98 



Ex his jam valoribus colligitur : 



X sin (p — Y cos (p == (/— ô') sin (n + 1 ) Ô -f-(/H-6r) sin (« — 1 )$ 

 X cos CJ) + Y sin Cp =3 (/— ôT) cos (72 -h 1 ) a -4- (/+ ôT) cos (n — 1 )e , 

 quae acquationcs, ductae in ^Cjiirznâ^, et integratae, si brevita- 

 tis gratia ponatur f -\- g z:^ b ci f — g ^^a^ dabunt : 



/aCpCX sinCp - Y C0SC|)) — _ "■^'^"^Çn+O^ _ n6cos(n-0^ 



fd<^ (X cos,$ -V- Y sin (t)) = -h ''"';;^^|-^^ + "^""/^7'>^ • 



§.8. Si igitur pro integralibus hi valores substituantur, no- 

 strae coordinatae erunt : 



a cos (71 -f- 1 ) ^ -f- b cos (n — i ) ô 



— -4:7 COS (/j -i- 1) ^ — ^^j-^ COS (;j — 1) ô 

 a sin (n -f- 1) -f- 6 sin (n — l;$ 



— ^^^ sin Oi-h 1) — ,1^77 sin Qi — 1) 0. 



At binis membris rite conjunctis istae coordinatae pro curvis quae- 

 sitis cum ellipsi eommunem rectificationem habentibus , ita erunt 

 expressae : 



X :zi. —^^ cos(7î-i-l)^— ^^i-TT cos (77 — l) ^ 



yz:z—^^ sin(n-i-l)$ ~ :;;z:r\ sin(7z —1)0, 



quae expressiones a supra allatis aliter non diffei-unt nisi quod hic 

 littera b négative sit sumta. Ubi notandum, casu quo n:zzQ ipsam 

 ellipsin esse prodituram. Posito enim nzn Q fiet : 



X z^:ia -\- b) cos Q et 2/ z=: (a — b) sin Q. 



§.9. Si sumatur 11 :zz 2 prodibit sine dubio curva post 

 ellipsin simplieissima. Repeiùetur autem : 



a; zz -^ cos 3 — b cos $ et f/ =3 y sin 3 $ — 6 sin 0. 



Loco Y scribamus litteram c et quaeramus chordam yxx-+yyzzzz. 



