Bisect 8 until you get 1, then go 1 either side of the middle
Step-by-step explanation:
It looks like you have no requirement that the segments be on the same line, or that one segment is divided into the ratio 3:5.
Perhaps the easiest is to draw a line, mark two points a convenient distance apart, and use your compass to repeatedly copy that length to the end of itself until you have lengths of 3 and 5. Here's one way to do that:
Make marks A and B on a line, with A to the left
Copy length AB to the right of B and mark the point C (now AC is 2 units)
Copy that same length to the left of A and mark the point E (now EC is 3 units)
Copy length AC to the right of C and mark the point D (now BD is 3 units, and ED is 5 units)
Segments BD and ED are in the ratio 3 : 5.
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Another way to do this is to start with a segment of a length you can consider to be 8 units. Call it AB. Construct the perpendicular bisector, and call the midpoint C. Construct the perpendicular bisector of AC and call the midpoint D. Construct the perpendicular bisector of DC. Its midpoint E divides the segment so that ...
