. 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 . joint. By counterdevelopment, Q:^4 returns to Qks. Hence, if we divide AEBand Q&3, each into the same number of equal parts, numberedsimilarly from B and Q as zero points, the points of the hori-zontal projection, KPQ, of the helix considered, will be a,t theintersection of the projecting lines from 1, 2, 3, etc., onAEB, wi
. 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 . joint. By counterdevelopment, Q:^4 returns to Qks. Hence, if we divide AEBand Q&3, each into the same number of equal parts, numberedsimilarly from B and Q as zero points, the points of the hori-zontal projection, KPQ, of the helix considered, will be a,t theintersection of the projecting lines from 1, 2, 3, etc., onAEB, with parallels to Kk3, through the corresponding pointson Q&3, as shown in the figure. Thus, M2and Bt are projectedfrom 2 and 3 upon the second and third parallels from Q. 83. Horizontal projections of intradosal helical coursing joints.— In like manner, RAT, one of the parallels drawn throughpoints of equal division on CDX is the development of so much ofcoursing joint as lies on the given segment of the cylinder takento form the arch. Tr5 is, therefore, its proportion of the pitch(76) of a coursing joint, and AEB is its vertical , as before, divide Tr5 and AEB into the same number ofequal parts, number similarly from B and r5 as zero points,. STONE-CUTTING. 65 and the intersections of projecting lines from 1, 2, 3, etc.,with the parallels to Rrfi through the like numbers on Trs, willbe points R . . R2, R3, etc. of the coursing helix RST. 84. Construction of horizontal projections of helices from theirdevelopments. — The above constructions, having been insertedto render them more intelligible by their analogy with Fig. 50,it will now be shown that the sinusoid (Theor. II.) projectionof the helix can be found from its circular projection and devel-opment. For the same parallels that divide Q^4 = Q&3, thepitch of KPQ — AEB into equal parts, divide the develop-ment, KQ15 of the same helix into the same number of equalparts ; and the like is true of ^R{£. Henc
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