Palladio
The Geometric Mean.
"....the length and breadth of the room being known, we will find a number
that has the same proportion to the breadth as the length has to the number
sought.......if the place we intend to vault is nine feet long and four feet
wide, the height will be six feet"
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 multiplied by itself will give 36) is 6. Thus the height of
the room is 6.
Here is a summary of the Arithmetic and Geometric means:
Title Page:Introduction
Plato: The Timaeus
Pythagoras: Music and
Space
Alberti: Harmony and
Proportion
Palladio: The
Proportion of Rooms-
The Arithmetic Mean
The Geometric Mean -
The Harmonic Mean
Summary: The Square
Root of 2
Text,
images and graphics
© J. Boyd-Brent, 1995-2002
- An Article from About Scotland
Art Pages
This page from:
www.aboutscotland.com/harmony/prop5.html
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