About the Book
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. 1846. Excerpt: ... AO'B be described, and if C D be drawn perpendicular to A B, and the angles CAD, C B D, be made equal to B C T, fig. 6; then each half of fig. 10 being constructed as in fig. 8, the angles at m, m, m," m'," will be respectively equal to the angle P m S, P'm' S', Q" m" S," Q" rri" S," in fig. 6. Also, in fig. 10, the angles CAE, C A g, C A h, C B i, C B k, C B F, will be the hypothenuses at the point A, O, O', 0," O'," B, in fig. 6. We may here observe, fig. 6, that the angles which the tangent planes make with the plane of the base in the first quadrant are acute; and those in the second quadrant are obtuse, and are the supplements of the angles P m S; and, moreover, that all the angles which constitute the hypothenuses of the trehedral are acute, whether in the first quadrant or second quadrant of the semicircle A OB. SECTION II.--On The Projection Of A Straight Line Bent Upon A Cylindric Surface, And The Method Of Drawing A Tangent To Such A Projection. PROBLEM I. Given the development of the surface of the semi-cylinder, and a straight line in that development, to find the projection of the straight line on a plane passing through the axis of the cylinder, supposing the development to encase the semicylindric surface. Fig. 11. Let A B C be the development of the cylindric surface, B C being the development of the semi-circumference, and let A C be the straight line given. Produce C B to D, making B D equal to the diameter of the cylinder. On B D, as a diameter, describe the semicircle BED, and divide the semicircular arc BED into any number of equal parts, at 1, 2, 3, &c; and its development B C into the same number of equal parts, at the points/, g, h, &c. Draw the straight lines fk, gl, hm, &c, parallel to B A, meeting A C at the points k, l, m, &c; als...
