Roof Framing Book Table of Contents

Holy Grail of Roof Framing 
Geometry & Trigonometry

Complex Roof Framing Simplified

Trade secrets from Euclid, Cistercian monks, French Compagnons ,German Zimmermann and the American Carpenters & Builders of centuries past that only a limited few were allowed to know.

Possible Table of Contents
-----------------------------------------------------------------------

Developed Geometry From The Past

Finding the Lines of Descriptive Geometry by Monge

Folding Roof Surfaces

Hip Rafter Roof Plane Alignment

HAP-- Height Above Plate

Roof Framing Kernels

Prism Plane Geometry - Unbacked Shoulder of Hip Rafter

Understanding Plan Angles

Understanding Tangent Lines

Hip Rafter Offset/Shift

Hip Rafter Backing Angles -- Equal & Unequal Pitched Roofs

Hip Rafter Dihedral Angle for Hip Rafter Backing Angle

Back Bevel Angles -- Top Cut Angles

Hip Rafter Head Cuts -- Equal & Unequal Pitched Roofs

Jack Rafter Head Cuts -- Equal & Unequal Pitched Roofs

Using a Framing Square As A Protractor

Framing Square Usage for Laying out Rafters

Pyramid Hip Roof Rafters -- Equal & Unequal Pitched Roofs

Hexenschnitt -- The Witches Cut, Square Tail Fascia

Shed Roofs

Shed Roofs with Sloping Ridges

Shed Roofs with Walls not Parallel to the Ridge

Equal Pitched Gable Roofs

Unequal Pitched Gable Roofs

Unequal Pitched Gable Rafters with Unequal Plate Heights

Lapping Rafters Ridge Cut Angles for Equal & Unequal Pitched Roofs

Pitch To Plate Roof Trigonometry

Trapezoid Ground Plan Roof  with Unequal Overhang

Trapezoid Ground Plan Roof  with Equal Overhang

Octagon Hip Rafters

Octagon Roof Framing 4 Butt Hip Rafter Method

Octagon Roof Framing 4 Butt Hip Rafter Method with Purlin Structural Ring

Octagon Roof Framing with Gazebo Cupola

Hexagon Hip Rafters

Pentagon Hip Rafters

Polygon Roof Framing Angles

Curved Elongated Hexagon Roof Framing

Curved Elongated Octagon Roof Framing

Cupola Roofs

Snub Nose Hips

Clipped Hip Rafters

Dutch Hip Roofs

Tudor Roofs

Broken Hip Rafters

Blind Valley Rafters

Hidden Valley Rafters

Scotch Valley Rafters

Hip Dormer

Gable Dormer

Shed Roof Dormers

Drag Dormer
Schleppdachgaube

Triangular Dormer
Dreiecksgaube

Sloping Ridge Dormers

Drag Hipped Dormer

Abgewalmte Schleppdachgaube

Trapezoidal Dormer

Trapezgaube

CutIn Shed Roof Dormers

Barrel Roofs with Purlins

Barrel Roofs with Ribs

Eyebrow Roofs with Purlins

Eyebrow Roofs with Ribs

Circular Roofs

Octagon Foot Print on Circular Roofs

Elliptical Roofs

Ski Slope Rafters

Gambrel Roof Framing Angles

Dutch Gambrel Roof

Pent Roofs with Curved Rafters
Pultdach

Prow Roof Angles

Unequal Pitched Octagons

Unequal Sided Octagon Geometric & Trigonometric Roof Framing Development

Bay Window Rafters with Unequal Overhang

Bay Window Rafters with Equal Overhang

Bay Window Dog Leg Valley Rafters

California Valley Sleeper Bevel Cuts

Valley Sleeper Saw Blade Bevel Angle Geometric Development

Purlin Angles

Purlin Lip Cut Angles

Purlin or Dormer Square Tail Fascia Layover Cuts

Frieze Block Angles

Segmental Arch

Tudor Arch 
Ogee Arch 
Rampant Arch 
Lancet Arch 
Gothic Arch 
Morrish Arch 
Semicircle Arch 
Segment Arch 
Pointed Arch 
Elliptical Arch 
Equilateral Arch 
Double Curvature Arch 
Trompe Arch 
Catenary Arch

Lofting Equal Height Ordinates for Arches to Ellipses

Groin Vault Plotting -- Lofting Equal Height Ordinates for Elliptical Cross Vault

Semi-Circular Square Groin Vault
Semi-Circular Rectangular Groin Vault
Segmental Square Groin Vault
Segmental Rectangular Groin Vault
Gothic Square Groin Vault
Gothic Rectangular Groin Vault
Semi-Circular Hexagon Groin Vault
Segmental Hexagon Groin Vault
Gothic Hexagon Groin Vault
Semi-Circular Octagon Groin Vault
Segmental Octagon Groin Vault
Gothic Octagon Groin Vault
Semi-Circular Dodecagon Groin Vault
Segmental Dodecagon Groin Vault
Gothic Dodecagon Groin Vault
Semi-Circular Hexadecagon Groin Vault
Segmental Hexadecagon Groin Vault
Gothic Hexadecagon Groin Vault

Crown Molding Angles --> Square Tail Fascia -- Frieze Block -- Purlin Angles

Hopper Angles

Creeper Rafters

Plumb bevel --> Level Bevel --> Edge Bevel
Edge bevel creeper
Edge bevel purlin
Face bevel purlin

Plywood Cuts

Hip Rake Walls Rotated into Roof Surface Plane

Hip Rafter Diamond Post Calculations

Alhambra Granada Ad Quadratum Ground Plan

Octagonal Baptismal

Joe Bartok Roof Framing Studies

Complex Roof Framing by Billy Dillon

Unequal Pitched Valley Rafter Framing by Tim Uhler

One Length Method© by Richard Birch Irregular Hip & Valley Rafters

The Cube Method

Framing Square Usage for Plan Angles

Simplified Roof  Framing

Timber Framing

Fourteen Working Planes of  Roof Framing Geometry

Log Joinery Framing

Traditional Roof Framing Geometry Layout

Shiftungen Technique

Traité de Charpente, Art of Line

Rabattement Surface, Folding Plane or Folding Roof Surface

Drawn Down Method

Devers de Pas

Reciprocal Roof Framing  Geometry

Prismatic Foot Print

Rafters Rotated Plumb To Earth

Rafters Rotated Plumb To Roof Surface

Skewed Rafters Rotated Plumb To Earth

Skewed Rafters Rotated Plumb To Roof Surface

Saint Andrews Cross

Claw Angles

Stereotomic & Descriptive Geometry
Stereotomy (masonic projection) techniques

Spiral - Helix  - Circular Stair Geometric Development

Tangent Handrailing & the Prism Plane

Platonic Solids

Trigonometry Formulas

Unit Circle

Circle Tangent To Hip Rafter

Law of Sines

Law of Tangents

Law of Cosines

Cosine Trigonometry Formulas

Law of Sines Trigonometry Formulas

Pythagorean Trigonometric Identities

Tetrahedrons

Tetrahedron Slices Folded & Unfolded

Canadian & American Geometric Roof Framing Development & Framing Square Usage
Compound Miter Angle and Saw Blade Bevel Angles

Saw Blade Angle Development

Direction Of Saw Travel

Bartok, Hawkindale, Martindale and McKibben-Gray Hip-Valley Roof Ratios Angle Formulas.

Bevel angles for three dimensional connections

Euclid's Elements

Euclid's 47th Proposition

Pythagorean Theorem

Thales’ Theorem to Construct a Right Triangle

Formula for a golden ratio ellipse
Formula for a golden ratio stairs
Formula for a golden ratio Roof slope Angle

Vitruvian Man

Conic Sections
conic section, ellipse, parabolas, hyperbolas

Solid Geometry
Horizontal Plane
Vertical Plane
Horizontal Trace of Oblique Plane
Vertical Trace of Oblique Plane

Planar Geometry

Circle Geometry

Umbra Recta
Orthography and Scenography

WorldSkills Carpentry Competition Training

Japanese Carpentry

trait de charpente

Euclid

Zimmerman

Compagnonnage
FreeMasons masonic projections technique
Cistercian monks -> French Compagnons ->Carpenters’ masterworks, twisting and turning beyond the geometrical kernel

Ad Quadratum - Daisy Wheel - Ad Triangulum

1. Sand Geometry
2. Light Geometry
3. Egyptian Geometry
4. Greek Geometry
5. Roman Geometry
6. Arabic/Islamic Geometry
7. Persian Geometry
8. Pythagoras Geometry
9. Euclidean Geometry 
10. Vitruvian Geometry
11. Archimedes Geometry
12. Apollonios Geometry
13. Sacred Geometry
14. Vesica Piscis Geometry
15. Ad Triangulum Geometry
16. √3 Geometry
17. Ad Quadratum Geometry
18. √2 Geometry
19. Golden Ratio phi
20. Star of David or Solomon's seal 
21. Thunder Mark's
22. Euclidean six point geometry
23. Empirical geometry
24. Descriptive Geometry 
25. Spherical Elliptical Geometry 
26. Equilateral triangle Geometry
27. Stone Cutting Geometry
28. Trompes(ribless, conical vaults)

Bibliography

Euclid of Alexandria (200 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, Le premiere tome dell’architecture
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) British 
Asher Benjamin (1773 – 1845) American 
Nicolas Fourneau (1722 – 1792) French
Louis Mazerolle (1800) French
JD Boucher (1800) French
Emile Detatille (1800) French
Billon Freres (1800) French
Robert Willis (1800 – 1875) British

Art de la charpenterie; by A. R. Emy. 1841-42
J. Newlands. Carpenters' and joiners' assistant; 1860

Hetsch Holzarchitectur des mittelalters; by C.Botticher. 1841

J.C. Krafft  1815

Traité sur l'art de la charpente théorique et pratique: Anweisung zur theoretisch-praktischen Zimmermanns-Kunst. Treatise on the art of carpentry, with the theory and practice

W. Pain,  Practical House Carpenter 1799

T. Tredgold, Elementary Principals of Carpentry 1821

J. Smith, Specimens of Ancient Carpentry 

Nicolai  Zabaglia 1743
Leonardo da Vinci
François Mansart
Gabriel-Philippe de LaHire
Charles-François-Antoine
Nicolas Fourneau
Peter Nicholson
Louis Mazerolle
JD Boucher
Emile Detataille
Cabanie
Robert Ridial
Ira Samuel Griffith
William A. Radford
Alfred W. Woods
G.C. Volland

G.C. Schulze
Armand Rose Emy Traitè de l’Art de la Charpenterie
J. B. Rondelet
Charles A. King
J. W. Riley
Simplified Roof Framing by J. D. Wilson and S. O. Werner 1927
A Roof Cutter's Secrets by Will Holladay 2006
Marie-Thérèse Zenner
Timber Framers Guild 

Nexus Network Journal
The Edinburgh Encyclopedia

Elementa Geometriae- 1482

Gilbert Emery

Jean-Michel Emery

Philippe Nairière

Marie-Paule Raimbault

Peter Kübler
Albert Müller
Andreas Großhardt
Hans Wittmann
Roland Schumacher
Michael Riggenbach

Manfred Euchner 

Von Franz Krÿ¤mer

Silas Hawes Framing Square 1814

Eagle Square Manufacturing Co. 1846

Howard square 1881

Sargent Square 1914
Nicholls Square 1901
Chappell Master Framing Square 2010



U.S. Patent Documents for Carpentry Squares

247353	September 1881	Howard
492532	February 1893	Gilmer
651057	June 1900	Roberts
672455	April 1901	Nicholls
691192	January 1902	Smith et al.
937202	October 1909	Bailey
1102689	July 1914	Sargent
1196519	August 1916	Caylor
1236817	August 1917	Bick
1241976	October 1917	Hill
1463605	July 1923	Walters
1477002	December 1923	Parkhill
1704462	March 1929	Crandlemere
2654954	October 1953	Lawrence
4200990	May 1980	West
4420891	December 1983	Orem
5727325	March 1998	Mussell
6105266	August 2000	Cote
6725555	April 2004	Moore
6868616	March 2005	Allemand
7854070	December 2010	Vajentic

------------------------------------------------------------------------------

550 Ausseur (J. J.) Traité de la Coupe de Bois, ou Art du

Trait du Menuisier en Bâtiment, 4to. 35 plates, 1/. 4s. Paris, 1819

551 Barlow's (P.) Essay on the Strength and Stress of

Timber, 8vo. plates, 16*. 1817

552 Crocker's (A.) Timber Dealer's Guide, 4s. 6d. 1813

553 Essai sur les Bois de Charpente, 12mo. 3*. 6d.

Paris, 1763

554 Emerson's Principles of Mechanics, plates, neat, 15s.

1773

555 Fourneau (Nie.) l'Art du Trait de Charpenterie, 4 tom.

folio, 87 plates, sewed, 4L 4s. Pans, 1820

556 Hassenfratz's (J. H.) Traité de l'Art du Charpentier,

4to. 28 plates, II. 10*. Pans, 1804

557 Jousse (M.) Art de Charpenterie, folio, plates, 1/. 10*.

Paris, 1751

558 Krafft, Plans, Coupes, et Elévations de diverses Pro

ductions de l'Art de la Charpente exécutées tout en France que dans les Pays Etrangers, large and thick folio, about 400 plates, neatly half-bound, 8/. 18*. 6d. Paris, 1805

559 Krafft's (J. C.) Treatise on the Art of Carpentry, with

the Theory and Practice, folio, 180 plates, 5/. 15*. 6d.

SCO Krafft's (J. C.) Carpentry (Part 1 of the Work), comprising, Des Assemblages, Traits de Jupiter, Armatures des Poutres, Courbs en Planches, des Soffites, Pans de Bois, Planchers, 30 plates, 1/. 5s. Paris

561 Krafft's (J. C.) Carpentry (Part 2 of the Work), comprising Des Escaliers, 30 plates, 1/. 5s. Paris

562 Krafft's (J. C.) Carpentry (Part 4 of the Work), comprising Des Combles, 30 plates, 1/. 5s. Paris

563 Krafft's (J. C.) Carpentry (Part 5 of the Work), comprising Des Combles, Clochers, Coupoles, &c. 30 plates, II. 5s. Paris

564 Krafft's (J. C.) Carpentry (Part 6 of the Work), Construction of Theatres, 30 plates, 21. 12s. 6d.

Paris, 1822

565 Nicholson's (P.) Carpenter and Joiner's Assistant, 4to.

bound, 1/. Is. 1815

566 Nicholson's (P.) Carpenter's New Guide, 84 plates,

567 Nicholson's (P.) Treatise on the Construction of

Staircases and Handrails, 4to. 39 plates, bound, 18s.

1820

568 Pain's (W.) Practical House Carpenter, 4to. 146

plates, 15s. 1799

569 Smith's (J.) Specimens of Ancient Carpentry, 4to. 36

plates, 12s.

570 Tredgold's (T.) Elementary Principles of Carpentry,

4to. 22 plates, 1/. 4s. ' 1821

571 Zabaglia (Nicolai) Contignationes ac Pontes, ac Descriptioncs translationis Obelisci Vaticani, large folio, 54 plates, and a full length portrait of the

One of the reasons for me choosing

The Holy Grail of Roof Framing Geometry and Trigonometry

 for the title of my book.

Research on my mother’s maiden name of St. Clair.

Rosslyn Chapel was a rebuilding of the Temple of Solomon, designed by St. Clair

Research shows that ras or ros means wisdom. As such, could it be that the term ‘roslin’ means the St. Clairs , who were also the guardians of the fountain of wisdom pertaining specifically to the Holy Blood, the Holy Grail and the Holy Light.

Craft  Guilds --> Knights of the Templar --> St. Andrews Cross --> St. Clair -->Rosslyn Chapel --> Temple of Solomon --> Fountain of Wisdom --> Holy Grail