) sin i {d—c)
i A cos £ (a — e)
sin \ [a — b) sin f (a — c) sin % (a — d) sin ■*- (a— e)
, B cos \ (b — e)
sin^ (6 — a) sin £(& — c) sin %{b — d) sin ^(ò — e)
Ccosf(c — e)
+ ^
^ sin-*-
sin-*-(c — a)sin£(c— b) sin-t(c — d)sin±{c — e)
D cos £ {d — e)
sin A(d— a) sin (d — b) sin (d— c)sini(iZ — e)
E
etc. fiet
sin -*-(e — a) sin *-(e — ¿)sin£ (e— c) sin£(e — d)
T = A-\-A' sin£(i— a)cos£(i—b)
-f-A' sm%[t—a)sm^{t—b)
-f- A" sin \ [t — a) sin 4- (i — b) sin % (t— c) cos ^ {t—d)
-f- ./4""sin ^ [t — a) sin ^ [t—b) sin £ [t—c) sin \ [t — d)
+A sin £ [t — d) sin ±[t— b) sin \ [t — c) sin \ {t — d) sin \ [t — e) cos £ [t—/)
—^4, VI sin 4 —d) sin \ (t — b) sin \ [t — c)sin-|-(i— d) sin \ (t — e) sin-f (i—f)
+ etc.
quae progressio ad totidem terminos continuanda est, quot valores functionis X
dati sunt.
Coefficientes A, A", A", A" etc. etiam per algorithmum sequentem com
putari possunt. Designetur per B\ B", B ', B'” etc. id quod illi resp. fiunt, si
a, A, b, B, c, C, d, D etc.
resp. mutantur in
b, B, c, C, d, D, e, E etc.
Porro transeant
A, A, A", A w etc. in C\ C", C", C"" etc. vel in D', D", D", D'"’ etc. etc.
si