Having satisfied myself that even in rough country,Pentacles could be constructed with reasonable perhaps good accuracy, I have made no attempt to address that issue again in the following slides. Also The orientation of the diagram has been changed so that the N-S lines actually do run North-South not 3 degrees off N-S.

## The First Lines

To construct the next pentacle it is first necessary to draw extension lines from the two existing pentaclesThis diagram shows the centre line extensions existing pentacles and the N-S alignment lines.

To identify these lines they have been allocated numbers (1-5, Left to Right)

Another line is required to be be drawn drawn at right angles across the N-S lines and through the intersection point. it will originate from the southernmost point of the left hand Pentagon (E-W line).

## Not Obvious

It is now possible to locate the point at which the line running at right angles intersects the fourth N-S line. A line can then be drawn from where the centre line coming from the left intersects N_S line two to where the E-W line intersects N-S line four.

## The Unique Circle

A line is drawn from the point of the left hand existing pentacle (lies on N_S line one) to the point of the left hand existing pentacle(lies on N-S line five). A line is constructed parallel to this line, starting at the intersection of the E-W line and N-S line four.(South construction line)

A circle is then constructed. Only one circle can be drawn which is based on the centre point and passes through through the intersection of The North and South construction lines and N-S line three.

## The Small Pentagram

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Within this circle, it is now possible to draw a small pentagram. This pentagram is the key to drawing the new pentacle.

## The Pentacles Emerge

All this can be achieved by using the unique properties of the pentacles without the measurement of a single angle and without any measurement of distances.

Nevertheless the angles of both the pentagam are now known and can immediately be used to plot directions.

From the pentagram it is now a relatively easy task to create two pentacles, one within the pentagram by joining the points of the pentagram and a second outside the pentagram simply by extending the sides

## The Topography

Returning to the 3D topographical view it can be seen that the second, larger pentacle spreads well outside the central hill on which the smaller pentacle is situated. There is of course no reason why the smaller pentacle should sit so neatly on the hill. it could just as easily been draped down the side or from the top to bottom of a steep cliff! After more experimentation I believe the same basic technique could be used in any situation.

## Final Construction

The first two sides of the main pentacle. This is achieved by drawing lines through four of the points of the new medium sized pentacle.

Now the pentacle can be completed by drawing lines through all the points. There has still been no need to construct angles or make measurements. All this has been achieved by drawing straight lines and one small circle.

## The Lincoln Pentacle is unique

The new pentacle stretches out from the previous existing pentacles over rugged terrain. As can be seen the elevations conform to no specific pattern, unlike the pentacle at Rennes le Château where all the points are on or close to hilltops.

It is possible that the pentacle at Rennes le Château was and is famous because of this unique property. Concurrence with hilltops would be a chance event and most unusual.

## On The Ground

The google elevation profiles are now marked up to show the positioning of the central small pentacle in two different directions the darker red portions of the elevation graph show the positioning of the central small pentacle

Eventually I walked over every kilometre of this terrain, looking for ancient pegs or marker stones. I did not find any despite being able to pick out with some confidence the north-south lines and the centre lines.

The only point where there might have been difficulty in construction would have been where the lines ran through a large copse of trees. I came to the conclusion that the lines would have been partially cleared at ground level underneath the tree canopy.

I spent some time walking around the small central pentacle. On the ground I became convinced that the tracks in the area touched every point of the pentacle. This is not confirmed by Google earth though they come very close. There is also a minor track which runs across the pentacle and passes very close to the centre. This does not show at all on Google.