Introductio in analysin infinitorum

CONTINUIS. 297 meratore penultimo simplici: eademque lex in denominatoribus observatur. Scriptis ergo ordine litteris $a, b, c, d$, &c., ex iis fractiones inventæ facile formabuntur hoc modo $\frac{1}{0}; \frac{a}{1}; \frac{ab+1}{b}; \frac{abc+a+c}{bc+1}; \frac{abcd+ab+ad+cd+1}{bcd+b+d}$ ubi quilibet numerator invenitur, si præcedentium ultimus per indicem supra scriptum multiplicetur atque ad productum antepenultimus addatur; quæ eadem lex pro denominatoribus valet. Quo autem hac lege ab ipso initio uti liceat, præfixi fractionem $\frac{1}{0}$, quæ, etiamsi e fractione continua non oriatur, tamen progressionis legem clariorem efficit. Quælibet autem fractio exhibet valorem fractionis continuæ usque ad eam litteram, quæ antecedenti imminet, inclusive continuata. 360. Simili modo altera fractionum continuarum forma $a + \frac{\alpha}{b+\frac{\beta}{c+\frac{\gamma}{d+\frac{\delta}{e+\frac{\epsilon}{f+\&c.}}}}}$ dabit, prout aliis aliisque locis abrumpitur, sequentes valores $a = a$ $a + \frac{\alpha}{b} = \frac{ab+\alpha}{b}$ $a + \frac{\alpha}{b+\frac{\beta}{c}} = \frac{abc+\beta a+\alpha c}{bc+\beta}$ $a + \frac{\alpha}{b+\frac{\beta}{c+\frac{\gamma}{d}}} = \frac{abcd+\beta ad+\alpha cd+\gamma ab+\alpha\gamma}{bcd+\beta d+\gamma b}$ &c., Euleri Introduct. in Anal. infin. parv. Pp quarum