Dependencies on Euclid Book II. Most of the propositions in Euclid Book II are results analogous to simple algebraic applications of the distributive property.  Upon first inspection, the propositions that are chosen to be recorded seem like random properties.  e.g. II.8 is analogous to $(A+2B)^2=4(A+B)B+A^2$.  
I would understand why these propositions we recorded if future propositions depended on these in their proofs.  Although, the only propositions in Book II which depend on previous propositions are the last four.  Are there propositions in future books which depend on the remaining "unused" propositions of Book II?  Or are they included because Euclid was recording every geometric result that the Greeks knew?
 A: The results of Book II are indeed hardly (if at all) used in the remaining geometric books. There are a few algebraic applications in connection with perfect numbers as well as in Book X on the 
classification of incommensurable lines. This is why the content of Book II was once classified as "geometric algebra".
Unguru attacked geometric algebra by seriously misrepresenting the claims of classical historians of mathematics; you will find more on that in recent articles by Blasjo and Hoyrup on geometric algebra. Geometrically, Book II deals with transforming rectangles into squares; algebraically, this is the theory of completing the square, which is used when solving problems that we write as quadratic equations. Thus Euclid lays the foundation for the methods for solving such problems that the Greeks may have inherited from the Babylonians (who knew how to find the sides of rectangles with given circumference and area, i.e., how to solve systems of equations of the form $x+y=a$, $xy = b$;
see Hoyrups Algebra in cuneiform). 
Observe that I am not saying that the Greeks solved quadratic equations in this way. If you want to know how they did that look into the works of Archimedes, Aristarch, Heron and Diophantus. Solving quadratic problems is part of logistics: basic arithmetic as well as field measurement etc.; all the maths where the sizes of lines, areas and 
angles are measured in feet, square feet or degrees is part of logistics. Therefore Euclid does not say that the area of a parallelogram is the product of the base and the height (as Heron does) but that its area equals that of a rectangle with the same base and the same height.
In a similar way, Euclid's number theory books cover the part of arithmetic that can be expressed without using fractions (which are also part of logistics), which is why Euclid is making such a fuss about 1 being so special (and as indivisible as a geometric point). 
