460 
DE AEQUATIONIBUS CIRCULI SECTIONES DEFINIENTIBUS. 
elicum cpw, 9aw, 9Bio etc. deduci posse; et similiter se habebunt functiones 
Y', Y" etc. 
Ex. I. Sit n = 17, f = 8 atque designet 9 cosinum. Hinc fit 
Z — (<2? 8 -J- £ P 
7 
^ 3 + tg^ /i +tV^ 3 — -Aoox— T ' Y x-\- irhr) S 
oportetque adeo \]Z in duos factores quaternarum dimensionum ^,y resolvere. 
Periodus P = (8, 1) constat ex (2, 1), (2, 9), (2, 13), (2,15), unde y erit produc 
tum e factoribus 
x—910, x—99(0, x—918(0, x — 9l5(o 
Substituendo £ [k] -j-£\n — k] pro 9 k io, invenitur 
9(o-f-99(o-f-9l 3(o-{-91510 = £(8,1), (9(o) 2 —{— (991a) 3 -¡-(91 3(o) 3 -(-(9l5(o) 2 = 2—}— p(8,1) 
perinde summa cuborum = -§-(8, 1) —|—(8, 3), summa biquadratorum = 
+tV(8, 1); hinc per theorema Newtonianum coeificientibus in y determinatis 
prodit 
y = x^ £(8,l)<2? 3 -|-4-0(8,l) —f- 2 (8, 2>)~)xx — -£0(8,1) -f- 3 (8, 3)}<2?-[- -^((S,!)-)-(8,3)) 
y' vero ex y derivatur commutando (8, 1) cum (8, 3); substituendo itaque pro 
(8,1), (8,3) valores — *+*^17, — I 7 fit 
y = ^ + {i — ir\ln)x? — (i + iVl7)®« + (i + i\/l7)»—Ar 
y= * 4 +(i+iVl7)* 3 —(f — i\/l7)®— T v 
Simili modo \jZ in quatuor factores binarum dimensionum resolvi potest, quo 
rum primus eftt (x — 9 w) [x — 91 3 w), secundus [x — 9 9 w) [x—915 w), tertius 
[x— 9 3 w) [x — 9 5 (0), quartus (<2? — 9 10 w) (<2? — 9 11 w), omnesque coefficientes 
in his factoribus per quatuor aggregata (4, 1), (4,9), (4,3), (4,10) exprimi poterunt. 
Manifesto autem productum e factore primo in secundum erit y, productum e ter 
tio in quartum y'. 
Ex. II. Si, omnibus reliquis manentibus, 9 sinum indicare supponitur, 
ita ut 
Z = x™— V^ 14 + W# 12 — W^ + fiHM? 8 —+ tHvM+tMt* 
in duos factores 8 dimensionum y, y' resolvere oporteat, erit y productum e