Finding a lost centre

“Ein punckt zu vinden der ab gethan ist vnd nit west wo der zirckel gestanden ist”: so the workshop booklet Geometria deutsch, attributed to Mathes Roriczer, sets out to find the point of an arc when nobody knows where the compass stood. Take two points on the arc where you will, set the compass in the one, open it to the other and swing an arc; then the same from the other point. The two swings cross above and below. Do the same again beside them, as far off as you will. Lay a line through each pair of crossings: where the two lines meet, the booklet says, “in dem selben punckt ist der zirckel gestanden”. Each line halves a chord at right angles, and every such line runs through the centre, as Euclid shows at the opening of his third book; so the point is exact. Set the compass there and it closes the circle the arc was taken from.