Monge was a man of considerable merit as a geometrician, and, while
living, stood preeminent above his contemporaries in the French school
of that day. He is the author of several works, but his most popular one
is entitled "Gèomètrie Descriptive. par G. Monge, de l'Institut des
Sciences, Lettres et Arts, de l'Ecole Polytechnique; Membre du Sénat
Conservateur, Grand Officier de la Legion d'Honeur et Cointe de
l'Empire."
The programme to this work is interesting, as it urges the necessity of
making geometry a branch of the national education, and points out the
beneficial results that would arise therefrom. The following is the
translation:--
To draw the French nation from the dependence, which, even in the
present day it is obliged to place in foreign industry, it is necessary
first to direct the national education towards the knowledge of those
objects which require a correctness which hitherto has been totally
neglected; to accustom the hands of our artists to the management of the
various instruments that are necessary to measure the different degrees
of work, and to execute them with precision; then the finisher becomes
sensible of the accuracy it will require in the different works, and he
will be enabled to set the necessary value on it. For our artists to
become, from their youth, familiar with geometry, and to be in a
condition to attain it, it is necessary in the second place to render
popular the knowledge of a great number of natural phenomena that are
indispensable to the progress of industry; they will then profit for the
advancement of the general instruction of the nation, which by a
fortunate circumstance it has at its disposal, the principal resources
that are necessary for it. Lastly, it is requisite to extend among our
artists the knowledge of the advancement of the arts and that of
machines, whose object is either to diminish manual labour or to give to
the result of labour more uniformity and precision; and on those heads
it must be confessed we have much to draw from foreign nations.[1] All
these views can only be accomplished by giving a new turn to national
education.
[1] Monsieur Monge has drawn much from our countryman,
Hamilton's work on Stereography but he has not mentioned his
work.
This is to be done, in the first place, by making all intelligent young
men (who are born with a fortune) familiar with the use of descriptive
geometry, so that they may be able to employ their capital more
profitably both for themselves and the nation, and also for those who
have no other fortune than their education, so that their labour will
bring them the greater reward. This art has two principal objects, the
first to represent with exactness, from drawings which have only two
dimensions, objects which have three, and which are susceptible of a
strict definition; under this point of view it is a language necessary
to the man of genius when he conceives a project, and to those who are
to have the direction of it; and lastly, to the artists who are
themselves to execute the different parts.
The second object of descriptive geometry, is to deduce from the exact
description of bodies all that necessarily follows of their forms and
their respective positions; in this sense it is a means of seeking
truth, as it offers perpetual examples of the passage from what is known
to what is unknown, and as it is always applied to objects susceptible
of the minutest evidence, it is necessary that it should form part of
the plan of a national education. It is not only fit to exercise the
intellectual faculties of a great people, and to contribute thereby to
the perfection of mankind, but it is also indispensable to all workmen,
whose end is to give to certain bodies determined forms, and it is
principally owing to the methods of this art having been too little
extended, or in fact almost entirely neglected, that the progress of our
industry has been so slow. We shall contribute then to give an
advantageous direction to national education, by making our young artist
familiar with the application of descriptive geometry, to the graphic
constructions which are necessary in the greater number of the arts, and
in making use of this geometry in the representation and determination
of the elements of machinery, by means of which, man by the aid of the
forces of nature, reserves for himself, in a manner, in his operations
no other labour than that of his intellects. It is no less advantageous
to extend the knowledge of those phenomena of nature which may be turned
to the profit of the arts. The charm which accompanies them will
overcome the repugnance that men have in general for manual operations,
(which most regard as painful and laborious,) as it will make them find
pleasure in the exercise of their intellect; thus there ought to be in
the formal school a course of descriptive geometry.
As yet we have no well compiled elementary work on that art, because
till this time learned men have taken too little interest in it, or it
has only been practised in an obscure manner by persons whose education
had not been sufficiently extended, and were unable to communicate the
result of their lucubrations. A course simply oral would be absolutely
without effect. It is necessary then, for the course of descriptive
geometry, that practice and execution be joined to the hearing of
methods; thus pupils will be exercised in graphic construction of
descriptive geometry. The graphic arts have general methods with which
we can only become familiar by the use of the rule and compass. Among
the different applications that may be made of descriptive geometry,
there are _two_ which are remarkable, both for their universality and
their ingenuity; these are the constructions of _perspective_ and the
strict determination of the _shadows_. These two parts may finally be
considered as the completion of the art of describing objects.