Euclid X.6 porism
- Alexis Doval
If there are two numbers as D and E, and a straight line as A, then it is possible to make a straight line F such that the given straight line is to it as the number D is to the number E. (VI.9) And if a mean proportional is also taken between A and F, as B, then A is to F as the square on A is to the square on B, that is, the first is to the third as the figure on the first is to that which is similar and similarly described on the second. (VI.19,Cor.) But A is to F as the number D is to the number E, therefore the number D is to the number E as the figure on the straight line A is to the figure on the straight line B.
You need to construct line F and the mean proportional line B to demonstrate the porism. You can drag point J to vary the given length of line A.