"Newton regarded the curve f(x,y) = 0 as the locus of the intersection of two moving lines, one vertical and the other horizontal. The x and y coordinates of the moving point are then functions of the time t, specifying the locations of the vertical and horizontal lines... The motion is then the composition of a horizontal motion with velocity vector having length \dot{x} and a vertical motion with velocity vector having length \dot{y}. ...the velocity vector is the parallelogram sum of these ...It follows that the slope of the tangent line to the curve is \frac{\dot{y}}{\dot{x}}."