My comment:

Jane,

What's fun about these drawings are the platonic solids on the table in the drawing. John Brown, 1661, also had the platonic solids in his portrait/drawing with his carpenter's rule/square.

A Note on the Wooden Carpenter’s

Rule from Odyssey Shipwreck Site 35F

http://www.shipwreck.net/pdf/OMEPaper10_000.pdf

Sim

**Expanding on my comment:**

There are exactly five regular polyhedra (platonic solids).

Euclid's book of Elements book XIII

The 5 Platonic solids:

The Tetrahedron (3 equilateral triangles at each vertex)

The Hexahedron (3 squares at each vertex, cube)

The Octahedron (4 equilateral triangles at each vertex)

The Dodecahedron (3 pentagons at each vertex)

The Icosahedron (5 equilateral triangles at each vertex)

Compound Saw Miter and Saw Blade Bevel angles for building the 5 Platonic Solids out of wood Wood polyhedron or Wooden Polyhedra

John Brown an mathematical instrument maker, 1661, had the platonic solids in his portrait/drawing with his carpenter's rule/square.

John Brown portrait with the platonic solids.

Pepys worked with John Brown to design a custom-made rule, which Pepys called the “most useful that ever was made, and myself had the honor of being as it were the inventor of this form of it.”

The Diary of Samuel Pepys

The mathematical practitioners of the seventeenth century all subscribed to the Vitruvian vision of the architect as a geometrical paragon. With the platonic solids in the drawings/ portraits it showed how the mathematical practitioners studied Euclid's books of Elements. The mathematical practitioners were in the process of developing Analytic geometry, ( Descartes. In Book III of La Géométrie ) but wanted to show how their mathematical instruments were based on solid geometry already proven by Euclid's propositions.

Elucidation of the stuff is self evident.

Euclid's book of Elements book XIII

The 5 Platonic solids:

The Tetrahedron (3 equilateral triangles at each vertex)

The Hexahedron (3 squares at each vertex, cube)

The Octahedron (4 equilateral triangles at each vertex)

The Dodecahedron (3 pentagons at each vertex)

The Icosahedron (5 equilateral triangles at each vertex)

John Brown an mathematical instrument maker, 1661, had the platonic solids in his portrait/drawing with his carpenter's rule/square.

John Brown portrait with the platonic solids.

Pepys worked with John Brown to design a custom-made rule, which Pepys called the “most useful that ever was made, and myself had the honor of being as it were the inventor of this form of it.”

The Diary of Samuel Pepys

The mathematical practitioners of the seventeenth century all subscribed to the Vitruvian vision of the architect as a geometrical paragon. With the platonic solids in the drawings/ portraits it showed how the mathematical practitioners studied Euclid's books of Elements. The mathematical practitioners were in the process of developing Analytic geometry, ( Descartes. In Book III of La Géométrie ) but wanted to show how their mathematical instruments were based on solid geometry already proven by Euclid's propositions.

Elucidation of the stuff is self evident.

We hold these truths to be

*self*-*evident , and need no further explanation.*
Stuff = roof framing geometry

Stuff = tangent handrailing geometry

Stuff = Regulating lines of Geometry

Stuff = Ad Quadratum , square rotated in circle

Stuff = Ad Triangulum ,

Stuff = Daisy Wheel

Architecture and Mathematical Practice in England, 1550-1650

The mathematical practitioners wanted to introduce to the English skills that were monopolized by foreigners. This must be in reference to the Islamic Moors . Such as the Alhambra, Granada Spain.

The roof over the Hall of the Abencerrajes is unique because the roof actually follows the Ad Quadratum ground plan that is used to develop the octagonal ground plan. Squares rotated in the circle.

The mathematical practitioners wanted to introduce to the English skills that were monopolized by foreigners. This must be in reference to the Islamic Moors . Such as the Alhambra, Granada Spain.

The roof over the Hall of the Abencerrajes is unique because the roof actually follows the Ad Quadratum ground plan that is used to develop the octagonal ground plan. Squares rotated in the circle.

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