. 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 . , and the radials, OA and OD. This arc, AD, may be accurately determined by laying off any suitable fractional part, as — of it, n times. Or, from a table of sides of inscribed regular polygons, we can find thelength (here ft.) of the chord equal to one side of theregular polygon (here a heptagon), indicated by the nu
. 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 . , and the radials, OA and OD. This arc, AD, may be accurately determined by laying off any suitable fractional part, as — of it, n times. Or, from a table of sides of inscribed regular polygons, we can find thelength (here ft.) of the chord equal to one side of theregular polygon (here a heptagon), indicated by the numberof compartments. Setting off each way from A, D, etc., 3 ft. on the outer cir-cumference, as at AE and AF, and drawing the radii, as OEand OF, we have the piers, as shown at Ee/F, and HhH ; andthe area GFIJ which is to be covered by the radiant arch. Thisarch is here represented as closed at its ends by twelve inchwalls ; which, with the piers, form alcoves. 2°. The intrados of the radiant arch will, in any case, natur-ally be a right conoid (114), extending from OF to OG, andwhose springing plane will be the same as that of the annulararch; viz., the horizontal plane containing the diameter conoid will then be generated by the straight line OF, STONE-CUTTING. 121 moving so as to be parallel to the springing plane as a planedirector, while moving upon the vertical line at O, and somecurve o£ a height equal to oc2, and included symmetrically be-tween OF and OG. 3°. Two systems. — At this point, there is a choice betweenthe two methods, one or the other of which would be mostnaturally chosen. First. The curved directrix may be the ellipse whose trans-verse axis is the chord of any arc, as ooY, or GF, included be-tween OG and OF, and whose semi-conjugate axis is a verti-cal, equal to oc2 at the middle point of such chord. Second. The curved directrix, may, instead, be the curve ofdouble curvature, formed by wrapping upon some of the verticalcylinders, as
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