This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 edition. Excerpt: ...n', will pierce the horizontal plane in a line OD, drawn from the point O to the point D, where a tangent to the directing ellipse at the point projected in m, m', at the same height as n', also pierces the /wrizontal plane. 1st. Through the point projected in n, n, draw the projections Om and o'm' of ...
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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 edition. Excerpt: ...n', will pierce the horizontal plane in a line OD, drawn from the point O to the point D, where a tangent to the directing ellipse at the point projected in m, m', at the same height as n', also pierces the /wrizontal plane. 1st. Through the point projected in n, n, draw the projections Om and o'm' of an element of the surface, and project the line ab into a'b'. As the lines BC and bo are parallel, there obtains BC' bo:: mC: no; but BC=B'O'; oob'O', and mC--m'o'; no=n'o'; therefore, B'O' b'O' m'o' n'o', which shows, from the properties of ellipses having a coniX mon axis, that the curve b'n'C is an ellipse. 2d. Let tangents be drawn to the two ellipses at the corresponding points m' and n', at the same height above A'B'. These tangents will intersect the common axis at the same point E', and the other axis at points D' and d' such, that O'D' O'd'y.m'o' n'o'. Projecting the points D' and d' into the respective planea of the two ellipses at D and d, and observing that O'D'= CD; O'd'=od; m'o'=mC; andn'o'=no; there obtains CD: Cm:: cd: en; that is, the line joining the points D and d passes through the point O. Remark. This surface is a right conoid of which the horizontal plane is the plane director. JProb. 6. To const/met a tangent plane and a normal line to the conoid at any point, as n, n. Draw the projections of the element Om, o'm! of the Burface at the given point. Find where the tangent to the directing ellipse at the point m, ml pierces the horizontal plane. Join this point J) with O. Through n draw a parallel to CD, and where it cuts OD, at d, draw a line XT parallel to Om. This is the horizontal trace of the tangent plane at n, n'. For the tangent line at the given point to the ellipse projected in db pierces the horizontal...
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All Editions of Descriptive Geometry, as Applied to the Drawing of Fortification and Stereotomy: For the Use of the Cadets of the U.S. Military Academy
