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** **** Theorems II and III**

Addition March 2012:

Those that follow below are of a similar nature as the basic structure on which they are found remains

A Prism and three smaller prisms.

Swannies Second Theorem :

A Circle and three smaller circles -

See diagram and lay out thereof below:

The square shaped diagram, above on the right, shows an opened up trirectangular tetrahedron. This shape was chosen to show the nice ratios it gives, more so if for a specially shaped construction -

unit: 1u^2 + 2u^2 + 2u^2 + 3u^2 = 8u^2

and (1u^2)^2 + (2u^2)^2 + (2u^2)^2 = (3u^2)^2 De Gua

i.e. 1u^3 + 4u^3 + 4u^3 = 9u^3 Swannie

A model conforming to these values is shown on the page Art. The Second Theorem is now used to find the circles. Going **from green to red** (by projection) **to blue** is shown. Likewise (or by the shorter method mentioned in the Method) the yellow circles are found.

So yellow + yellow + a dash of blue = green and in this case, deviding the green circle -**pi(x^2 + y^2 + z^2) = pi(w^2)** where x, y, z, and w are the radii of the circles. ** Swannies Third Theorem :** A theorem for the

A Semi-

of the circles on the other faces. As derived from 4/3pi r^3, the voume of a sphere.

Model: See below.

**Above on the left:** A 'thick' illustration of Pythagoras; an easy way to 'give Pythagoras volume', with formula a^2.d + b^2.d = c^2.d and in this case: a^3 + ab^2 = ac^2. Here the thickness of the cuboids are the same; in theorems III and V the heights of the shapes are the same.**Above on the right:** A trirectangular tetrahedron with an equilateral base fitted with a semisphere. On the rectangularfaces semi polystyrene australorp shaped eggs were fitted (because you can buy them cheap and it takes much effort to make/shape the required items -

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