I am curious when the following Definition was formulated. Is this a product of Dan Shanks' work?
The following algorithm computes the simple continued fraction expansion of $\frac{P+\sqrt{D}}{Q}$, where $D$ is a nonsquare positive rational and $P$, $Q\neq0$ are any integers. Let $P_0=P$, $Q_0=Q$, and $a_0=\left\lfloor \sqrt{D}\right\rfloor$. For $i\geq1$, define
$P_i=a_{i-1}Q_{i-1}-P_{i-1} \tag{A}$
$Q_i=\frac{D-P_i^2}{Q_{i-1}} \tag{B}$
$a_i=\left\lfloor \frac{P_i+\sqrt{D}}{Q_i} \right\rfloor. \tag{C}$