De curvis, quarum rectificatto per quadraturas mensuratur. 4-51 



sequenti modo se habebuot. Ponatur z = — tang^? scu tang ^ = -^ /iz, ac statuatur 



05= /- et V = 2^, 



nn cos* f "^ nn cos* <p 



erit semper, quicunque numerus pro n assumatur, /y{dx^-¥-dy^) = /dzV{i -¥-zz). Facile autem 

 ang. 9p eliminatur ob y{xx-*-yy) = j"» '^"d® fit 



coS9? = -,r hmcque y—— = cosnq), 



nV{xx-*-yy) y{^xx-*-yy) 



At si variabilem z retinere velimus, erit 



n nz n(n— i)(n — 2) n'2' n(n— l)(n — 2)(n — 3)(n — 4) n»zS 



12 1.2.3 8 1.2.3.4.5 32 



X = 



— etc. 



n — 2 



1 - /. nnzz\ 2 

 _„n(^l-^_j 



n(n— 1) nnzz n(n— l)(n — 2)(n — 3) n*z* 

 ' 1~2 4" -^ -1.2. 3. 4 l6 ®*^- 



r = 



« — ^2 



nn2z\ 2 



1 /. nnxzN 

 -nn(^lH-— ^ 



quae formulae, quoties n sumitur numerus integer positivus, finito terminorum numero constabunt. 

 Verum priores semper, etiamsi pro n statuatur numerus fractus, ad aequationem finitam deducunt. 

 Veluti si n = — > cum sit • 



iJSI^ 8liCll7&ia lllJfii!:)'! 



erit hinc cos (p = — ^^^^ 1 = ^lizf^y unde obtinetur 



' xx-i-yy xx-t-yy 



__e4_^ {yy-xx)* ^^^ {yy ^ xxY =. &k(xx -*-yy)^ 

 xx-i-yy (xx-t-yy)* ^•' "^ ' ^ '^ 



pro linea ordinis octavi. - 



»U ftll r-^- = \ -H ', irl/ 



tunj ■'i.jjii.ijjiH/ luyjijii ■jiSiji 



♦\ 'H>f'MRl)9b Pfjp /0 



* 



