a = 0° 
A = 4- 408 
a 
= 30° 
A' = 4- 89 
a = 60° 
b = 90° 
B = -j- io 
b' 
= 120° 
B' = 4- 338 
b" — 150° 
c — 180° 
C= 4-1238 
c 
= 210° 
C = 4-1511 
c = 240° 
d = 270° 
D = 4-1462 
d' 
= 300° 
D' =+ 1183 
d" = 330° 
THEORIA INTERPOLATIONIS METHODO NOVA TRACTATA. 309 
Distribuamus hanc periodum primo in tres periodos quaternorum terminorum 
A' =— 66 
B" — -f- 807 
C" = —j— 1583 
D" = -j- 804 
In formula 
X' = y-)-y'cosa7-|-y"cos 2 oc 
-}- d' sin <2? -f-3 " sin 2 oc 
fit itaque 
y = \ [A -j- B -)— C -}- D) — 7 79,5 
y' = ^(4.cosa-(-^cos&-}- Ceos c-j-Deos i?) = %{.A — C) = — 41 5',0 
3' = ^{Asma-\~Bsmb-\- Csinc-j-Dsini?) — %[B — D) = — 7 26',0 
y"= y(4cos2a-f - -® cos2 ^+^ ,cos2c +-^ cos2 ^) — — B-\-C—D) 
— H-43',5 
3" = ^.[Asm'la A-B&in 2b -|- Csin 2c -|- -D sin 2d) — 0 
et similiter pro periodo secunda ac tertia. Hoc modo emergit 
Pro periodo 
ubi y — 4x 
T 
r 
T 
8' 
t" 
8" 
prima 
0° 
4-779,5 
— 415,0 
— 726,0 
4-43,5 
0 
secunda 
120° 
4-780,2 
— 404,5 
— 721,4 
4“ 0,9 
+ 17,1 
tertia 
240° 
-¡-782,0 
— 413,5 
— 713,3 
+ 11,7 
— 20,3 
Hic porro exhibetur y per formulam 
^-(779', 5 + 780,2 + 782,0) 
-j-1-(779,5 -f-780,2 cos 120° —f- 7 82,0 cos 240°) cos 4,^ 
-)- 1(7 8 0,2 sin 1 20°-|-7 82,0 sin 240°) sin 4# 
sive per 
780,6— 1,1 cos4a?— l,0sin4#, et perinde 
y' per —411,0— 4,0cos4.2?4- 5,2sin4a? 
3' per —720,2— 5,8cos4<a?— 4,7sin4o? 
y" per 4~ 21,7 4~ 21,8 cos 4 x— 1,1 sin 4 x 
8" per — 1,1-j- 1,1 cos 4 #4-21 sin 4# 
Quibus valoribus in X' substitutis prodit formula 12 valores propositos exhibens 
m