’ 
THEORIA INTERPOLATIONIS METHODO NOVA TRACTATA. 
273 
Multiplicentur hae aequationes resp. per 
i 
(a — b){a— c)(a — d). • 
1 
.. (a t) 
') 
{b— a) (è— c)(i — d) .. 
1 
. .{b t) 
(c — c) (c — b) (c — d) .. 
i 
..(c — t) 
1 
1 
? « 
-M 
i ® 
..(d-t) 
nnium 
1 -m — 2 
l 
(t — a) [t — b) {t — c).. 
prodeatque inde per productorum additionem 
A 
: cum 
(a — b) (a — c) (a — d) . 
1 B 
. .(a — t) 
1 {h — a ){b—c){b — d). 
1 C 
..(b-t) 
1 (c — a) (c — b) (c — d) • 
I D 
. . (c — t) 
• 
1 (d—a){d—b){d—c) . 
-f- etc. 
1 T 
..{d-t) 
H 
C+. 
1 
1 
o* 
C-+, 
1 
cs. 
-d)... 
ii con- 
im m. 
3spon- 
X va- 
t va- 
m-f-1 
Tunc ex art. 1, ubi m idem denotabat, quod hic nobis est m-\-1, facile conclu 
detur, fieri W = 0; quamobrem multiplicando per (t—a) (t— h) (t— c)... prodit 
rp {t— V) — c ) {t • • • A 
(a — b){a— c){a— d) . . . 
■ {t— a) {t — c) {t — d) . . . j) 
' (J — o) (b — c) {b— d) ... 
. {t— a) (t — b) {t — d). . . p 
' (c —a) (c — b){c — d). . . 
■ [t—a){t — b){t — c) . . . t\ 
[d—a){d—b){d—c) ... 
—f— etc. 
4. 
Formula in art. praec. inventa, ita comparata est, ut sponte sine omni cal 
culo pateat, si pro t quantitatum a, b, c, d . . aliqua in illa substituatur, valorem 
respondentem A, B, C, D.. inde prodire. Neque hoc solo respectu sese commen 
dat: certo enim ad usum practicum longe commodissima est, saltem quoties uni- 
35