Question

Geometry Construction help!?

Answer 1

Okay, first of all, you'd have to construct the segment that represents the product of the two given segments (don't forget to add the unit segment).

Answer 2

And next?

Answer 3

Well, the process of square root involves a "capable arch".
First draw the segment "r.s" on a line, and to that line add the segment "u" making i all "r.s+u" segment.
Find the mediatrix of the segment "r.s+u" and using the intersection of the mediatriz and the segment "r.s+u" as a center, draw a semicircle that intersects both extremes of the segment "r.s+u", that'll make a "capable arch" C .

To finish it off, you draw a perpendicular line to "r.s+u" on the endpoint of the segment "r.s" and it will intersect the capable arch "C" on a point "P".
So, the endpoint of segment "r.s" and the point "P" on "C" will define the segment \(\sqrt{r.s}\)

Answer 4

Alright, and then the second one? How would I do that?

Answer 5

Well, you have already defined \(\sqrt{r.s}\) just use the compass and transport it two times on a line. and you'll create the segment \(\sqrt{rs}+\sqrt{rs}\) which is \(2\sqrt{rs}\)

Answer 6

So it's just enlarging it twice then?

Answer 7

yes.

Answer 8

Alright, thank you for your help!