Construction of Components of Major

Proof

 * Euclid-X-33.png

From Construction of Rational Straight Lines Commensurable in Square Only whose Square Differences Incommensurable with Greater:

Let $AB$ and $BC$ be rational straight lines which are commensurable in square only such that:
 * $AB^2 = BC^2 + \rho^2$

such that $\rho$ is incommensurable in length with $AB$.

Let $BC$ be bisected at $D$.

From Construction of Parallelogram Equal to Given Figure Exceeding a Parallelogram:

Let a parallelogram be applied to $AB$ equal to the square on either of $BD$ or $DC$, and deficient by a square.

Let this parallelogram be the rectangle contained by $AE$ and $EB$.

Let the semicircle $AFB$ be drawn with $AB$ as the diameter.

Let $EF$ be drawn perpendicular to $AB$.

Join $AF$ and $FB$.

Also see

 * Definition:Major (Euclidean)