The watershed between the Vaal and Caledon is formed by chains of hills, which, leaving the main range of the Drakensberg at Mont aux Sources, sweep in semicircles west and south.
Right angled at C, semicircles are described on the three sides, thus forming two lunes Afcda and Cgbec. The sum of the areas of these lunes equals the area of the triangle ABC.] As for Euclid, it is sufficient to recall the facts that the original author of prop. 8 of book iv.
Cases of circles touching one another and inscribed in the figure made of three semicircles and known as ipl Xos (shoemaker's knife) form the first division of the book.
These intersections determine the centres of the semicircles CC which form the ends of the respective knuckles.
These semicircles and the circles A'A' are joined by tangents and short arcs struck from the centre of the figure.