Saturday, March 23, 2013

There are no decimal points in Geometry

Time line of roof framing geometry for carpentry
 stéréotomie --> trait de charpentre --> the art of the line


  • Pythagoras of Samos (500 BC) Greek
  • Euclid of Alexandria (300 BC) Greek 
  • Archimedes of Syracuse (287 – 212 BC) Greek
  • Apollonius of Perga (262 – 190 BC) Greek 
  • Marcus Vitruvius Pollio (80 – 70 BC) Roman
  • Anthemius of Tralles (474 – 558) Greek - Roman
  • Abul Wafa al-Buzjani (940 – 998) Persian, Baghdad 
  • Villard de Honnecourt (1225) Cistercian Order of France
  • Matthäus Roritzer (1435 – 1495) German
  • Albrecht Dürer (1471 – 1528) German
  • Rodrigo Gil (1500 – 1577) Spanish
  • Andrea Palladio (1508 – 1580) French
  • Philibert De l'Orme, (1515 – 1576) French
  • Francois Derand (1588 – 1644) French 
  • Mathurin Jousse(1607 – 1692) French
  • Gérard Desargues(1591 – 1661) French 
  • Amédée-François Frézier(1682 – 1773) French
  • Gaspard Monge (1746 – 1818) French
  • Peter Nicholson (1765–1844) Scottish 
  • Asher Benjamin (1773 – 1845) American
  • Nicolas Fourneau (1786) French
  • Jean Baptiste Rondelet, (1802) French
  • Jean-Charles Krafft (1805) French
  • Charles François Antoine  Leroy, (1844) French
  • Colonel Armand Rose Emy  (1771-1851) 1856 French
  • Joseph Alphonse Adhémar (1854) French
  • Louis Mazerolle (1866) French 
  • B. Cabanie (1864) French 
  • JD Boucher (1890)French 
  • Emile Detataille (1890) French 
  • Pierre-François Guillon (1848 - 1923) French
  • King, Charles A. (Charles Albert), b. 1865 American
  • Townsend, Gilbert, b. 1880 American
  • Hodgson, Frederick Thomas, 1836-1919 American
  • Griffith, Ira Samuel, 1874-1924 American
  • Gould, Lucius D., b. 1814 American
  •  Tredgold, Thomas, 1788-1829 American
  • Hicks, Isaac Perry, 1856-
  • Radford, William A., 1865
China's roof framing geometry is at  least 3000 years old. Chinese carpentry techniques and design were first exported to Korea and then, around 700 AD, to Japan. (Jan Lewandoski,  Timber Framing 2004-12)


300 BC
Euclid of Alexandria
Euclid’s Elements
Book XI – Steretomery --> roof framing kernel for tetrahedron - tetrahedral
Book XII – Proportional Steretomery
Book XIII – Platonic Solids --> Dihedral Angle --> Hip Rafter Backing Angles


Book XI Proposition 6
If two straight lines are at right angles to the same plane, then the straight lines are parallel.



80-BC
Vitruvius
These stereotomic plots were used to build monuments.
Complex body of knowledge from the empirical approach of building monuments.

(1260)
Villard de Honnecourt 
 Here begins the method to draw the line figures and the art teaches geometry for easy work.



(1500)
Albrecht Dürer  Uses drawings techniques of the Free Masons



(1550)
Philibert Delorme
The three lost points of  this ancient art. First speed square. 




(1627)
Mathurin Jousse 
 Théâtre de l'art de la charpenterie



(1643)
Gérard Desargues
Called it projective geometry

 (1767) 
Nicolas Fourneau
 L'art du trait de charpenterie


(1799)
Gaspard Monge
Discloses  the secrets of the Free Masons Stereotomery and calls it Descriptive Geometry

(1828)
Peter Nicholson
Father & Brother were Free Masons

Geometry is the science of extension, and magnitude, and
consists of theory and practice.
The theoretical part is founded upon the reasoning of self.
evident principles ; it demonstrates the construction, and shows
the properties of regularly defined figures. The theory is the
foundation of the practical part ; and without a knowledge of it,
no invention to any degree certain can be made.



CONSTRUCTION  OF  HIPPED   ROOFS.

[Plates XXVL-XXIX.]

23.  Plates  XXVI. XXVII. XXVIII. and  XXIX. exhibit  the  construction of hipped roofs.    By 
means of the plan we have the seats of all the lines; therefore, if we have the heights of these 
lines, we can easily find their lengths by drawing a right-angled  triangle,  of which one of the  
legs is the seat of the line on the plan, and the other the difference of the  heights  of each end 
of the line from its seat.-See ORTHOPROJECTION,  Problem vi.-We may  find all  the  angles  from 
the  principles of projection ;  but  the  method  employed throughout  all the figures exhibited 
in the four plates is that used in the construction  of tetrahedral (tetrahedron),  Fig. 3, Plate  XXIX.


tetrahedron ...... he studied Euclid 
original spelling ... trehedrals

(1866)
Louis Mazerolle
Traité Théorique et Pratique de Charpente


(1880)
Pierre-François Guillon
Founder of The Practical School of Stereotomy Applied to Construction



(1864)
B. Cabanie
Charpente Generale Theoique Et Pratique



(1890) 
JD Boucher 
Problems of  the Art of Carpentry by 
Emile DELATAILLE & B. Cabanie were students of JD Boucher ?


(1890)
Emile DELATAILLE 
L'art du Trait Pratique de Charpente





trait de charpente -- > art of line drawing
4 techniques de Trait de charpente
Le Rembarrement,
La Herse,
La Sauterelle
Le Croche.

Rembarrement
The processes of the trait de charpente which uses the lines drawn to the sides of the plan view for the bevel angle cuts.

Herse
The processes of the trait de charpente which uses the roof surface plane  to establish angle cuts.


Sauterelle
The processes of the trait de charpente which uses the intersection of the geometric planes. The geometric planes are parallel to the face of each beam and enables precise calculations of angle cuts and beam lengths.

Croche
The processes of the trait de charpente which uses ???


























Traité de stéréotomie (charpente et coupe des pierres)
Author: Jules Pillet
Publisher: Paris, C. Delagrave; Leipzig, H. Lesoudier, 1887. & 1923




Traité de stéréotomie, comprenant les applications de la géométrie descriptive à la théorie des ombres, la perspective linéaire, la gnomonique, la coupe des pierres et la charpente; avec un atlas composé de 74 planches infolio, 
par C. F. A. Leroy
print 1844
AUTHOR:  Leroy, Charles François Antoine 1780 (ca.)-1854

Traitè de la Charpenterie by Hassenfratz, 1804
Hassenfratz, J. H., Traitè de la Charpenterie 1804, Paris.
He studied under Nicolas Fourneau

Traité théorique et pratique de l’art de bâtir by Jean Baptiste Rondelet, 1802


Traitè de l’Art de la Charpenterie written by the
Colonel Armand Rose Emy  (1771-1851) 1856,

It is quite probable that the ancient builders, carpenters and especially that the frequent use of wire-to-lead gives ideas on fairer lines projetantes had used the outset the method of projections to determine the exact form that would provide the faces of the segments or assemblies pieces of wood, but it was only an instinctive way, and processes specific to each question. As the first authors who described these methods confine themselves to indicate, in a way very tedious series of graphics operations to perform on the sketch, without relieving memory or spirit guide with some considerations geometry that would help treat similar cases, although a little different. It is in this spirit of routine practice written What the Treaty of architecture Philibert Delorme in 1576, Secrets of the architecture by Mathurin Jousse in 1642 (reviewed by Lahire book in 1702), The architecture of arches in 1643 by P. Derand, and the Treaty of cutting the stones first published in 1728 by the architect Delarue. It is even more modern work composed in 1786 by Furnace, skilled master carpenter, but who is occupied with the art of line; book is also written and distributed in a way that makes reading trèslàtigante. While, from 1738, Frézier, Chief Engineer, Landau, and then Director of the fortifications of Britain, issued a.Treaty of Stereotomy in 3 volumes to, in which he explained the principles of geometry combinations of rows and surfaces that are actually cut stones and wood, as well as practical methods that must be used to cut these materials. This work, which was a great success when he appeared, still deserves to be studied, and to keep the Frézier his share in the progress of science, it is fair to point out that already employed the horizontal and vertical projections to define segments.



Finally, at the School of Military Engineering was founded in 1748 in Mézières, Monge, who was in charge of teaching the Stereotomy from 1770 to 1784, and published many memoirs on the application of analysis to geometry, meditation also on how to meet a common bond that all the various processes used in the fortification, the layout of roads and canals, the device works in stone or wood, and his genius was there arise a new science independent of any special application to any art that is descriptive geometry, he taught at the Students of the School of Mézières, and later those of the École Polytechnique in 1794, and the normal schools Temporary formed in Paris in 1795. It is these lessons, then gathered in a separate volume, offered the first Treaty of Descriptive Geometry, General science whose methods are now bases all graphic arts.

In this volume, I tried to gather all interesting problems and can offer truly useful Cup stones and especially the construction of arches. As for the framing, alteration of my sight and the desire not to delay publication announced long ago, forced me to limit myself to the main questions on the roof and stairs while still embracing the art panels wooden walls , floors, bridges, arches and scaffolding are used to mount the vaults or other stone buildings, as well as naval carpentry. But to all of these questions, there should be a special book, and readers who wish further into this subject, find something to satisfy the great Treaty of carpentry in 2 volumes in-4 °, M-recently dialed. Emy, Colonel Military Engineers.



Traité de charpente

 Par Joseph Alphonse Adhémar


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