# Proof: By Euclid

• Let the diameter $AB$ of the given sphere be laid out, and let it have been cut at $C$ such that $AC$ is double $CB$.
• And let the semicircle $ADB$ have been drawn on $AB$.
• And let $CD$ have been drawn from $C$ at right angles to $AB$.
• And let $DB$ have been joined.
• And let the square $EFGH$, having (its) side equal to $DB$, be laid out.
• And let $EK$, $FL$, $GM$, and $HN$ have been drawn from (points) $E$, $F$, $G$, and $H$, (respectively), at right angles to the plane of square $EFGH$.
• And let $EK$, $FL$, $GM$, and $HN$, equal to one of $EF$, $FG$, $GH$, and $HE$, have been cut off from $EK$, $FL$, $GM$, and $HN$, respectively.
• And let $KL$, $LM$, $MN$, and $NK$ have been joined.
• Thus, a cube contained by six equal squares has been constructed.
• So, it is also necessary to enclose it by the given sphere, and to show that the square on the diameter of the sphere is three times the (square) on the side of the cube.

Thank you to the contributors under CC BY-SA 4.0!

Github:

non-Github:
@Fitzpatrick