To readers following this thread, with maybe a tiny interest in the design for this classic table, I wish to add some detail on the workup I did.
My model has been modified to correct some things I thought were deficient in my earlier attempt. First, I went and looked at some images on the web of tables like this that were built and can be seen and studied. I concluded that my early model was close but not right. My overall length was good at about 36" with leaves up, but its depth made it too broad. And my leaves were a little too broad at 6-1/8".
So I began by trying to find a true ellipse of the right size, one that when chopped with leaf lines, would yield a center rectangle of the right size and leaves closer to 5-1/2". This image shows the construct of an ellipse that works.
Next, I tested the ellipse to see how circular arcs would come close to tracking the ellipse, with chord lengths equal to the rectangular tray's sides, and arc heights of 5-1/2" on all sides. Circular arcs make the construction easier when building, in that trammels can be used to do the layout.
The arcs tracked the ellipse almost perfectly. My table model, shown here with dimensions, shows the table without the slight bullnose edge all around the outside of the leaves. That bullnose is outside the edge shown, thus to lay out the part for cutting, you need to draw a concentric arc about 1/8" larger in radius and cut the blank for the leaf to that line.