Behold! The Circle Squared Beyond Refutation

Subtitle:The Grand Problem No Longer Unsolved

Content:

Preface
A Short Historical Sketch
Carl Theodore Faber
Carl Theodore Heisel
Indorsement, One of Many
Chapter I: The Grand Problem No Longer Unsolved
  Brief and Infallible Method of Squaring the Circle
Chapter II: A New Law in Geometry
  An Eternal Difference Exists Between a Square and an Irrational Quantity
Chapter II: The Point and Line
  An Explicit Explanation of the First Principles of Mathematics
  The Divisibility of the Point and Line
Chapter IV: The Origin of the Line
  An Explicit Explanation of the First Principles of Mathematics
  The Origin of the Line
Chapter V: The Square, "So-Called," of the Hypothenuse
  An Explicit Analysis of the Hypothenuse of the Right Angle Triangle Together with its Square, "So-Called". A Lacking Link in the Demonstration of the World Renowned Pythagorean Problem.
Chapter VI: The Lacking Link
  An Explicit Explanation of the Hypothenuse of the Right Angle Triangle Together with its Square, "So-Called". A Lacking Link in the Demonstration of the World Renowned Pythagorean Problem.
Chapter VII: The Lacking Link, A New Law in Geometry
  A Lacking Link Leading to the Solution of Unsolved Problems
Chapter VII: The Harmony of Measure and Number
  An Explicit Explanation of a New Law in Geometry. The Harmony of Measure and Number.

Section Two
  Diagrams and Numerical Demonstrations

Chapter IX: The Circle Squared Beyond Refutation
  Rules for Squaring the Circle Numerically
Chapter X: The Exact Area of the Quadrant of any Circle
  Numerical Demonstration and Solution of the Exact Area of the Quadrant of Any Circle.
Chapter XI: The Exact Area of the Octant of any Circle
  Numerical Demonstration and Solution of the Exact Area of the Squares, Triangles, Sectors, and Segments of the Octant of Any Circle.
Chapter XII: The Exact Area of the Octant of any Circle
  Numerical Demonstrations and Solution of the Exact Area of the Octant of Any Circle by Equation.
Chapter XIII: Area of Octant, Quadrant, and Circle Proved
  A Numerical Demonstration Proving the Exact Area of the Octant and Quadrant of Any Circle
Chapter XIV: True Area of Octant, Quadrant, and Circle
  Another Demonstration Proving the True Area of the Octant and Quadrant of Any Circle
Chapter XV: 1:3 13/81 Equals the True Value of Pi
  Numerical Demonstrations Proving the True Value of Pi
Chapter XVI: True Area of Circle Proved by 9:8 Ratio
  Rule for Squaring the Circle by 9:8 Ratio
Chapter XVII: The Inscribed Dodecagon
  The Exact Area of Dodecagon
Chapter XVIII: The Converted Dodecagon
  Rules for Converting an Inscribed Dodecagon into a Similar Polygon with Exactly the Same Area and Perimeter as the Area and Circumference of its Circumscribed Circle
Chapter XIX: The Inscribed Hexagon
  The Harmony of Measure and Number Between Squares, Regular Polygons and Circles
Chapter XX: The Converted Hexagon
  Rules for Converting an Inscribed Hexagon into a Similar Polygon with Exactly the Same Area and Perimeter as the Area and Circumference of its Circumscribed Circle.
Chapter XXI: Many Sided Regular Polygons
  Rules for Finding the Exact Length of the Sides and Perimeter of Many Sided Regular Polygons
Chapter XXII: Irrational Numbers
  An Irrational Number Always Lacks One Unit of Measure, or b² of the Formula a² + 2ab + b² from Being a Square Number.
Chapter XXIII: Table of Artificial Square Roots
Chapter XXIV: The Artificial Root of Irrational Quantities
  The Artificial Root of Irrational Quantities Always Equals a² + 2ab Only of the Formula a² + 2ab + b². Rules for Finding Artificial Root of Irrational Quantities.
Chapter XXV: Growth of Squares and Circles
  With Tables Illustrating the Growth of Squares and Circles
Chapter XXVI: The Combined Area of Two Equal Squares can Never Form a Third Perfect Square
  Numerical Demonstration That Half a Square Number, or Double a Square Number Always Equals an Irrational Number.
Chapter XXVII: The Artificial Root of the Irrational Number 2
  With Numerical Demonstration Illustrating that Two Equal Squares will Always Form an Irrational Quantity One Unit of Measure, of b², from Being a Perfect Square.
Chapter XXVIII: The Forty Seventh Problem of Euclid
  Disproving that the Sum of the Squares of Two Sides of a Right Angle Triangle Equals the Square of its Hypothenuse and the Pythagorean Problem is the Exception and not the Rule.
Chapter XXIX: Euclid's Radius by Half Circumference Equals Area of Circle
  With Demonstration Proving the Same
Chapter XXX: Decimals
  Demonstrating the Impossibility of Obtaining Accurate Results with Decimals
Chapter XXXI: Harmony of Squares and Circles
  The Proof of the Pudding is the Eating of it.
Chapter XXXII: Harmony of Measure and Number
  Nature as well as the Positive and Exact Science, Rebels Against the Idea of an Infinite Line, an Infinite Area, or Infinite Solid Contents, as Nature Abhors a Vacuum.
Chapter XXXIII: Cubes and Spheres
  Perfect Harmony of Measure and Number Between Squares and Circles and Cubes and Spheres with Table of Proof.
Chapter XXXIV: The Circle Squared
  Demonstration so Simple that a School Boy can Understand it.
Chapter XXXV: Summary
  The True Value of Pi

Addenda

Three Artificial Square Roots for Irrational Quantities
Table of Approximate, Infinite Decimal Square Roots of Irrational Quantities
Tables of Exact Artificial Geometrical Square Roots of Irrational Quantities
Illustrations and Demonstrations of Artificial Geometrical Square Roots of Irrational Quantities
Table of Infinite Decimal and Exact Artificial Geometrical Square Roots or Irrational Quantities
Demonstrations of Exact Artificial Geometrical Square Roots of Irrational Quantities
Demonstrations of Exact Artificial Geometrical Square Roots of Irrational Numbers of Circle Areas
Beauty, Balance, and Harmony in Growth of Irrational and Square Areas Demonstrated
Growth of Irrational and Square Areas Illustrated
Growth of Squares, Parallelograms and Circles by Two Units of Measure
Beauty, Balance, and Harmony Between Irrational And Square Areas
Two Equal Square Areas Can Never Form a Third Square Area
9:8 Ratio Between Irrational and Square Areas
Beauty, Balance, and Harmony Between Square and Circle Areas
The Great Secret of the Harmony Existing Between the Circumference of any Circle and the Perimeter of its Square of Equal Area is the Ratio 9:8
Growth of Circle Areas by Two Circular Units of Measure
Proving that a Circumscribed Square can Never be Equal to Twice the Area of its Inscribed Square
The Circle Squared Beyond Refutation
Behold! The Circle Squared Beyond Refutation
Again Behold! The Circle Squared Beyond Refutation. So Simple that a Child can Understand it.
Lo and Behold! The Circle Squared Beyond Refutation. Solved by the very Method Claimed by the Modern Mathematical World to be Impossible. A Line Segment Equal to the Square Root of Pi
Any Science to be a True Science must be Exact and Positive
Demonstrating and Proving the Exact Length of Lines and Surface Areas of Circles of Diameters of From One to Ten Units
Problems Demonstrating the Exact Length of Lines, Surface Areas, Ratios, Relations, and Proportions of the Areas of Segments, Triangles, Sectors, Octants, Quadrants, Inscribed Octagon, Square of Equal Area of Circle of Diameter of Two Units
The 9:8 Ratio and 3 13/81 = 256/81 Ratio
Area of Squares, Circles and Polygons Equal and Interchangeable
Table of Length of Lines of Inscribed Octagon of Circles of Diameters of from One to Ten Units
Table of Surface Areas of Inscribed Octagon of Circles of Diameters of from One to Ten Units
Table of Proof. The Circle Squared
Synopsis of Areas of Segments, Triangles and Octants of Inscribed Octagon
Difference in Approximate and Exact Results
New Field of Exact Thought and Reasoning
The Circle Squared Beyond Refutation
Ratios and Relations of Squares and Circles
Ratios and Relations of Quadrants of Circles
Ratios and Relations of Octants of Circles
Ratios and Relations of the Area of Segment and Triangle of Octant of any Circle
Beauty, Balance, and Harmony in the Relations and Ratios in the Length of Lines, Chords, and Areas of Circles and their Inscribed Octagons
Illustrating the Inaccurate Results Obtained by the Approximate, Assumed, Applied Science of Mathematics as Taught Today
Another False Assumption Dispelled
Circular and Spherical Units of Measure
Exact Cubic Contents of the Sphere
Exact Surface Area of the Sphere
How Much Does So Much Plus a Little More Amount to?
Definitions and Axioms
Beauty, Balance, and Harmony Existing Everywhere in this New Exact Science of Mathematics and Geometry
The True and Exact Value of Pi, 3 13/81 = 256/81
The Side of the Square of Equal Area of Every Circle Equals 8/9 of the Length of its Diameter
The Accepted but Mistaken Idea of Geometry as Taught Today Clarified
The Wonderful Harmony that Develops in the Solution of the Problem of Squaring the Circle
Growth of the Square and the Circle by the Algebraic Formula a² + 2ab + b²
Proving that the Circumscribed Square of any Circle can never be Equal to Twice the Area of its Inscribed Square
A Simple Method for Squaring the Circle
The Golden Triangle of Enoch
The Heisel Modulus, 6561:20736::1:3 13/81 = 256/81
Our Frist Edition Accepted and Complimented as Being Written with that Strength of Mind that Only the God of Truth Could Have Given
A Revolution in Mathematics and Geometry has been Inaugurated
The Remuneration or Reward for a Lifetime of Thought and Study
Conclusion
Finally
Summary. The Decimal System of Numeration as the Stumbling Block of Professional Mathematicians
Any Science to Be a True Science Must Be Exact and Positive and Not Approximate, or So Much Plus or Minus a Trifle

Date: 1934

Pages: 300

Binding: Hardcover Black Suede Gilt

Publisher: Sacred Science

Author: Carl Theodore Heisel & Carl Theodore Faber

ISBN:

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