# construction of fourth proportional

Task. Given three line segments^{} $a$, $b$ and $c$. Using compass and straightedge, construct the fourth proportional of the line segments.

*Solution.* Draw an angle ($\alpha $) and denote its vertex (http://planetmath.org/Angle) by $P$. Separate from one side (http://planetmath.org/Angle) 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 parallel^{} 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:

$$a:b=c:x$$ |

Justification: the intercept theorem.

The below picture illustrates this solution:

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

$$a:b=b:x$$ |

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 |