If a is a segment, how to geometrically draw a segment equal to 1/a (a has an unknown value)?

I can think of a way for rational values of a.

Draw a base line

Draw segment "a*" as a perpendicular line to the base line

Draw a line segment of length 1 as a perpendicular line to the base line that is parallel to a and on the same side of the base line as a

Now, mark off segments of 1 unit along segment a

Draw a line from the top of segment a to the base line. This line will pass along the top of line 1 as well

Connect the first segment marker from line a to the point. This will cross line 1 at a value of 1/a

**if the number is rational, such as 154/47, then the first line will be a length of 154 units and the second line will be a length of 47 units