The ascending passage

The ascending passage is formed from similar geometry constructions to those used on the previous pages. The ellipse that is highlighted on the drawing is a copy of the principal ellipse, a polar cross section of the Earth, and is inscribed within the two faces and base line of the pyramid. The method of constructing of the ascending passage in the geometry is first to inscribe the ellipse inside these three tangent lines (mouse over the elements to highlight them)

• The base of the pyramid
• The southern face of the pyramid
• The northern face of the pyramid

When this construction is performed it creates three tangent points on the three lines. Using these points the ascending passage is formed as follows :

• Line 1: A line is constructed from the northern face tangent point down to the lower tangent point, which is the base center of the pyramid.
• Line 2: A similar line is constructed from the southern face tangent point down to the base center of the pyramid.
• Line 3: From the northern tangent point, a line is constructed perpendicularly to line 2 meeting line 2 at what will be called the 'upper perpendicular intersect point'.
• Line 4: From the upper perpendicular intersect point a line is created that is perpendicular to line 1, which meets line one at the ' lower perpendicular intersect point'.

If you open the object information panel for the ascending passage line you will see that the angle from the geometric construction is 26° 1' 34.01" and that it varies from that of the surveyed value by 0° 5' 6.02" which is well outside the surveying error margins.