Huygens (Descriptio automati planetarii, 1703) uses the simple continued fraction for the purpose of approximation when designing the toothed wheels of his Planetarium.
For the convergence of the continued fraction of the second class there is no complete criterion.
Muir, The Expression of a Quadratic Surd as a Continued Fraction (Glasgow, 1874).
Similarly the continued fraction given by Euler as equivalent to 1(e - 1) (e being the base of Napierian logarithms), viz.
Lambert for expressing as a continued fraction of the preceding type the quotient of two convergent power series.
A continued fraction may always be found whose n th convergent shall be equal to the sum to n terms of a given series or the product to n factors of a given continued product.
The infinite general continued fraction of the first class cannot diverge for its value lies between that of its first two convergents.