Picard, in a recent memoir,* established the following theorem: Les seules surfaces algebriques dont toutes les sections planes sont unicursales, sont les surfaces re/lees utnicursales et la surface du quatrie?ne degre de Steiner. In the present article I wish to give ainother proof of the same theorem, and to develop several allied propositions in the geometry of n-dimensions. Picard notices at once that a surface of the kind under consideration, viz., of which every plane-section is unicursal, must be itself unicursal, and, accordingly, that there is a 1. 1 correspondeince between a point of the surface and a point of a plane (determined respectively by the honmogeneous coordinate-sets (X, y, t, u), (a, 3, y/)) defined by the equations (I) x_-fi (x, lB, y/), y =f2 (a, 1S, YK), z =f3(a, , ), t =f4 (a, >), where the f are integral homogeneous functions of a, 13, y of, say, degree n. It is shown, 1. c., pp. 77, 78, that there is no loss of generality in assuming that all the multiple points conmmon to the triply-infinite systemn of curves (2) Af, ( 3, y) + Bf2 (a (, y) + Cf3 (a, ,, y) + Df4 (a, (, y) = o are ordinary multiple poinlts, and that in these points the curves have no common tangents. Let xk be the lnumber of k-ple points comimon to the f-curve-systemi. To every curve of the system of curves (2) corresponds, in virtue of (1), the plane-section of the surface lying in the corresponding plane of the triply-infinite system of planes (3) Ax+By+ C% +Dt 0. Every plane-section is unicursal; so every curve of system (2) must be unicursal.