With different kinds of Regular Figures with the same area, it is not possible for any of the sides ever to be equal. Nevertheless, when once the ratio of the sides of two equal areas has been taken; the same kind of equality for the same [figures] will always be kept. And conversely: if the ratio of the sides be kept the same, the figures themselves will be equal [in area]. If the area situated inside any of the allowed regular Figures shall be 4, the side shall be:

We will be able to make use of these Logarithms: For given the side of any figure(of those placed above); of another, by all means given equal, to find [the length of ] the side. For let the side of a Hexagon be given of 5 parts; I desire to find the side of the Dodecagon, with area equal to the Hexagon.
The difference of the Logarithms of the sides of the Hexagon and the Dodecagon added together, being taken away from the Logarithm of five; the remainder will be the Logarithm of the required side.
Or by Ch. 15:

If the area of the Hexagon, of which the side being given of 5 parts; or of the Dodecagon, of which the side being found of 2408582914 we wish to find: or Chapter 28 should be consulted: by taking the sides with double the Logarithms.

The equality of the figures is being taken from the equality of the Logarithms.

Or by the Logarithms of this chapter can be found the side of the Square, equal in area to the same Hexagon. For

Therefore we have the area of the same three figures, the Hexagon, the Dodecagon, and the Square, all surely by this method equal to 649519053.