Euclid Book 2 propositions

Before diving into some propositions from Euclid's second book some language barriers:

•  The statement "the rectangle contained by 'a' and 'b' " meant a rectangle with a the side length 'a' and ''
• The statement "a together with b" means a+b

Proposition II 4
If a straight line is cut at random, the square on the whole is equal to the squares on the segments and twice the rectangle contained by the segments.

In modern terms: This is just squaring a binomial (a+b)(a+b)
note:

• The whole is (a+b) so squaring the whole would yield (a+b)^2
• The segments would be a and b
• rectangle contained by the segments will be ab

Proposition II- 5:
If a straight line is cut into equal and unequal segments, the rectangle contained by the unequal segments of the whole together with the square on the straight line between the points of section is equal to the square on the half.

In modern term: (b-x)x+[(b/2)-x]^2 = (b/2)^2
note:

• (b/2)-x  is CD

• Let b (or AB) be a line and divide it into equal and unequal segments
• The equal segment is b/2 or AC and CB
• The unequal segment is AD and DB

Proposition II 11
To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment

In the above diagram the straight line is 'a' where a= x+a-x
In modern term the proposition states that a(a-x)= x^2
note: 
Unanswered Question

1. In book 1, all the propositions lead to the proof of the Pythagorean theorem so do all the proposition, in book 2, lead to any major theorem?

Evaluation:
Complexity: 7
interesting: 8
quality: 7