Archytas of Tarentum (c. 430 B.C.) solved the problems by means of sections of a half cylinder; according to Eutocius, Menaechmus solved them by means of the intersections of conic sections; and Eudoxus also gave a solution.
This result is modified if the action of the load near the section is distributed to the bracing intersections by rail and cross girders.
But if the load is distributed to the bracing intersections by rail and cross girders, then the shear at C' will be greatest when the load extends to N, and will have the values wXADN and -wXNEB.
The first pair of intersections may be either real or imaginary; we proceed to discuss the second pair.
A further deduction from the principle of continuity follows by considering the intersections of concentric circles.