Hope everyone had a great Christmas but there are still a few leftover presents to unwrap it looks like.
First of all I would like to that Jim Alison for the insight pertaining to this topic from one of his presentation articles on his website long ago regarding Vesica derivatives. Only he focused his values on sq.rt. units of 2,3,4, etc. I would also like to thank Hugh Franklin for his inspirational insight into the fundamental relationship of Vesicas to Pi ratios of conversion of units. Only he focused his research on precision values of both Pi and sq.rt.3 values. The thing is, very little in the real world of observations corresponds to Ideal values of either mathematical or geometric formulas. That is where derivatives of both Vesica units as well as Pi units reveals a lot of hidden relationships between both Megalithic cultures units, as well as Ancient Egyptian cubit units. But I will try to keep this topic as simple as possible to start off with.
The simplest version of a Vesica ratio is 7/4 or 1.75 units. Let's assign a Ft. value to this ratio and give it a spin on the HF dial as 1/2 of this vesica ratio at .875 becomes the radius of a MY unit using the familiar seked Pi value 22/7 = 2.75 MY, which I believe Jim Wakefield has some special interest in due to it's correspondence to an MY of 33 inches when multiplied by 12 ins. Very Saxon way of doing things and this old ratio was part of medieval architects units also. 33 / 1.6 = 20.625 ins. makes a familiar ERC unit also I think. But I can manipulate this set of units by changing Pi values to obtain other interesting units also. A MY of 2.75 Ft. divided by 25/8 = .88 x 2 = 1.76 Vesica derivative value. Already we are seeing the relationship between these two Pi values of 22/7 and 25/8 being expressed as Vesica values. But lets' move onto some more interesting species now.
John Michell as well as myself noted a MY unit of 2.7216 Ft. in the past which he observed as an extension product of 2.7 Ft. x the Samos Ft. at 1.008 ratio to the English Ft. One has to keep in mind something interesting about this ratio in that it is the product of two others, namely the 176/175 x 441/440 = 126/125 or, 1.008. But I can also express this as a volumetric unit divided by another vesica value of 1.728 Ft. or 2.7216/1.728 = 1.575 being a factor of either the Polar Meridian Circ. in inches x 1,000,000,000, or a cubic inch of Barley grain weight as well. What is more, I can also change the Vesica ratio to 2.7216 Ft. / (864/275) Pi = .86625 x 2 = 1.7325 Ft. which is our old prehistoric Pisces Oxyrhychus species found on the Giza Plaza perimeter among other places. Isn't this fun? it gets even more convoluted than this though.
Let's try another example now of vesica of Jacob's favorite ERC of 1134/55 or 20.61818 ins. / 12 = 1.71818 Ft. next. Using the same vesica formula of HF modified as 1.71818 / 2 = .8590909 x 22/7 seked Pi = 2.7 Ft. MY. But I can also reverse this MY unit using the Fibonacci Pi of 864/275 = .859375 x 2 = 1.71875 Ft. as yet another species of vesica derivative units of familiarity. These two linked forever by the 3025/3024 ratio between the two Pi units. But there's no reason I couldn't have just as easily used the old Sumerian Pi value of 25/8 as the divisor to obtain the 1.728 Ft. so called Sacred Egyptian Cubit of Michell and Jacob's delight.
But now here's where David Kenworthy's units come into play next. I was wondering where I had seen his value of a cubit unit 20.83333 ins. before. Actually the history of that unit goes back a very long way as J.Michell knew from the metrologic writings of a very mysterious researcher named William Stirling long ago in his book entitled "The Canon", which I have a copy of also for reference. I had been studying the vesica aspects of this species for a while now before he came to the Mysteries board also in some discussions mostly with Jacob I'm sure he may recall here:
<[grahamhancock.com];
I had dubbed this species of Vesica fish the 'Pneuma' fish because this cubit value / 12 ins. = 1.736111 Ft., also has an inverse value of .576, which is the Greek Gematric notation value of Pneuma, either breath or spirit interpretation. So lets use this vesica value as before and put the ol HFC spin on it as, 1.736111r / 2 = .8680555r x 864/275 Fib.Pi = 2.72727r Ft. MY, which is also the inverse value of the Barleycorn unit. .36666r. used by HF. This is more or less what I was getting at in my last post to David before X-mas found here:
<[grahamhancock.com];
This is just the opening of a lot more to come involving these different ratio aspects of Vesica's, Pi's, Cubit's and MY's though. But that should be eye opening enough for this post presentation for starters.
Have fun working with these units and let me know what you discover using this method OK? it really gets involved and one can switch gears and vesicas in so many different ways.
Stephen
First of all I would like to that Jim Alison for the insight pertaining to this topic from one of his presentation articles on his website long ago regarding Vesica derivatives. Only he focused his values on sq.rt. units of 2,3,4, etc. I would also like to thank Hugh Franklin for his inspirational insight into the fundamental relationship of Vesicas to Pi ratios of conversion of units. Only he focused his research on precision values of both Pi and sq.rt.3 values. The thing is, very little in the real world of observations corresponds to Ideal values of either mathematical or geometric formulas. That is where derivatives of both Vesica units as well as Pi units reveals a lot of hidden relationships between both Megalithic cultures units, as well as Ancient Egyptian cubit units. But I will try to keep this topic as simple as possible to start off with.
The simplest version of a Vesica ratio is 7/4 or 1.75 units. Let's assign a Ft. value to this ratio and give it a spin on the HF dial as 1/2 of this vesica ratio at .875 becomes the radius of a MY unit using the familiar seked Pi value 22/7 = 2.75 MY, which I believe Jim Wakefield has some special interest in due to it's correspondence to an MY of 33 inches when multiplied by 12 ins. Very Saxon way of doing things and this old ratio was part of medieval architects units also. 33 / 1.6 = 20.625 ins. makes a familiar ERC unit also I think. But I can manipulate this set of units by changing Pi values to obtain other interesting units also. A MY of 2.75 Ft. divided by 25/8 = .88 x 2 = 1.76 Vesica derivative value. Already we are seeing the relationship between these two Pi values of 22/7 and 25/8 being expressed as Vesica values. But lets' move onto some more interesting species now.
John Michell as well as myself noted a MY unit of 2.7216 Ft. in the past which he observed as an extension product of 2.7 Ft. x the Samos Ft. at 1.008 ratio to the English Ft. One has to keep in mind something interesting about this ratio in that it is the product of two others, namely the 176/175 x 441/440 = 126/125 or, 1.008. But I can also express this as a volumetric unit divided by another vesica value of 1.728 Ft. or 2.7216/1.728 = 1.575 being a factor of either the Polar Meridian Circ. in inches x 1,000,000,000, or a cubic inch of Barley grain weight as well. What is more, I can also change the Vesica ratio to 2.7216 Ft. / (864/275) Pi = .86625 x 2 = 1.7325 Ft. which is our old prehistoric Pisces Oxyrhychus species found on the Giza Plaza perimeter among other places. Isn't this fun? it gets even more convoluted than this though.
Let's try another example now of vesica of Jacob's favorite ERC of 1134/55 or 20.61818 ins. / 12 = 1.71818 Ft. next. Using the same vesica formula of HF modified as 1.71818 / 2 = .8590909 x 22/7 seked Pi = 2.7 Ft. MY. But I can also reverse this MY unit using the Fibonacci Pi of 864/275 = .859375 x 2 = 1.71875 Ft. as yet another species of vesica derivative units of familiarity. These two linked forever by the 3025/3024 ratio between the two Pi units. But there's no reason I couldn't have just as easily used the old Sumerian Pi value of 25/8 as the divisor to obtain the 1.728 Ft. so called Sacred Egyptian Cubit of Michell and Jacob's delight.
But now here's where David Kenworthy's units come into play next. I was wondering where I had seen his value of a cubit unit 20.83333 ins. before. Actually the history of that unit goes back a very long way as J.Michell knew from the metrologic writings of a very mysterious researcher named William Stirling long ago in his book entitled "The Canon", which I have a copy of also for reference. I had been studying the vesica aspects of this species for a while now before he came to the Mysteries board also in some discussions mostly with Jacob I'm sure he may recall here:
<[grahamhancock.com];
I had dubbed this species of Vesica fish the 'Pneuma' fish because this cubit value / 12 ins. = 1.736111 Ft., also has an inverse value of .576, which is the Greek Gematric notation value of Pneuma, either breath or spirit interpretation. So lets use this vesica value as before and put the ol HFC spin on it as, 1.736111r / 2 = .8680555r x 864/275 Fib.Pi = 2.72727r Ft. MY, which is also the inverse value of the Barleycorn unit. .36666r. used by HF. This is more or less what I was getting at in my last post to David before X-mas found here:
<[grahamhancock.com];
This is just the opening of a lot more to come involving these different ratio aspects of Vesica's, Pi's, Cubit's and MY's though. But that should be eye opening enough for this post presentation for starters.
Have fun working with these units and let me know what you discover using this method OK? it really gets involved and one can switch gears and vesicas in so many different ways.
Stephen