Friday, May 17, 2013

Ad Quadratum, the Sacred Cut, & Roman Architecture

More from SBE Builders:

Ad Quadratum ground plan geometrically developed for hip and valley rafters.

More about Geometry, Medieval Gothic Framing, Ad Quadratum, the Sacred Cut, & Roman Architecture


I first saw the picture of roof over the Hall of the Abencerrajes at Alhambra Granada in the documentation for the Carpenters Master Framing Square (Chappell Framing Square) about a year ago. 
Then a couple of months ago I was in the process of studying some polygon roof framing angles and started to draw out the roof the Hall of the Abencerrajes thinking it was based on some type of Octagonal ground plan. That's when I discovered it was based on the two squares rotated in the circle, Ad Quadratum, that all other medieval cathedral baptismal's are based on. It's not a cathedral, unless it has a baptismal based on the sacred cut. 

Ad Quadratum, the Sacred Cut, & Roman Architecture

Stonemasons and carpenters of the medieval ages learned how to draw out Ad Quadratum, Ad Triangulum, Seed of Life (Daisy Wheel), like you I learn our ABC's. The ground plan of any cathedral would start with Ad Quadratum, then they would use Ad Triangulum for the elevation and then use the daisy wheel to transfer angles. And when they got bored or drunk they would use their compass to inscribe the Seed of Life (Daisy Wheel) on stone or timbers. 


Excerpt from course at Dartmouth:

Three Systems of Proportions
In this course we'll cover the three main systems of proportion in architecture.
  • 1. A system based on the musical ratios, used by Alberti and Palladio, which we'll cover in our unit on Renaissance architecture.
  • 2. A system based on the golden ratio, such as Le Corbusier's Modulor, which we'll look at in our unit on twentieth century architecture.
  • 3. A system based on the square, apparently used by the Romans, the subject of this unit.

Ad Quadratum
Pisa DuomoSlide 7-11: Pisa DuomoCalter Photo
Analysis of buildings at Pompeii and Herculaneum suggest that the design of the Roman house at all scales is based on the geometry of the square; they are said to be built ad quadratum.


The Sacred Cut
In addition to the ad quadratum figure and the root-two rectangle, we have a third geometric system based on the square. It is called the Sacred Cut.

Tons Brunes
Secrets of Ancient GeometrySlide 1-1: Secrets of Ancient Geometry and Its UseCover of Brunes' Book
This name was coined by the Danish Engineer Tons Brunes, in his book The Secrets of Ancient Geometry and Its Use. In that book he claims the sacred cut is found in the layout of many ancient building, including the Parthenon.


Note: this book is out of print and very expensive on Amazon, but you can find information for download via a google search online. Very interesting and informative.


Geometry at Work: A Collection of Papers Showing Applications of ... - Page 26
Cathy Gorini - 2000 - Preview
... many researchers have studied the geometric and spiritual bases of ancient structures [7, 16, 17, 19]. This paper will discuss the work of Tons Brunes, a Danish engineer, who hypothesized a system of ancient geometry that he believed ...

Magdalene's Lost Legacy: Symbolic Numbers and the Sacred Union in ... - Page 23
Tons Brunes has offered an interesting explanation that relates to the heavenly properties of seven and to its associations with the Goddess and the moon, showing how the menstrual feminine (lunar) cycle of twenty-eight days related to the ...


the golden ratio:

The Sacred Cut:

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