Let AB, the diameter of a semicircle,
be divided at C so that \(\dfrac{AC}{CB}=r\).
If DE is the diameter of the circle inscribed in the
arbelos ACB, then \(\dfrac{DE}{AB}=\dfrac{r}{r^2+r+1}\).
"Arbelos" means shoemaker's knife in Greek.
Lemma 6 with Archimedes in the
background as shown in 1584 book by Andre Thevet
Books of Lemmas Index
Proposition 1
Proposition 2
Proposition 3
Proposition 4
Proposition 5
Proposition 6
Proposition 7
Proposition 8
Proposition 9
Proposition 10
Proposition 11
Proposition 12
Proposition 13
Proposition 14
Proposition 15
