How from the description of deficient figures in a parallelogram, any number of mean proportionals may be found out between two given strait lines.
14. If these deficient figures, which I have described in a parallelogram, were capable of exact description, then any number of mean proportionals might be found out between two strait lines given. For example, in the parallelogram A B C D, (in [figure 8]) let the three-sided figure of two means be described (which many call a cubical parabola); and let R and S be two given strait lines; between which, if it be required to find two mean proportionals, it may be done thus. Let it be as R to S, so B C to B F; and let F E be drawn parallel to B A, and cut the crooked line in E; then through E let G H be drawn parallel and equal to the strait line A D, and cut the diagonal B D in I; for thus we have G I the greatest of two means between G H and G E, as appears by the description of the figure in [article 4]. Wherefore, if it be as G H to G I, so R to another line, T, that T will be the greatest of two means between R and S. And therefore if it[it] be again as R to T, so T to another line, X, that will be done which was required.
In the same manner, four mean proportionals may be found out, by the description of a three-sided figure of four means; and so any other number of means, &c.
Vol. 1. Lat. & Eng.
C. XVII.
Fig. 1-8
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