**Since** **the** **area** **of** **a** **circle** **equals** **that** **of** **the** **rectilineal** **triangle** **whose** **base** **has** **the** **same** **length** **as** **the** **circumference** **and** **whose** **altitude** **equals** **the** **radius** (**Archimedes**, **KIKXou** **A** **ir**, **prop**.**i**), **it** **follows** **that**, **if** **a** **straight** **line** **could** **be** **drawn** **equal** **in** **length** **to** **the** **circumference**, **the** **required** **square** **could** **be** **found** **by** **an** **ordinary** **Euclidean** **construction**; **also**, **it** **is** **evident** **that**, **conversely**, **if** **a** **square** **equal** **in** **area** **to** **the** **circle** **could** **be** **obtained** **it** **would** **be** **possible** **to** **draw** **a** **straight** **line** **equal** **to** **the** **circumference**.