To two given straight lines to find a mean proportional.
Let AB, BC be the two given straight lines;
thus it is required to find a mean proportional to AB, BC.
Let them be placed in a straight line, and let the semicircle ADC be described
on AC;
let BD be drawn from the point B at right angles to the straight line AC,
and let AD, DC be joined.
Since the angle ADC is an angle in a semicircle, it is right.
And, since, in the right-angled triangle ADC, DB has been drawn from the right
angle perpendicular to the base,
therefore DB is a mean proportional between the segments of the base, AB, BC.
Therefore to the two given straight lines AB, BC a mean proportional DB has been found.
Q.E.F