Mathematics for Engineering Students

Cover Mathematics for Engineering Students
Mathematics for Engineering Students
S S Samuel Smith Keller
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39- As in Fig. 39 let A A' be the major axis, F and F' the foci. Taking, say, AB as radius and F' as centre describe arcs m and m' . Then taking A'B as radius, and F as centre describe arcs n and n'\ their intersections R and S will be points on the ellipse. Taking any desired number of points as C, D, etc. , perform the same operation, thus determining any desired number of points. A smooth curve through these points will be an approximate ellipse. ART. 76#. The two following methods of ellips...e con- struction are used by draftsmen. The first based upon the relation between the ordinates of points on the ellipse and those on the auxiliary circles as shown in Art. 97 give a true ellipse; the second gives what is known as a circular-arc-ellipse and is only an approximation. Io6 Analytical Geometry. First Method: Let O be the centre of the ellipse- A A' the major axis; BB' the minor axis; BCB' the minor circle and ADA' the major circle. (Fig. 390. ) Take any num- ber of points on the major circle as R, S, T, etc.

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