"In Galilei's hypothesis of inextensible fibres u is supposed constant = r and the resistance of the base of fracture becomesr \int ydxdy = \frac{r}{2} \cdot \int y^2dx.On the supposition that the fibres are extensible we ought to consider their extension by finding what is now termed the neutral line or surface. Varignon however, and he is followed by later writers, assumes that the fibres in the base ACLN are not extended; and that the extension of the fibre through H' varies as DH, in other words he makes the curve GK a straight line passing through D. Hence if r' be the resistance of the fibre at B, and DB = a, the resistance of the fibre at H = r'y/a or the resistance of the base of fracture on this hypothesis becomes\frac{r'}{3a}\int y^3dxThis resistance in the case of a rectangular beam of breadth b and height a becomes on the two hypotheses\frac{ra^2b}{2} and \frac{r'a^2b}{3}...his results are practically vitiated when applying the true ( Leibniz-Mariotte) theory by his assumption of the position of the neutral surface, but in this error he is followed by so great a mathematician as Euler himself."