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Geometry Problem 645: Archimedes' Book of Lemmas: Proposition 6, Arbelos

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.
 

Arimedes Lemma 6, Arbelos and Inscribed circle
 
 


Lemma 6 with Archimedes in the background as shown in 1584 book by Andre Thevet

Archimedes Lemma 6, Arbelos and Inscribed circle, Archimedes in the background


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

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