Hi Hans
Quote 'But isn't decimal in this case referring to the use of base 10?"
Yes Hans it is and many get confused by this;
The Indus / Saxon meaure 39.6 inches in 3 feet of 13.2 is equivalent to the metre its 1.00584 of a modern meter.
And the yard 39.6 inches is both 39.6 inches and 50 digits.
When looking at Degrees minutes and seconds it is a based 60
So 51.84 degrees = 51 degree 50 minutes 24 seconds your calculator picks this up when using the tan cos or sin function and uses 60.
The Babylonians got it..
What is special about the Saxon system?
I think that the Saxon system originated through the study of astronomy and
mathematics, starting with the discovery of the significance of the number
360.
The vernal equinox occurs about 23 September in the southern hemisphere
and about 21 March in the northern hemisphere. It is the time of year when
the hours of daylight equal those of the night.
There are 360 degrees in a circle, and we know this has an ancient origin.
We know the year is about 360 days in length. The remarkable thing is that
the number 360 can be measured in a day, and it may be that this was the
reason to choose this number above all others as the basis of a system.
The Encyclopaedia Biblica (1899–1903) states:
The division of the day into 12 parts and the further development of the
sexagesimal system as a whole had commended itself to the Babylonians
from their observation that, at the vernal equinox, the time between the
appearance of the first direct ray of the sun and that of visibility of the
entire disk above the horizon amounted to 1/360th of the time during
which the sun was visible in the heavens, or the 720th part of a full day
reckoned from one sunrise to another. (p 1037)
This statement seems reasonable, because the diameter of the sun is taken as
one-half of a degree and appears to move 15 degrees in an hour, taking about
two minutes for the disc to rise.
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Vernal equinox
See my paper for the diagrams [
www.bing.com]
In Figure 4, the diameter of the circle represents a flat surface, perhaps a
desert or plane in the Middle East or India. I have tried to represent sunrise
at the time of the vernal equinox. The sun begins to rise, first hugging the
horizon then the circumference of an imaginary circle. There is the first
direct ray of sunlight heralding the sunrise and then the sun climbs above the
horizon, appearing more powerful by the second unrelenting in its climb —
unstoppable.
Figure 4 Sunrise at the time of the vernal equinox
In reality the sun does not rise, the sun is stationary, our Earth spins at 900
miles an hour and we roll into it, normally while lying asleep in bed.
I like to imagine the first person watching this sunrise and realising for the
first time the importance of the discovery: For if our sun gave us the number
360 then perhaps there is an order and purpose to our universe, one we might
even be able to measure.
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Imagine an experiment using a water jar with a small hole at the bottom
through which a cup was filled during the time the sun rose. You would be
left with not just a cup of water but at least three measures:
• a weight of water
• a measure of length (for example, an equal weight of barleycorns laid
end-on-end)
• a measure of time (one sun of two minutes).
Could this be the basis for a system?
To find 360 in the Saxon system, we can look at a land measure: the acre.
The acre
The acre is an old measure and its origins have created a great deal of
comment. Until now, many people would not believe that an ancient British
measure had anything to do with Egypt. Let me demonstrate some
coincidences.
An acre in our present system is 40 rods ×4 rods or 660 × 66 imperial feet,
giving a total area of 43 560 square feet. There are 16.5 feet in a rod.
Therefore, to calculate how many acres in a square measured in imperial
feet, square the length of the base and divide by 43 560. If the base of the
Great Pyramid is 755.7 imperial feet, it would contain 13.11025 acres
exactly:
755.7 × 755.7 ÷ 43 560 = 13.11025
The architects did not have electronic calculators and so calculations took a
little time. However, using the Saxon system of measuring makes finding an
acre very easy, because there are 36 000 square Saxon feet in an acre. The
base of the Great Pyramid measures 687 Saxon feet (755.7 imperial feet).
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There are two quick ways to calculate the acreage:
• The first method is to divide the length of the base by 6, square it and
divide by 1000:
– 687 ÷ 6 = 114.5
– 114.5 × 114.5 = 13110.25
– 13110.25 ÷ 1000 = 13.11025 acres
• The second method is to square the length of the base and divide by
36 000:
– 687 × 687= 471 968
– 471 968 ÷36 000 = 13.11025 acres.
It was clear to me that the measure of 36 000 square Saxon feet in an acre
was significant, because it contained the number 360.
Best
Jim