Walter Schreiner, Nov.2011
DELI doubling of the volume (cube)
First Measure, edge of the cube applied to the ruler.
Second right angle. (Circle)
Third half edge length construct. (Circle)
4th Enter points, with a vertical line with full-length (A) and draw half-length (C) of the edge.
5th Enter points, horizontal lines at right angles with half-length (D) and are characterized by a whole plus half the length (B) of the edge.
6th Line a = connecting the dots: vertical line length (A) and a horizontal line half the length (D).
7th Just connect the dots b =: vertical line half the length (C) with a horizontal line 1.5 times length (B).
8th Straight c = connection from the intersection of the lines a and b (e) point to the horizontal length of 1.5 times (B). The distance (E) - (B) is the edge length of the cube with twice the volume.
9.Genauigkeit: twice the volume is about 1% plus.
With this article I wish to emphasize the development of modern mathematics 500 BC to 200 BC in Greece. Of course, the mathematical knowledge of Egypt and Babylonia, a major part in the
Development of this base, which has components for thousands of years.
In the 5th century BC Apollo was the task of the cube-shaped altar in the temple of DELOS to double, but using only ruler and compass. The scholars from the Athenian period, and in consequence of the Hellenistic quickly realized that this problem is solvable. Of course there were many solutions, but none corresponded to the task only ruler and compass use. Examples: Oinopides about 420 BC, Archytas.
Taranto 428-365 BC Galt used as a genius in many areas, Menaechmus 350 BC Hippocrates and Eudoxus's solution (a pupil of Archytas). In the Platonic sense, which had pointed to the strict guidelines of using only ruler and compass were, therefore, all attempts to solve the wrong.
Besides, whether on the time axis of mathematics about 800 - BC 200th noted. From myth to logos, the invention of demonstrative mathematics, science had marked all over again. Why it worked is hard to find, but the interplay between religion and science from the Pythagoreans in the sign of the pentagram was the beginning (ionic Thales period 625-547 BC and Pythagoras 570-500 BC). As a result, there were the academies of Plato and Aristotle (Athenian period, about 500 - 300 BC), with the forums mathematics and philosophy, which was taken here on the economic return of the academies.
Not to mention the mathematical techniques they learned at that time in Egypt and Babylon. So really all the philosophers of the time axis of mathematics were there for some time to understand the mysteries of mathematical technique.
Graphic: GeoGebra

Just only rule and compass. That shows a very high degree of approximation.