Page:International Library of Technology, Volume 53.djvu/59

GEOMETRICAL DRAWING. §1

Problem 20.— To find an arc of a circle having a known radius, which shall be equal in length to a given straight line.

Note. — There is no exact method, but the following approximate method is close enough for all practical purposes, when the required arc does not exceed ${\tfrac {1}{2}}$ of the circumference.

Construction. — In Fig. 53, let A C he the given line 3${\tfrac {1}{2}}$" long. At A, erect the perpendicular A O, and make it eqtial in length to the given radius, say 4" long. With O A as a radius, and O as a center, describe the arc A B E. Divide A C into four equal parts, A D being the first of these parts, counting from A. With D as a center, and a radius D C, describe the arc C B intersecting A B E in B. The length of the arc A B very nearly equals the length of the straight line A C.

Problem 21. — An arc of a circle being given, to find a straight line of the same length. This is also an approximate method, but close enough for practical purposes, when the arc does not exceed ${\tfrac {1}{2}}$ of the circumference.

Construction.— In Fig. 54, let A B be the given arc; find the center O of the arc, and draw the radius O A. For this problem, choose the arc so that the radius will not exceed $1{\tfrac {3}{4}}$". At A, draw A C perpendicular to the radius (and, of course, tangent to the arc).