Solids bounded by planes and rectilinear edges

10. This would appear to be the place to indicate the manner of constructing the projections of solids bounded by planes and rectilinear edges, but for this operation there is no general rule. One perceives, for instance, that, according to the way in which the position of the apexes of solid angles of a solid are defined, the construction of their projections can be more or less simple, and that the nature of the work must depend on the method of definition. In this respect it is like algebra, in which there is no general procedure for solving a problem in equations. In each particular case, the step depends upon the way in which the relation between the quantities given and those unknown is expressed; and it is only through varied examples that one is able to accustom beginners to see these relations and write them into equations. It is much the same for descriptive geometry. It is through numerous examples and through the use of the straight edge and compass in the classroom that one can acquire the habits of the constructions and can accustom oneself to the choice of the simplest and most elegant methods in each particular case. But also, as in analysis, when a problem is put into an equation, procedures exist for treating these equations and for deducing the unknown quantities; in the same way, in descriptive geometry, when the projections are produced, general methods exist for constructing all which results from the form and the position of bodies.

Section of the original text in French

It is not without reason that we compare here descriptive geometry with algebra; the two sciences have very close resemblances. There are no constructions of descriptive geometry which cannot be translated into analysis; and when the questions have not more than three unknowns, each analytical operation can be regarded as the portrayal of an act in geometry.

It is desirable that the two sciences should be cultivated together; in the most complicated analytical operations descriptive geometry will carry that clarity which is its very nature and, in its turn, analysis will bring to geometry that generality which is fit and proper.

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