Proof
Apply I.1 to obtain an equilateral triangle; produce its sides
(Postulate 2); describe a circle with centre at one endpoint of the
given segment cutting one of the produced sides; the cut-off equals
the given segment by Definition I.15 and Common Notion 1.
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Full neighborhood
Depends on (6)
- I.1Proposition I.1On a given finite straight line to construct an equilateral triangle.
- 1Postulate 1To draw a straight line from any point to any point.
- 2Postulate 2To produce a finite straight line continuously in a straight line.
- 3Postulate 3To describe a circle with any centre and distance.
- I.15Definition I.15A circle is a plane figure contained by one line such that all the straight lines falling upon it from one point among…
- 1Common notion 1Things which are equal to the same thing are also equal to one another.
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