In a Geometrical Mean the first amount is in proportion to the second amount as the second is to the third. a is to b as b is to c. Or a:b = b:c.
In Palladio's example;
6 exeeds 4 by a third of 6 which is 2,
just as 9 exeeds 6 by a third of 9 which is 3.
Or 4:6:9. Or 4:6 = 6:9.
Practically this means, in the words of Palladio;
'..we find this by multiplying the lesser extreme with the greater; because the square
root of the number which will result from such a multiplication will be the
number we seek."
In his example we multiply the lesser extreme, or
width, which is 4, by the greater extreme, which is 9, to get 36.
The square root of 36, (i.e. the only number which when multiplyed by itself
will give 36) is 6. Thus the height of the room is 6.
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