In order to raise the French nation from the position of dependence on foreign industry, in which it has continued to the present time, it is necessary in the first place to direct national education towards an acquaintance with matters which demand exactness, a study which hitherto has been totally neglected; and to accustom the hands of our artificers to the handling of tools of all kinds, which serve to give precision to workmanship, and for estimating its different degrees of excellence. Then the consumer, appreciating exactness, will be able to insist upon it in the various types of workmanship and to fix its proper price; and our craftsmen, accustomed to it from an early age, will be capable of attaining it.

It is necessary in the second place to make popular a recognition of a number of natural phenomena indispensable for the progress of industry, and to exploit, through the advancement of the general instruction of the nation, the fortunate condition in which it finds itself of having at its command the principal resources which are necessary.

Finally, it is necessary to disseminate among our craftsmen the knowledge of the processes used in the crafts and in machines which have for their object either the diminuation of manual labour or the imparting of more uniformity and precision to the results of workmanship; and in this respect it must be admitted that we have much to learn from foreign nations.

All these objectives can only be reached by gaining a new direction to national education.

This is to be done in the first place by familiarising all young persons of intelligence with descriptive geometry, that those of independent fortune may be someday in a position to use their capital usefully for themselves and the state, as well as those who have no fortune but their education, that they may someday be able to impart a higher value to their workmanship.

This art has two principal objects.

The first is to represent with exactness upon drawings which have only two dimensions such objects as have three and which are susceptible of rigorous definition.

From this point of view it is a language necessary to a man of genius, who conceives a project, to those who are obliged to direct its execution, and finally to the craftsmen who are obliged to make the different parts.

The second object of descriptive geometry is to deduce from the exact description of bodies all which necessarily follows from their forms and respective positions. In this sense it is a means of investigating truth; it perpetually offers examples of passing from the known to the unknown; and since it is always applied to objects with the most elementary shapes, it is necessary to introduce it into the plan of national education. It is not only fitted to exercise the intellectual faculties of a great people, and to contribute thereby to perfecting the human species, but, moreover, it is indispensable to all workmen whose aim is to give bodies certain defined forms; and it is principally because the methods of this art have up to the present time been too little disseminated, or even almost entirely neglected, that the progress of our industry has been so slow.

It will be a contribution, therefore, towards giving an advantageous direction to national education, if we familiarise our young craftsmen with the application of descriptive geometry to the graphical constructions which are necessary in a great many of the arts and crafts, and make use of this geometry for the representation and determination of the elements of machines by which man, controlling the forces of nature, reserves for himself, so to speak, no other labour in his work but that of intelligence.

It is no less advantageous to disseminate a knowledge of the phenomena of nature which can be turned to account in the arts and crafts.

The charm which accompanies these studies will conquer the repugnance which men have in general for intense thought and make them find pleasure in that exercise of their intellect which almost all regard as painful and irksome.

Accordingly, there must be a Course of Descriptive Geometry at the Ecole Normale.

But as we have no elementary, well-executed book upon this art, either because hitherto scientific men have taken too little interest in the subject, or because it has been practised in an obscure manner by persons whose education has not been sufficiently attended to and who do not know how to communicate the results of their meditations, a simple oral course would be absolutely useless.

It is necessary for the Course of Descriptive Geometry to associate practice and execution with the listening to a description of the method. Therefore the students ought to exercise themselves in the graphical constructions of descriptive geometry. The graphical arts have general methods with which it is only possible to become familiar by the use of the straight edge and compass.

Among the different applications which can be made of descriptive geometry there are two which are remarkable, both by their generality and by the ingenuity which attaches to them; these are the constructions of perspective and the rigorous determination of shadows in drawings. These two parts can be considered as the complement of the art of graphically describing objects. Here one exercises those persons who, being destined one day to teach the procedures of descriptive geometry, will have to be cognisant with all its ramifications.

It follows that the methods of projections will be applied to the graphical constructions necessary in the greater number of crafts, such as the work of stone-cutters, carpenters, and so on.

Finally the rest of the duration of the course will be employed firstly on the description of machine elements and then the study of their forms and effects, followed by that of complete machines, of which it is most important to spread knowledge; so that machines will have as their object the giving of more precision and uniformity to work and the employing in production of the forces of nature to augment the national power.

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