I prove two theorems: Let Xn n+1be a hypersurface and let x X be a general point. If the set of lines having contact to order k with X at x is of dimension greater than expected, then the lines having contact to order k are actually contained in X. A variety X is said to be covered by lines if there exist a finite number of lines in X passing through a general point. Let Xn M be a variety covered by lines. Then there are at most n! lines passing through a general point of X.
