. Stereotomy : Problems in stone cutting. In four classes. I. Plane-sided structures. II. Structures containing developable surfaces. III. Structrues containing warped surfaces. IV. Structures containing double-curved surfaces. For students of engineering and architecture . by No. 2, and finishit by its pattern. No. 4, with the pattern of the bed at DE,will complete that face. The arch square, No. 5, with the pat-tern of the intrados, will give the surface EEFF ; and in likemanner the whole convex surface can be wrought. All theedges of both ends of the stone being thus given, their patterns,w
. Stereotomy : Problems in stone cutting. In four classes. I. Plane-sided structures. II. Structures containing developable surfaces. III. Structrues containing warped surfaces. IV. Structures containing double-curved surfaces. For students of engineering and architecture . by No. 2, and finishit by its pattern. No. 4, with the pattern of the bed at DE,will complete that face. The arch square, No. 5, with the pat-tern of the intrados, will give the surface EEFF ; and in likemanner the whole convex surface can be wrought. All theedges of both ends of the stone being thus given, their patterns,with the straight edge, will serve to complete them. Otherwise: the plane and cylindrical ends can be wroughtnext after the top, by bevels Nos. 6 and 7, respectively. This problem includes the following simpler cases, added asexamples. Examples. — 1°. Let both ends be plane; one, vertical on PQ ; the other ver-tical on JR. Ex. 2°. Let the cylindrical end be replaced by a plane one, having JR. for itshorizontal trace, and a batter of ^. Ex. 3°. Construct a rampant (ascending) arch covering a straight flight ofsteps. Grroined, and Cloistered Arches. 51. Both of these kinds of arches are compound, beingformed by the intersection of two single arches, each of which. Fig. 3. 30 STEREOTOMY. is usually cylindrical. They are distinguished from each otheras follows : — In the groined arch, Fig. 3, that part of each cylinder is realwhich is exterior to the other. Thus EF, LM, eF, and KH arereal portions of elements. In the cloistered arch, that part of each cylinder is real whichis within the other. Thus in Fig. 3, HF and FM would be thereal portions of the elements. The groined arch therefore naturally covers the quadrangularspace at which two arched open passages, ABC and abc, inter-sect ; while the cloistered arch forms the doubly arched cover,or quadrangular dome, of a quadrangular enclosed room, orcell. Theorem I. Saving two cylinders of revolution, whose axes intersect, the p
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