Descriptive Geometry, as applied to the Drawing of Fortification and Stereotomy

by D. H. Mahan

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1872 Excerpt: ...of a given semi cylinder by a vertical plane, the diameter A'B' being horizontal, and suppose the bounding elements through A' and B' to be limited at a horizontal plane at the distance A A' below A'B', and to pierce this plane at the points JE and D, on a line parallel to AB and at a given distance from it; these elements being oblique both to the vertical plane and to the horizontal plane, and therefore not projected on either into their true lengths.. Let LM be the axis, and JED a bounding element of another semi cylinder, the right section of which is a semicircle; LM and JED being also in the given horizontal plane. It is proposed, with these data, to find the lengths of the elements of the oblique cylinder intercepted between the vertical plane of A'B'C' and the horizontal cylinder; the curve of right section of the oblique semi cylinder at any assumed point; and the development of the portion of it which lies between the given vertical plane and the horizontal semi cylinder. 1st. The simplest method of finding the true lengths of the elements between the vertical plane and horizontal cylinder will be to construct their projections on another vertical plane parallel to them. Let BJ¥ be the trace of such a plane on the horizontal plane containing the axis LM of the horizontal semi cylinder, and Be' its trace on the given vertical plane. This assumed plane cuts from the horizontal semi cylinder an ellipse of which DN is evidently the semi transverse axis, and the radius of the semi cylinder, which is equal to the distance between the axis and the bounding element JED, is the semi conjugate; setting off this distance from JV to J¥ on a perpendicular to DJ¥, and describing the quadrant of an ellipse DN on these lines as semi axes, it will b...

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