Let's examine the accuracy of the following approximate construction - to the extent that this examination is made possible by a four-figure function table. Let $C$ be the second trisection point of the diameter $AB$ of circle $k$ from $A$ (i.e., $AC = 2CB$), and let $D$ be one of the endpoints of the chord perpendicular to $AB$ at $C$. Finally, let $E$ be the intersection point of the circle centered at $A$ with radius $AD$ and the segment $AB$. Then the segment $BE$ is approximately equal to the side of a regular 17-gon inscribed in $k$.
Let's choose the radius of the circle $k$ as the unit. Then the side of the inscribed regular 17-gon is:

$$
a_{17}=2 \sin \frac{180^{\circ}}{17}=2 \sin 10.588^{\circ} \approx 2 \cdot 0.1838=0.3676
$$

On the other hand, from the right triangle $ABD$, using the Pythagorean theorem, and then applying the geometric mean theorem to the height $CD$:

$$
AD^{2}=AC^{2}+CD^{2}=AC^{2}+AC \cdot CB=AC \cdot AB=\frac{4}{3} \cdot 2=\frac{8}{3}
$$

and thus

$$
BE=AB-AE=AB-AD=2-\sqrt{\frac{8}{3}} \approx 2-1.6330=0.3670
$$

(The square root was calculated without a table, rounding the fourth decimal place.)

By comparing $BE$ with $a_{17}$, we see that the approximate value is smaller than the actual value, and the difference is 0.0006, which is less than 2% of the actual value.

Gábor Pettkó (Tatabánya, Árpád III. o. t.)

Note. The error in the construction can also be characterized by the difference by which the central angle corresponding to the chord $BE$ is smaller than $360^{\circ} / 17$, or by the difference by which the 17-fold central angle is smaller than $360^{\circ}$. The latter angle, using a multi-digit table, is found to be less than $0.5^{\circ}$.