Euclid's Elements - Book 1 Proposition 1
Proposition 1: On a given finite straight line [it is possible] to construct and equilateral triangle.
1. Below you will find Euclid's instruction to construct an equilateral triangle. Using the GeoGebra applet, follow these instruction.
Let AB be the given finite straight line.
With center A and distance AB let the circle BCD be described;
again, with center B and distance BA let the circle ACE be described;
and from the point C, in which the circles cut one another, to the points A, B let the straight lines CA, CB be joined.
2. What postulates are being used to carry out the construction? Where?
3. Euclid claims that triangle ABC is equilateral. Why is that true?
4. To justify ABC is an equilateral triangle, you need to use one of Euclid's common notions. Can you identify which common notion and where in your argument you need it?