Octagon constructions and a lockable square house
Two compass methods for building a square and octagon in a circle, plus a securable dwelling
Two parallel columns teach quick compass constructions: the right column makes a quadrangle and turns it into an octagon, dividing a square into eight equal parts; the left column raises a square and octagon on a given line a b and divides a circle into eight parts. Each column carries a labelled diagram at the top of the page. Below, a perspective of a roofless square house accompanies a note on arranging a household so that no servant or lodged stranger controls the exit at night: closing the single door m shuts up the whole house.
On this page
Dividing a square into eight equal parts
Draw line d e, set the compasses on d for line g f and on e for line h m, then draw s p through the two intersections. A circle centred at c on the cross marks the square's corners; measure b c transferred to a b and d r on every face divides the square into 8.
Dividing a circle into eight equal parts on line a b
From line a b, arcs struck from a (M n) and from b (o p) give two intersections through which line c d is drawn, making four right angles at centre S. A circle there is quartered, and halving one quarter carries the division to eight faces.
A dwelling secured by a single door
A roofless square house is drawn in perspective. The note advises arranging servants' and guests' quarters so that at night they are not masters of the exit and cannot reach the owner's rooms; closing the door m shuts up the whole house.
