construction of fourth proportional
Task. Given three line segments , and . Using compass and straightedge, construct the fourth proportional of the line segments.
Solution. Draw an angle () and denote its vertex (http://planetmath.org/Angle) by . Separate from one side (http://planetmath.org/Angle) of the angle the line segments and , and from the other side of the angle the line segment . Draw the line and another line parallel to it passing through . If the last line intersects the other side of the angle in the point , then the line segment is the required fourth proportional:
Justification: the intercept theorem.
The below picture illustrates this solution:
Note. The special case gives the third proportional of and :
Title | construction of fourth proportional |
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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 |