Home By Laws History Philosophy Geometry What's New Links

Click this Button to return to the Liverpool Syracuse Masonic Website    Liverpool Syracuse Masonic Website


 

 

Masonic Geometry

“All of my best thoughts were stolen by the Ancients”

THERE REALLY IS NO SUCH THING as "Masonic Geometry," if one were to search through the official literature of the Craft. However, in that Geometry is the ‘basis of Freemasonry,’ many writers, myself included, have taken up the pen to ‘speculate’ on some possible correlations as to why Geometry may be its ‘basis.’ This, too, covers a large body of Masonic and other research, articles, books, magazines, charts, art, and related media ranging from the scholarly, to the speculative, and to the fringes thereof.

In the pages of this website a selection of material is presented to reflect some of the interesting aspects of this Geometry and the numerous efforts to sort out the ‘meaning’ of it. Other aspects of this may also be found in our pages relating to Masonic History and Masonic Philosophy.

Below you will find selections categorized, where appropriate, into such topics as may be convenient for what may be uploaded from time to time. While our archives are large, alas our labor is significantly less, so check back periodically for new additions to our postings.

Masonic Geometry Part I         A View of Contemplative Geometry in Freemasonry
Masonic Geometry Part II        Preston’s ‘Masonic’ Geometry
Masonic Geometry Part III       Fra Luca Pacioli, Leonardo DaVinci and Others . . .
Masonic Geometry Part IV       From a Point to a Line to a Superfices to a Solid
Masonic Geometry Part V        Receptions of a Mason

Dew Drop Lecture

Freemasonry
and a View of the
Perennial World Philosophy

Perceptions of the Craft Ritual,
The Prevailing View and the Perennial Search for Light

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

by Lee Miller
Chancery Press, Liverpool, New York
copyright 1999, all rights reserved

Table of Contents

About the author

Preface

Table of Contents

List of Illustrations and Figures

 

I               Introduction - The Hidden Mysteries of Freemasonry.

 

II             Morality, Symbology and Allegory

Section I                  The Prevailing View.

Section II                 The Language of Symbol and Allegory

Section III               The Perennial Philosophy

 

III            Operative and Speculative Masonry - Then and Now

Section I                  Behold.

Section II                 The Masonic Charioteer.

Theo and the Horse/Lions

Further Light

 

IV            The Ritual of Freemasonry - The Aprons of Blue Lodge.

 

V             Preparation

Section I                  Passage - The Quarry.

Theo and the Brass Mine

Section II                 The Preparation Room - An idealization of the Room and its purpose.

Section III               The Door

Theo and the Door

 

VI            Geometry - The ‘Basis’ of Freemasonry

Section I                  1\2\3\2\1 - The Builder’s Art & Divine Proportion

Section II                 Occurrences of Phi in Contemplative Geometry.

The Double Pentagon and Phi

Relationship of the Five Platonic Solid Edges to Phi

Section III               The Point of Masonry - From a Point, to a Line, to a Superfices, to a Solid.

Kaballah - The Tree of Life in KST

Section IV               Thor’s Hammer - Another View of the ‘Solid.’

Section V                 The First Proposition of Euclid and a Perspective of the Vesica Pisces

Section VI               The ‘Six-pointed Three Dimensional Star,” by Way of the First Proposition of Euclid.

Section VII              Variations on the Square and Triangle - as Found in Operative, Speculative, Royal Arch and Concordant Masonry.

Section VIII             Further Commentary & Speculation - re: Rosslyn Chapel

The Triads of the Sephiroth

Further Observations - Geometric Facts & Speculation

 

VII           The Five Senses and Perception

Section I                  Life is But a Dream . . .

Scroll I     Diversity

Scroll II   Choice

Scroll III  Whence Arises Thought?

Scroll IV  Here and There

Scroll V   Now is the Hour

Scroll VI  Time on our Hands

Section II                 The Senses

Scroll VII                 The Five Senses

Part I       Sight

Part II      Hearing

Part III    Touch

Part IV    Taste

Part V      Smell

Part VI    The Hierarchy of the Senses

 

Section III (Part I)   Sens-itivity - The Sphere of Awareness, The Sphere of Perception & The Level of Sens-itivity.

Scroll VIII               Sphere of Awareness

Direct Focal Awareness

Perceptual Awareness

Section IV               The Sphere of Perception

                Scroll IX                  Perception I

Scroll X                   Perception II

Parable - The ‘Master’ on Wisdom & Remembrance

 

VIII         A ‘Final’ Visit to Boaz and Jachin - A Discussion of the Allegory of Pillars and Passing, Duality and Unity.

 

IX            Section I                  The Royal Arch Banners - and the Arms of the Most Ancient & Honorable Fraternity of

                                                Free and Accepted Masons.

Section II                 Theo and Another View of the Four Veils 136

 

X             Observations on the Triple Tau - a Symbol of the Holy Royal Arch, and Variations of the Matrix in the Craft and some other Bodies of Masonry.

Epilogue - to Observations on the Triple Tau

 

XI            A Visit to the Sixth Liberal Art - Astronomy - A Perspective from the Seed, the Point.

 

XII           Section I                  Spiritus Mundi - An Overview of Freemasonry and the Perennial World Philosophy. Then and Now.

An Evolutionary Journey

Section II                 ‘This Book . . . ‘

 

XIII         Epilogue.

 

Appendices.

 

I               From Temple to Temple - An alternate allegory for Preparation.

II             Euclid’s Elements - Book I, Proposition I.

III            Extract of ‘Timaeus’ - from the ‘Dialogues of Plato.’

IV            The Golden Verses of Pythagoras.

V             Matthew 7:7 & 8 - concerning the ‘Knocks.’

I Corinthians 15 - on Death, Immortality and Raising.

VI            The ‘Fama’ - an excerpt Re: ‘the Learned of Spain and Europe . . .’

VII           “The Old Poet’s Rhyme”

VIII         “Of Wisdom and Fools”

“The No-Letter Poem”

IX            Address of M\W\ Joseph D. Evans on Grand Lodge Library and Masonic Teachings - 1855

X             Phi Progression Values

XI            “Echoes from the Cocoon”

XII          The Constitutions (Preamble) & Landmarks of the Grand Lodge, F&AM, New York

XIII         “Mother Earth”

XIV         Pythagorean Triangle – Golden Proportion Proof

 

Bibliography

 

Illustrations and Figures.

 

Frontispiece - The Three Grand Masters and ‘KST Module’

 

I.              Introduction

Fig, 1.1                    Golden Progression Graphic

Fig. 1.2                    1/f Progression

Fig. 1.3                    Caduceus

 

II.            The Perennial Philosophy - ‘Mexican Tablet No. 1231’

 

III.           Operative and Speculative Masonry

Section I. Operative / Speculative Masonry

The Hermit

Section II The Masonic Charioteer

Fig. 3.2.1.                Arms of the Antient Grand Lodge

Fig. 3.2.2.                The Chariot - The ‘Merkabah’ - The Vision of Ezekiel

 

IV.           The Aprons of Blue Lodge

Entered Apprentice & Fellowcraft

Master Mason

 

V.            Section II:              Preparation

An Idealized Layout for a Preparation Room

Nascita di Venere - Birth of Venus,” by S. Botticelli

 

VI.           Section I:               The Builder’s Art & Divine Proportion.

Fig. 6.1.1. a-g.         Four: The Square and Cross.

Fig. 6.1.2.                The Equilateral Square with Interior Angles of 90o.

Fig. 6.1.3a.              The ‘Cross-Supported’ Square.

Fig. 6.1.3b.              The Masonic Apron.

Fig. 6.1.4.                The Diagonal of a Square, by the 47th Proposition of Euclid.

Fig. 6.1.5.                The Progression of the Diagonal of the Square.

Fig. 6.1.6.                The Golden Rectangle and a:b::b:c.

Fig. 6.1.7.                The Theorem of Thales and the Right Angle in a Semicircle.

 

VI.           Section II:              Occurrences of Phi.

Fig. 6.2.1.                The Double Pentagon and Phi.

Fig. 6.2.2.                The Double ‘Eastern Star.’

                Fig. 6.2.3.                Solomon’s Seal.

Fig. 6.2.4.                The Pentagonal Pyramid (aka the ‘Chrysler’ logo).

Fig. 6.2.5.                The Pentagonal Pyramid as faces of an Icosahedron.

Fig. 6.2.6.                The Golden Rectangle in an Icosahedron.

Fig. 6.2.7.                The Equilateral Triangle of a ‘Geodesic Dome.’    

Fig. 6.2.8.                The Octahedron ‘Nested’ at the Phi Points of a Face-Triangle of an Icosahedron.

Fig. 6.2.9. a-e.         The Outer Hexagonal Perimeter of the Hexagon, Icosahedron, Cube, Octahedron . . . and the Star Tetrahedron.

Fig. 6.2.10.              The Nested Pentagon and Pentagram and Phi.

Fig. 6.2.11.              The Pentagonal Spiral.

Fig. 6.2.12.              Relationship of the Five Platonic Solid Edges to Phi.

Fig. 6.2.13.              Face-view of an Icosahedron.

 

VI.           Section III:            The Point of Masonry.

Fig. 6.3.1.                The Focal Point.

Fig. 6.3.2.                ‘Two’ Points.

Fig. 6.3.3.                The Line.

Fig. 6.3.4.                The Line as a Radius (The Objective Radius . . . Sun).

Fig. 6.3.5.                The Objective and Subjective Radii (Sun and Moon).

Fig. 6.3.6.                The First Intersection (P2, P3)  (Vesica Pisces - 1st Proposition of Euclid).

Fig. 6.3.7.                The Second Extension - (P4 - P7).

Fig. 6.3.8.                The Third Extension - (P6).   

Fig. 6.3.9.                The KST SS Module with Star of David.

Fig. 6.3.10.              The KST ‘Sanctorum’ Module.

Fig. 6.3.11.              Projection of Double Cubes in the ‘Sanctorum’ of KST.

Fig. 6.3.12a.            Double Cubes.

Fig. 6.3.12b.            Star Tetrahedron in a Cube.

Fig. 6.3.13.              Star of David in the U.S. Seal.

Fig. 6.3.14.              Kaballah - The Tree of Life in KST

 

VI.           Section IV.             Thor’s Hammer.

Fig. 6.4.1.                The Tetraktys.

Fig. 6.4.2.                The Tetraktys and the Star of David.

Fig. 6.4.3.                Thor’s Hammer.

Fig. 6.4.4.                Views of the ‘Swastika’ or Flyfot signs.

Fig. 6.4.5.                The Octahedron as Thor’s Hammer.

Fig. 6.4.6.                The Tetraktys (Tetraktys) of the Preston Lecture.

Fig. 6.4.7.                The Tetraktys and the ‘Ten’ Points.

Fig. 6.4.8.                An Icosahedron, consisting of 20 Equilateral Triangles.

 

Section V.                The First Proposition of Euclid.

Fig. 6.5.1.                The First Proposition of Euclid.

Fig. 6.5.2.                Euclid’s First Proposition (Book I) with subjective triangle.

 

VI.           Section VI.             The “Six-Pointed Three Dimensional Star” by way of the First Proposition of Euclid

Fig. 6.6.1.                The Point.

Fig. 6.6.2.                The Duality.

Fig. 6.6.3.                The Linear Duality.

Fig. 6.6.4.                Line OP1 as the Radius of a Circle with a Center of O.

Fig. 6.6.5.                The Objective and Subjective Circles, with Radii.

Fig. 6.6.6.                Glyph for the Sun and the Moon.

Fig. 6.6.7.                The Lodge Room as the Sun and the Moon.

 

VI.           Section VII.           Variations of the Square and Triangle.

Fig. 6.7.1.                The 1:2:SR3 Square.

Fig. 6.7.2.                The Master at the Hypotenuse.

Fig. 6.7.3.                The Warden’s Squares and the Equilateral Triangle.

Fig. 6.7.4.                The Lozenge.

Fig. 6.7.5.                The Star of David, by the 1:2 Square (‘As above, so below).

Fig. 6.7.6.                The First Proposition of Euclid, with Subjective Equilateral Triangle.

Fig. 6.7.7.                The Symbolic 1:2 Lodge, by 1:2 Squares.

Fig. 6.7.8.                The Symbolic 1:2 Lodge, by Equilateral Triangles.

Fig. 6.7.9.                The Symbolic Lodge, by the Vesica Pisces and Gothic Arch.

 

Section VIII

Fig. 6.8.1                 Cluster of Fig. 6.3.9.

Fig. 6.8.2.                Tree of Life.

Fig. 6.8.3.                Kabbalah - The Tree of Life in KST.

Fig. 6.8.4.                Rosslyn Chapel Floor Plan (with Tree of Life Overlay)

Fig. 6.8.5.                Star Tetrahedron in a Cube.

Fig. 6.8.6.                The Triads of the Sephiroth.

Arms of the Antient Free and Accepted Masons

The Caduceus

28 - A Perfect Number (Grid)

 

VII.          Life is But a Dream . . .

Scroll IV.                 Here and There: North, South, East & West.

Scroll VII.VI.           The Hierarchy of the Senses. Perception.

Section III.I             Sens-itivity.

 

VIII.        A ‘Final’ Visit to Boaz and Jachin.

The Altar of Burnt Offerings.

The Veil of (the Saitic) Isis.

The High Priestess.

 

IX.           The Royal Arch Banner.      Section I

Fig. 9.1.1.                Arms of the Antient & Honorable Fraternity of F&AM.

Fig. 9.1.2.                The Four Gospels from the Book of Kells.

Fig. 9.1.3.                The Four Banners of the Royal Arch.

Fig. 9.1.4.                The Grand Banner of the Royal Arch.

Section II                 Another View of the Four Veils.

Fig. 9.2.1 .               The Four Suits Unified.

Fig. 9.2.2.a-d.          The Four Suits.

The Octahedron (see also Thor’s Hammer [q.v.]).

 

X.            Observations on the Triple Tau and Variations of the Matrix.

Fig. 10.1.                 The Triple Tau, Triangle and Circle of the R.A.M.

Fig. 10.2.                 The T. H. of the Early Royal Arch.

Fig. 10.3.                 The Arch of Bro. Robert H. Brown.

Fig. 10.4.                 The Triple Tau and Symbol of the High Priest in the Astronomical Matrix.       

Fig. 10.5.                 The Broken Triangle and Trowel of the Cryptic Degrees in the Matrix.

Fig, 10.6.                 The Templar Cross of the Knights Templar in the Matrix.

Fig. 10.7.                 The Teutonic Cross Of the S.G.I.G., 33o in the Matrix.       

Fig. 10.8.                 The Cube and Star of David (Tetrahedron) in the Matrix.

Fig. 10.9.                 The Square and Compasses of the Craft Degrees in the Matrix.

Fig. 10.10.               The ‘Christian’ Triple Tau, a variation.

Fig. 10.11.               The ‘Platonic’ Triple Tau, a variation.

Fig. 10.12.               The .Triple Trowel.’

 

XI.           A Visit to the Sixth Liberal Art.

Fig. 11.1.                 The Zodiac Wheel.

Seal of the Ancient Grand Lodge.

Taurus.

Leo.

Scorpio (as the Eagle).

Aquarius.

 

XII.          Spiritus Mundi

Master Mason’s Apron. (PM)

 

Appendices:

Appendix II            The First Proposition of Euclid.

 

Appendix III           Extract of ‘Timaeus’ from the ‘Dialogues of Plato.’

Fig. AIII.1.              The 45o Isosceles Triangle.

Fig. AIII.2.              The Scalene 90o Triangle.

Fig. AIII.3.              The Equilateral Triangle formed from a Double Unit (30, 60, 90 triangle).

Fig. AIII.4.              . . . 3 Times the Square of the Lesser Side, proved.

Fig. AIII.5.              Triangle with an Hypotenuse Twice the Lesser Side (2:1).

Fig. AIII.6.              Two Such Triangle, from Fig. 5., joined at the diagonal.

Fig. AIII.7.              Three such joined Triangles, from Fig. 6., conjoined at a Common Center.

Fig. AIII.8.              A Tetrahedron.

Fig. AIII.9.              An Octahedron.

Fig. AIII.10.            An Icosahedron.

Fig. AIII.11a.          An Equilateral Quadrangle of with four Isosceles Triangles. 

Fig. AIII.11b.          A Cube.

 

Appendix XIV        Pythagorean Triangle – Golden Proportion Proof

 


Contact
Gary L. Heinmiller, Director
boazz@twcny.rr.com

 
For problems or questions regarding this Web site contact Webmaster.
Last updated: 22 April 2008