II.2 Proposition II.2
If a straight line be cut at random, the rectangle contained by the whole and both of the segments is equal to the square on the whole.
Proof
Let the straight line AB be cut at random at the point C.
Describe on AB the square ADEB (I.46), and through C draw
CF parallel to either AD or BE (I.31), so that CF meets DE
at F. The square ADEB is thereby divided into two rectangles:
ADFC contained by AD and AC (and since AD=AB, this rectangle
is contained by AB and AC, by Definition II.1), and CFEB
contained by CF and CB (again, CF=AB, so this rectangle is
contained by AB and CB). Their sum (Common Notion 2) is the
whole square ADEB, which is the square on AB. Therefore the
rectangle on AB and AC together with the rectangle on AB and
CB equals the square on AB.
lines 74–74 in main.tex
