lines on a plane* (a piece of paper), the third dimension being represented by means of the other two. Next (if he is careful and wise) he makes a three-dimensional model. From the architect's drawings the engineer establishes his points, lays out his angles, and runs his lines upon the site itself. The mason follows, and with his footing courses makes ponderable and permanent the lines of the engineer. These lines become in due course walls—vertical planes. Floors and roofs—horizontal planes—follow, until some portion of three-dimensional space has been enclosed.
Substantially the same sequence holds, whatever the kind of building or the character of the construction—whether a steel-framed skyscraper or a wooden shanty. A line system, represented by columns and girders in the one case, and by studs and rafters in the other, becomes, by overlay or interposition, a system of planes, so assembled and correlated as to define a solid.
With nearly everything of man's creating—be it a bureau or a battleship—the process is as above described. First, a pattern to scale; next, an actual linear framework; then planes defining a solid. Consider almost any of the industries practiced throughout the ages: they may be conceived of thus in terms of dimensions; for example, those ancient ones of weaving and basket making. Lines (threads in the one case, rushes in the other) are wrought into planes to clothe a body or to contain a burden. Or think, if you choose, of the modern industry of book-making, wherein types are assembled, impressed upon sheets of paper, and these bound into volumes— points, lines, planes, solids. The book in turn becomes the unit of another dimensional order, in the library whose serried shelves form lines, which, combined into planes, define the lateral limits of the room.