"This rational analysis of design, _from which writing will spring_, is so essential in all its parts, that a child who, before being confided to my care, already wrote many of the letters, has taken six days to learn to draw a perpendicular or a horizontal line; he spent fifteen days before imitating a curve and an oblique. Indeed the greater number of my pupils, are for a long time incapable of even imitating the movements of my hand upon the paper, before attempting to draw a line in a determined direction. The most imitative, or the least stupid ones, produce a sign diametrically opposite to that which I show them and all of them confound the points of conjunction of two lines no matter how evident this is. It is true that the thorough knowledge I have given them of lines and of configuration helps them to make the connection which must be established between the plane and the various marks with which they must cover the surface, but in the study rendered necessary by the deficiency of my pupils, the progression in the matter of the vertical, the horizontal, the oblique, and the curve must be determined by the consideration of the difficulty of comprehension and of execution which each offers to a torpid intelligence and to a weak unsteady hand.
"I do not speak here of merely having them perform a difficult thing, since I have them surmount a _series_ of difficulties and for this reason I ask myself if some of these difficulties are not greater and some less, and if they do not grow one from the other, like theorems. Here are the ideas which have guided me in this respect.
"The vertical is a line which the eye and the hand follow directly, going up and down. The horizontal line is not natural to the eye, nor to the hand, which lowers itself and follows a curve (like the horizon from which it has taken its name), starting from the centre and going to the lateral extremity of the plane.
"The oblique line presupposes more complex comparative ideas, and the curve demands such firmness and so many differences in its relation to the plane that we would only lose time in taking up the study of these lines. The most simple line then, is the vertical, and this is how I have given my pupils an idea of it.