Completing the Pentagon.
In The Holy Place
we are told that the pentagon was completed when:
".... it was decided first to extrapolate the two missing pentagonal points from the triangle already found. The angles were measured, the distances matched and the lines drawn. The result was scarcely to be believed. Each of the other points is also upon a natural mountain feature."
From the map above we can see what we have to do. To find point C, la Soulaine, we draw lines at a 36 degree angle from Lincoln's original triangle A,D,B at both Bezu and Blanchforte. To find point E, Sierre de Lauzet, we draw lines at an angle of 36 degrees from triangle A,D,B at both Bezu and RLC. We should find these pairs of lines intersect on the spot heights and that the lengths of lines C - D and C - B are the same and that E - D and E - A are the same. We may even find that all four lines have the same length - now that would be truly astounding!Results
The line from Bezu to la Soulaine missed the spot height by 0mm. It was spot on!!
The line from Blancheforte to la Soulaine missed the spot height by 4mm. (treble checked)
The line from Bezu to Sierre de Lauzet missed the spot height by 1mm.
The line from RLC (church) to Sierre de Lauzet missed the spot height by 0mm. It was spot on!!
The length of the line from the la Soulaine spot height to Bezu (C - D) is 163mm.
The length of the line from the la Soulaine spot height to Blancheforte(C - B) is 155.5mm.
The length of the line from the Sierre de Lauzet spot height to Bezu (E - D) is 156.5mm.
The length of the line from the Sierre de Lauzet spot height to RLC church (E - A) is 157.5mm.
and, just to finish the set
The length of the line from RLC church to Blancheforte (A - B) is 164.2mm.
Mmm, now, if Blancheforte and la Soulaine could be moved ....Part 3
Finding point F and the length D - F.
This is what Henry says about point F and D - F.
"Point F does not indicate a visible structure. It is simply the intersection of the lines A-C and B-E. The point is fixed by the geometry of the mountains, as, obviously, is the distance D-F."
So yet again it is an easy matter to draw the lines and then measure D - F. If all goes well we should end up with a measurement of 188mm for the distance D - F.Results
As measured on the map, the distance D - F is 182mm.
Dang!! Disappointing by any standards i think.
And in case anyone is wondering what effect moving Blancheforte and la Soulaine to knock the pentagon more into shape would have on D - F, it would actually make the distance shorter!!
(In fact, to make D - F = 188mm the sides of the pentagon have to be around 160mm, co-incidently half way between the average of the three shorter sides and the average of the two longer sides.)Part 3
The 188mm distances on the map.
In Key to the Sacred Pattern
Henry lists six 188mm distances between pairs of churches (p 186). Lets see what the demonstrable facts really are:Results
As measured on the map the distance between RLC church and Rennes-les-Bains church is 189.5mm.
As measured on the map the distance between RLC church and Campagne-sur-Aude church is 190mm.
As measured on the map the distance between Antugnac church and Roquetaillaide church is 184.2mm.
As measured on the map the distance between Croux church and Bouriege church is 186.8mm.
As measured on the map the distance between Terroles church and St Salvayre church is 186mm.
As measured on the map the distance between Terroles church and Arques church is 184.5mm.
Not one is exact. The nearest to 188mm is out by just over 1mm, one is out by very nearly 4mm.Conclusion
I think the word 'disappointing' just about sums it up. I am very disappointed to have discovered what i have and very disappointed to have spent a large part of a holiday Monday doing it.
Does it matter? No, i don't think it does. What Henry Lincoln has accomplished goes way beyond mere numbers and angles. We all owe him a debt of gratitude for inspiring all those who have come after him. And oddly enough, it is by mistakes that great advances connected with RLC geometry have been made. Henry himself found that 'the sunrise line' as described by David Wood is not entirely accurate. Yet, as he acknowledged, without that error David Wood's geometry would not have come about.
So, all power to productive mistakes, and all power to Henry Lincoln!!!