◀ ▲ ▶Branches / Geometry / Elementseuclid / Book1planegeometry / 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.
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
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 @Calahan
 @Casey
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References
Adapted from CC BYSA 3.0 Sources:
 Callahan, Daniel: "Euclidâ€™s 'Elements' Redux" 2014
Adapted from (Public Domain)
 Casey, John: "The First Six Books of the Elements of Euclid"
Adapted from (subject to copyright, with kind permission)
 Fitzpatrick, Richard: Euclid's "Elements of Geometry"