Why the solution is more involved than needed?

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In Euclid's Elements the solution to the second problem/proposition is great but seems more complicated than needed. (link to the page)

Why not just take the length of $BC$ like it is done in the next proposition?

From the point $A$ draw the straight line $AD$ equal to C

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That can be done in the third proposition precisely because it was proved that it can be done in the second proposition.

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Proposition 1.1 says essentially that you can use your (modern) compasses to measure a line segment in one place and transfer it to another line. That needs to be proved, because all Euclid's compasses do is draw circles with given center and radius. If you pick them up they collapse.