Use the ruler to transfer measurements to a longer stick; a makeshift story pole or trammel. When marking, don't use the ends of the ruler; lead an inch reading from the graduated marks on the side of the ruler (errors at the end of the ruler add up and your eye can pick a marked line much easier then a dull imprecise end... just be sure to always add the extra inch back on the other end of your measurement... harder than it sounds sometimes).
Assuming that your 19 inch radius center point is tangent to the bottom and back of your sheet (i.e. 19 inches above the bottom and 19 inches forward of the rear), your 48 inch radius is centered on the bottom edge of your sheet, and there is no flat line between the arcs (i.e. one radius flows into the other in a continuous tangential spline) using Pythagoras, the center of the large radius should be about 40-15/16 inch forward from the original rear edge of the sheet.
48 - 19 = 29
This is the hypotenuse of the right triangle that is defined by: the center of the 48 inch radius; the center of the 19 inch radius; the base line; and the vertical perpendicular leg between the center of the 19 inch radius and the base line.
sq root of (29 squared - 19 squared) + 19 = 40.9 inches
This is the base of the above described triangle (the sq root of the hypotenuse sq'd minus the opposite side sq'd) plus the offset from the rear of the original 19 inch radius' center along the horizontal baseline.
Clear as mud, right?
So if you draw a point 19 inches up and 19 inches back; then draw a point 40.9 inches back along the base; then draw a straight line between the two extending 19 inches past the small center; the two arcs will meet at that point; and the 19 inch radius will touch the bottom and back of the sheet tangentially.
Hope this is what you are intending, that my math and mental picture of the scenario are correct, and that it some how helps to solve your problem.
