Pagina:Werkecarlf02gausrich.djvu/25

IV. Pro ${\textstyle n=3}$ adest valor unicus ipsius ${\textstyle a}$, puta ${\textstyle a=1}$, cui respondet

$$\sin \omega =+0{,}8660254038\quad \quad {\phantom {\sin \omega =+0{,}8660254038}}$$

Hinc ${\textstyle 2\sin \omega =+\surd 3}$.
V. Pro ${\textstyle n=7}$ adsunt valores tres ipsius ${\textstyle a}$, puta ${\textstyle 1}$, ${\textstyle 2}$, ${\textstyle 4}$: hinc habentur sinus

$${\begin{array}{rl}\sin \omega {\phantom {1}}=+0{,}7818314825{\phantom {,}}&\\\sin 2\omega =+0{,}9749279122{\phantom {,}}&\\\sin 4\omega =-0{,}4338837391{\phantom {,}}&\\{\begin{array}{l}\hline {\text{Summa}}=+1{,}3228756556,\end{array}}&{\text{adeoque }}2\Sigma \sin a\omega =+\surd 7.\end{array}}$$

VI. Pro ${\textstyle n=11}$ valores ipsius ${\textstyle a}$ sunt ${\textstyle 1}$, ${\textstyle 3}$, ${\textstyle 4}$, ${\textstyle 5}$, ${\textstyle 9}$, quibus respondent sinus

$${\begin{array}{rl}\sin \omega {\phantom {1}}=+0{,}5406408175{\phantom {,}}&\\\sin 3\omega =+0{,}9898214419{\phantom {,}}&\\\sin 4\omega =+0{,}7557495744{\phantom {,}}&\\\sin 5\omega =+0{,}2817325568{\phantom {,}}&\\\sin 9\omega =-0{,}9096319954{\phantom {,}}&\\{\begin{array}{l}\hline {\text{Summa}}=+1{,}6583123952,\end{array}}&{\text{et proin }}2\Sigma \sin a\omega =+\surd 11.\end{array}}$$

VII. Pro ${\textstyle n=19}$ valores ipsius ${\textstyle a}$ sunt ${\textstyle 1}$, ${\textstyle 4}$, ${\textstyle 5}$, ${\textstyle 6}$, ${\textstyle 7}$, ${\textstyle 9}$, ${\textstyle 11}$, ${\textstyle 16}$, ${\textstyle 17}$, quibus respondent sinus

$${\begin{array}{rl}\sin \omega {\phantom {11}}=+0{,}3246994692{\phantom {,}}&\\\sin 4\omega {\phantom {1}}=+0{,}9694002659{\phantom {,}}&\\\sin 5\omega {\phantom {1}}=+0{,}9965844930{\phantom {,}}&\\\sin 6\omega {\phantom {1}}=+0{,}9157733267{\phantom {,}}&\\\sin 7\omega {\phantom {1}}=+0{,}7357239107{\phantom {,}}&\\\sin 9\omega {\phantom {1}}=+0{,}1645945903{\phantom {,}}&\\\sin 11\omega =-0{,}4759473930{\phantom {,}}&\\\sin 16\omega =-0{,}8371664783{\phantom {,}}&\\\sin 17\omega =-0{,}6142127127{\phantom {,}}&\\{\begin{array}{l}\hline {\text{Summa}}=+2{,}1794494718,\end{array}}&{\text{adeoque }}2\Sigma \sin a\omega =+{\sqrt {19}}.\end{array}}$$