construction of fourth proportional

Task.  Given three line segmentsMathworldPlanetmath a, b and c.  Using compass and straightedge, construct the fourth proportional of the line segments.

Solution.  Draw an angle (α) and denote its vertex ( by P.  Separate from one side ( of the angle the line segments  PA=a  and  AB=b, and from the other side of the angle the line segment  PC=c.  Draw the line AC and another line parallelMathworldPlanetmathPlanetmath to it passing through B.  If the last line intersects the other side of the angle in the point D, then the line segment  CD=x  is the required fourth proportional:


Justification: the intercept theorem.

The below picture illustrates this solution:

Note.  The special case  c=b  gives the third proportional x of a and b:

Title construction of fourth proportional
Canonical name ConstructionOfFourthProportional
Date of creation 2013-03-22 18:49:59
Last modified on 2013-03-22 18:49:59
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 7
Author pahio (2872)
Entry type Application
Classification msc 51M15
Classification msc 51M04
Related topic ConstructionOfCentralProportion
Related topic ProportionEquation