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