456 
DE AEQUATIONIBUS CIECULI SECTIONES DEFINIENTIBUS. 
tangto = ¿(1 —RR-^-R*— R G . . . ~R 2n ) 
sive (quoniam 1 — R~ n = 0, RR — jR 2w—3 = 2 i sin 2 to, R i — R ln ~ 4 = 2 i sin 4 to etc.), 
tang t*> = 2 (sin 2 u) — sin 4 to -f- sin 6 to . . . Ijl sin [n — 1) to) 
III. Quum habeatur 1 -\-RR-\-R i . . . -|- R ln ~* — o fit 
n = n-\ — RR-R\,.R 2n - 2 = (l —1) + (i—i22Z) + (l — R l ),..-\- (i— R 2n ~ 2 ) 
cuius aggregati partes singulae per 1 — RR sunt divisibiles. Hinc 
i~ e E “ (1 -\-RR-\-R A ) . . . -f- (l RR-\- R*. . . _|_ jR 2n—4 ) 
=' (%— 1) —|— (w — 2) jRR-\- [n— 3)jR 4 . . . -|- R 2n ~ A 
quocirca multiplicando per 2 , subtrahendo 
0 = [n — ^{l+RR + R* + R 2n ~ 2 ) 
rursusque per R multiplicando fit 
= (»-l)S + (*-3)S‘+(,-5)ff...-(»-3) il 2 “- 3 — (n—1) K‘ n ~' 
unde protinus deducitur 
cosecto = — 1) sinto—)— (n — 3) sin 3to . . . — [n— 1) sin [‘In — l)to) 
= ^(Jn— 1) sinio-)-(w — 3) sin 3t« -f- etc. -f- 2 sin [n — 2)to) 
quae formula etiam ita exhiberi potest 
cosecto = —-^-(2 sin 2 to-)- 4 sin 4 to -j- 6 sin 6to . . . -\-[n — 1) sin [n — 1) to) 
IV. Multiplicando valorem ipsius y^iir su P ra tra,ditnm per 1 -f- RR et 
subtrahendo 
0 = (ra —l)(l+JRJ2 + # 4 ...-f-JR 3w “ 2 ) 
prodit 
"i-Vjf = {»—i)RR-\-[n — — 6)Jf' — (n — 2) -R"‘- 2