III. SIX DIVISIONS OF ARCHITECTURE 77

a point (or crossed at it) over a polygon, c, or circle, d, and he will have every form of simple roof; the arched section giving successively the vaulted roof and dome, and the gabled section giving the gabled roof and spire.

As we go further into the subject, we shall only have to add one or two forms to the sections here given, in order to embrace all the uncombined roofs in existence; and we shall not trouble the reader with many questions respecting crossvaulting, and other modes of their combination.

§ 6. Now, it also happens, from its place in buildings, that the sectional roof over a narrow space will need to be considered before we come to the expanded roof over a broad one. For when a wall has been gathered, as above explained, into piers, that it may better bear vertical pressure, it is generally necessary that it should be expanded again at the top into a continuous wall before it carries the true roof. Arches or lintels are, therefore, thrown from pier to pier, and a level preparation for carrying the real roof is made above them. After we have examined the structure of piers, therefore, we shall have to see how lintels or arches are thrown from pier to pier, and the whole prepared for the superincumbent roof; this arrangement being universal in all good architecture prepared for vertical pressures: and we shall then examine the condition of the great roof itself. And because the structure of the roof very often introduces certain lateral pressures which have much to do with the placing of buttresses, it will be well to do all this before we examine the nature of buttresses, and, therefore, between parts (B) and (C) of the above plan, § 4. So now we shall have to study: (A) the construction of walls; (B) that of piers; (C) that of lintels or arches prepared for roofing; (D) that of roofs proper; and (E) that of buttresses.

§ 7. (3.) Apertures.-There must either be intervals between the piers, of which intervals the character will be determined by that of the piers themselves, or else doors or windows in the walls proper. And, respecting doors or windows, we have to determine three things: first, the proper

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