Between two Similar Solid Numbers exist two Mean Proportionals/Mistake
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Source Work
1926: Sir Thomas L. Heath: Euclid: The Thirteen Books of The Elements: Volume 2 (2nd ed.)
- Book $\text{VIII}$
- Commentary on Proposition $19$
This mistake can be seen in the edition as published by Dover: ISBN 0-486-60089-0.
Mistake
- [Euclid] next forms the products of $c, f$ respectively into the mean $b d$.
- Then $abc, cbd, fbd, def$ are in the ratio of $a$ to $d$ etc.
- For
\(\ds a b c\) | \(:\) | \(\ds c b d = a b : b d = a : d\) | ||||||||||||
\(\ds b d\) | \(:\) | \(\ds f b d = c : f\) | ||||||||||||
\(\ds f b d\) | \(:\) | \(\ds d e f = b d : d e = b : e\) |
The middle line of the above is incorrect -- it ought to read:
- $c b d : f b d = c : f$