◀ ▲ ▶Branches / Geometry / Elements-euclid / Book--1-plane-geometry / Proposition: 1.12: Constructing a Perpendicular Segment to a Straight Line From a Given Point Not On the Straight Line

Proposition: 1.12: Constructing a Perpendicular Segment to a Straight Line From a Given Point Not On the Straight Line

Euclid's Formulation

To draw a straight line perpendicular to a given infinite straight line from a given point which is not on it.

• Let $AB$ be the given infinite straight line and $C$ the given point, which is not on ($AB$).
• So it is required to draw a straight line perpendicular to the given infinite straight line $AB$ from the given point $C$, which is not on ($AB$).

Modern Formulation

Given an arbitrary straight line $AB$ and an arbitrary point $C$ not on the line, we may construct a perpendicular segment $\overline{CH}$ from the point to the line.

Table of Contents

Proofs: 1

Mentioned in:

Definitions: 1 2
Proofs: 3 4 5 6 7 8 9 10 11 12
Propositions: 13 14 15
Sections: 16

Thank you to the contributors under CC BY-SA 4.0!

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@Calahan

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References

Adapted from CC BY-SA 3.0 Sources:

1. Callahan, Daniel: "Euclid’s 'Elements' Redux" 2014

Adapted from (Public Domain)

1. Casey, John: "The First Six Books of the Elements of Euclid"

Adapted from (subject to copyright, with kind permission)

1. Fitzpatrick, Richard: Euclid's "Elements of Geometry"