To two given straight lines to find a third proportional.
Let BA, AC be the two given straight lines, and let them be placed so as to
contain any angle;
thus it is required to find a third proportional to BA, AC.
For let them be produced to the points D, E, and let BD be made equal to AC;
let BC be joined, and through D let DE be drawn parallel to it.
Since, then, BC has been drawn parallel to DE, one of the sides of the
triangle ADE, proportionally, as AB is to BD, so is AC to CE.
But BD is equal to AC; therefore, as AB is to AC, so is AC to CE.
Therefore to two given straight lines AB, AC a third proportional to them, CE,
has been found.
Q.E.F