Winslow's Comprehensive mathematics : being an extensive cabinet of numerical, arithmetical, and mathematical facts, tables, data, formulas, and practical . ter of lesser base. V= pitch, or angle of the side to the base. //= perpendicular height of generating cone, having D for its = slant height of generating cone, having D for its base. r— slant height of cone, having d for its base. H = i#X = JD X tan V—slW— QDf Dh D — d R cos V sin V =v//i2+a/>)2 u Rd = ^=T7 = v/(tf-/02 + G<02- cos V~ DDXtan V(D-d)_H(D-h~ 2D — D d) H-^r-Qdy, the height of the frustum. Rule. — From a c
Winslow's Comprehensive mathematics : being an extensive cabinet of numerical, arithmetical, and mathematical facts, tables, data, formulas, and practical . ter of lesser base. V= pitch, or angle of the side to the base. //= perpendicular height of generating cone, having D for its = slant height of generating cone, having D for its base. r— slant height of cone, having d for its base. H = i#X = JD X tan V—slW— QDf Dh D — d R cos V sin V =v//i2+a/>)2 u Rd = ^=T7 = v/(tf-/02 + G<02- cos V~ DDXtan V(D-d)_H(D-h~ 2D — D d) H-^r-Qdy, the height of the frustum. Rule. — From a common centre describe two concentric arcsof circles of sufficient length,taking R for the radius of oneof them, and r for that of theother. Next, draw a radiusfrom the centre to the outer arc,as o r R, diagram. Next, witha flexible measure, cut to the re-quired length, (the whole cir-cumference of one of the bases,when practicable), and bent tothe proper curve, measure offthat length on the curve, as fromR to v, and from the new-foundpoint, v, draw a radius to thecentre, o: then will R v n r bethe top, or a known aliquot part of the top, Special Cases. For a two-thirds pitch, or pitch of 60° (sometimes erroneouslycalled a half-pitch, because the angle of the side and axis is half as32 374 PATTERN CUTTING. great as that of the side and base).—From a common centre de-scribe two concentric semi-circles, taking the diameters of the givenbases, respectively, for the radii: take the greater semi-circle forthe top required. For a half-pitch, or pilch of 45°. — Describe two concentriccircles, taking the diameters of the bases multiplied by ,respectively, for the radii; take three-fourths of the greater circlefor the body, less one-fourth of its radius as a chord. For a third-pitch, or pitch of 30° (often erroneously called a half-pitch, because the angle of the base and side is half as great asthat of the side and axis). — From a common centre desc
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