|Given three numbers, to investigate when it is possible to find a fourth proportional to them.|
[The Greek text of this Proposition is corrupt. However, analogously to Proposition 18 the condition that a fourth proportional to A, B, and C exists is that A measure the product of B and C. ]
||Let A, B, and C be the given three numbers. It is required to investigate when it is possible to find a fourth proportional to them.|
Note that a fourth proportional d to a, b and c has to satisfy
a:b = c:d, so d would have to be bc/a. So the third proportional exists when a divides bc. No doubt that is what Euclid concludes in the missing part of this proposition.
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