"If Q be the total weight of the beam the differential equationEk^2 ad^3 y + Pa (dx)^2 dy + Qx(dx)^2 dy = 0is obtained... This is reduced by a simple transformation to a special case of Riccati's equation, which is then solved on the supposition that \frac{Q}{P} is small. Euler obtains finally for the force P, for which the rod begins to bend, the expressionP = \pi^2 \cdot Ek^2/a^2 - Q \cdot (\pi^2 - 8)/2\pi^2;which shews that the minimum force is slightly reduced by taking the weight of the beam into consideration."