Proposition: 1.11: Constructing a Perpendicular Segment to a Straight Line From a Given Point On the Straight Line

Euclid's Formulation

To draw a straight line at right angles to a given straight line from a given point on it. * Let $AB$ be the given straight line, and $C$ the given point on it. * So it is required to draw a straight line from the point $C$ at right angles to the straight line $AB$.


Modern Formulation

It is possible to construct a segment at a right angle to a given straight line $AB$ from an arbitrary point $C$ on the straight line.

Proofs: 1

Proofs: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Propositions: 25 26 27
Sections: 28

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



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"