Alan Andrews
Alan Andrews
Alan Andrews
Books by and about the geometrical techniques of Dr. Alan Andrews, developer of the Pitchfork, the ML Line and a number of excellent geometrically based tools.
Dr. Baumring Seminars
"Gann Harmony" The Law of Vibration - Gann 1-9 Seminars - By Dr. Jerome Baumring
"Gann Harmony" The Law of Vibration - Gann 1-9 Seminars - By Dr. Jerome Baumring
Gann Harmony: The Law Of Vibration, A Distillation of the Wisdom and Insights of W. D. Gann. The Investment Centre Gann Seminars, Volumes 1-9. The most important Gann Course, from Baumring who cracked Gann's complete system. A study of the Cosmological System behind Gann's work. A PhD study in Gann Science!
Gold Secrets Revealed
Gold Secrets Revealed
Gold Secrets Revealed
L. David Linsky's new book "The Key to Speculation in the Gold Market" reveals a method to accurately predict when Gold will make its tops and bottoms. Gold Market projections since 1974 have an accuracy of 90-99%, and insight into previously unknown cycles will allow any trader to capture Gold's primary swings for the rest of their life.
Swing Trading
Swing Trading
Swing Trading
Swing Trading works with short to intermediate term swings, usually with time periods from a few days to weeks, following a general changing trend and trading in each direction. Most systems consider position reversal, and try to trade short and long as the market changes direction. Gann taught swing trading first, with its relatively easy methodology.
Baumring Science List
Baumring Science List
Baumring Science List
In the 1980’s Dr. Jerome Baumring, created an advanced course on the scientific cosmological system behind Gann’s Law of Vibration, including over 100 important works. These ranged from core works that Gann himself studied relating to Natural Science and Philosophy, to valuable works in alternative or lesser known scientific traditions.
Chemistry
Chemistry
Chemistry
The origin of modern chemistry goes back to the mysterious science of Alchemy, which originated in Ancient Egypt, know to the Arabs as Kemi, the Black Lands. Alchemical experiments with chemicals and compounds led to the modern science of chemistry, although Alchemy incorporates spiritual and esoteric elements missing from chemistry.
Natural Philosophy
Natural Philosophy
Natural Philosophy
In the 1700-1800’s Natural Philosophers studied a wide range of scientific subjects, while not overly specializing in narrow and limited fields as scientists do today. WD Gann espoused this more holistic system of science, where the different branches were more easily integrated and the grand vision of the scientific system was more interlinked.
Pause Start Back Next Translation Society Titles Top Science Titles Top Metaphysics Titles Science Categories Metaphysics Categories Cosmological Economics Financial Astrology
The Sacred Science Translation Society began in 2004 as a project to translate a collection of the most important and rare works on Cosmology & Esoteric Science into English. Through Angel DonorsSubscribtion Contributions we raised over $40,000 to translate famous foreign masterpieces from French & German on critical subjects in Harmonics, Geometry, Esoteric Mathematics, & Ancient Cosmology.
Hans Kayser was one of the 20th century's leading scientists who made a profound mathematical, geometric and philosophical study of the Science of Harmonics. Now finally avaible in English though our Translation Society, Kayser's series of works explore the deepest principles of Pythagorean Harmony & Order.  His profound research reveals critical insights into Gann Theory & The Law of Vibration.
Our second translation is a French masterpiece on the establishment of a "Golden Rule" according to the principles of Tantrism, Taoism, Pythagoreanism, & the Kabala, serving to fulfill the Laws of Universal Harmony & contributing to the accomplishment of the Great Work. It develops a system of correspondences between the symbolic, geometrical, mathematical & astronomical systems of architecture of the ancient world.
The Law Of The Cosmos: The Divine Harmony According To Plato's Republic/Timeaus. The Platonic Riddle Of Numbers Solved contains hundreds of the most sophisticated diagrams on Sacred Geometry, Pythagorean & Platonic Number Theory, Harmonics & Astronomy with analysis & elaboration of Universal Order & Cosmic Law. Herman Hesse called him a Magisterludi of the Glass Bead Game.
THE ARCHEOMETER: Key To All The Religions & Sciences of Antiquity, Synthetic Reformation of All Contemporary Arts. The Archeometer is the instrument used by the Ancients for the formation of the esoteric Canon of ancient Art and Science in its various architectural, musical, scientific forms. A highly respected elaborations of the Universal System, by one of the great esotericists of the 19th century.
W.D. Gann Works
W.D. Gann Works
W.D. Gann Works
We stock the complete collection of the works of W.D. Gann. His private courses represent the most important of his writings, going into much greater detail than the public book series. Our 6 Volume set of Gann's Collected Writings includes supplementary rare source materials, and is the most reliable compliation of Gann's unadulterated vital work.
Dr. Jerome Baumring
Dr. Jerome Baumring
Dr. Jerome Baumring
The work of Dr. Baumring is the core inspiration upon which this entire website is based. Baumring is the only known modern person to have cracked the code behind WD Gann’s system of trading and market order. Baumring found and elaborated the system of scientific cosmology at the root of Gann’s Law of Vibration. There is no other Gann teaching that gets close to the depth of Baumring’s work.

Hans Kayser's Textbook of Harmonics - Excerpts §27. Parabola, Hyperbola, Ellipse

By Hans Kayser

Kayser’s harmonic research provides profound insights into W. D. Gann’s Law of Vibration and the function of parabolic and hyperbolic growth in space as described by Dr. Jerome Baumring.

Introduction

Hans Kayser’s work presents a masterful elaboration of the system of harmonics and vibration, looking at it from the standpoint of a universal system on order which applies from mathematics to geometry to astronomy and even to subjects such as the financial markets. Our clientele is deeply involved in the theory of the Law of Vibration developed by W. D. Gann, and this section will demonstrate to traders the valuable applications to Gann theory and analysis which Kayser’s work brings. Subjects like the parabolic and hyperbolic and elliptical growth in the markets and the use of ellipses and harmonic relationships between impulse waves and reactions through key lines, like the angles on Gann’s geometrical market charts can be seen in the Gann like diagrams below.

Let us imagine two tone-generating points surrounded by circles of equidistant waves. At some point, depending on the distance between the points, these circles of waves will intersect. In reality, of course, they will always be spheres, but projection on a plane is sufficient to discover the laws by which these intersection points occur. One must then simply imagine the relevant figures transposed into the spatial realm, turning an ellipse into an ellipsoid, a parabola into a paraboloid, and a hyperbola into a hyperboloid.

If we connect the intersection points of the two groups of concentric circles, we will trace out ellipses or hyperbolas (Fig. 167), depending in which direction we proceed. Since Fig. 167 is very easy to draw, the reader can derive the formula of the ellipse (Fig. 167a) and the hyperbola (Fig. 167b) by counting off the radii that generate the respective intersection points. This shows that the ellipse traces all the points for which the sum of their distance from A and their distance from B is equal, while the hyperbola traces all the points for which the distance from A minus the distance from B is equal.

Figure 167a
Figure 167a

Figure 167b
Figure 167b

Figure 168
Figure 168

We have thus achieved the derivation of the ellipse and the hyperbola through the intersection of two fundamental phenomena of general vibration theory: the two wave-spheres.

We can read off the parabola directly from our diagram (Fig. 168). Its ratios are:

      Major      
0/2 1/1 (0/0)        
0/3 2/2 2/1 (0/0)      
0/4 3/3 4/2 3/1 (0/0)    
0/5 4/4 6/3 6/2 4/1 (0/0)  
0/6 5/5 8/4 9/3 8/2 5/1 (0/0)
  c c g c′′ e′′ etc.
      Minor      
2/0 1/1 (0/0)        
3/0 2/2 1/2 (0/0)      
4/0 3/3 2/4 1/3 (0/0)    
5/0 4/4 3/6 2/6 1/4 (0/0)  
6/0 5/5 4/8 3/9 2/8 1/5 (0/0)
  c c, f,, c,, as,,, etc.
             

Figure 168

 Here is the proof that they are parabolas: the familiar parabola equation x2 = 2px changes into y2 = x for a parabola whose parameter is 1/2, i.e. the y-coordinates (perpendicular lines) are equal to the square roots of the corresponding x-coordinates (parallel lines). For the parabola 0/6 5/5 8/4 9/3 8/2 5/1 0/0 in Fig. 168, 5/1 is the perpendicular line 2 units away from the point 5/3 on the x-axis, and the length of the x-line 9/3-5/3 contains 4 units. The y-value 2, then, is the square root of the x-value 4. The x-value 0/3-9/3 has 9 units as its axis, the corresponding y-value 9/0-9/3 = 3 units. √9 = 3, etc. The apexes of these parabolas generate further parabolas. We obtain a beautiful image of these parabolas (Fig. 170) from their fourfold combination, anticipating what will be further discussed in §32.

The hyperbola also has a simple and interesting harmonic derivation. If we draw the partial-tone-values of its string-length measures perpendicularly (Fig. 171) and turn them sideways, always using unity as a measure, then we get perfect rectangles, identical in area to the unit-square. Connecting the corners then produces a hyperbola, whose equation is a2 = xy, as is generally known. In our case, this means that

1/1 · 1/1  
}
 
1/2 · 2/1 = 1
1/3 · 3/1  
etc.    

 

Figure 170
Figure 170

 

Figure 171
Figure 171

Figure 172
Figure 172

As we saw above, the hyperbola is the geometric location for all points for which the difference between the x- and y-coordinates is the same. Thus we can also explain their “harmonics,” as in Fig. 172.

The hyperbola, drawn in points, continuing endlessly in both the x- and y-directions, indicates that from any point placed on it, a rectangle of consistently equal area can be introduced between the curve and the axes A B C. If d – B = 1, then we have:

for: length: height: therefore, the quadrilateral’s area:
a2 1/4 4/1 1/4 · 4/1 = 1
b2 1/2 2/1 1/2 · 2/1 = 1
c2 3/4 4/3 3/4 · 4/3 = 1
d2 1 1 1 · 1 = 1
e2 4/3 3/4 4/3 · 3/4 = 1
f2 2/1 1/2 2/1 · 1/2 = 1
g2 4/1 1/4 4/1 · 1/4 = 1

Figure 173

The law of hyperbola construction therefore shows us an increasing arithmetic series (1/n 2/n 3/n 4/n ...) and a decreasing geometric series (harmonic n/1 n/2 n/3 ...)—a precise analogy to the intersecting major-minor series of our diagram.

And if we consider, moreover, that the ellipse is the geometric location for all points for which the sum of two distances has an unchanging value, then it is easy enough to construct the ellipse harmonically with reciprocal partial-tone logarithms, since their sum is always 1—for example, 585 g (3/2) + 415 f (2/3) = 1000. In Fig. 174, this tone-pair is drawn with a thick line and marked for clarification. We mark two focal points 8 cm apart (Fig. 174) for the construction of the ellipse, draw one circle around one focal point at radius 5.9 cm (585 g) and one around the other at radius 4.1 cm (415 f), then trace the intersection points of each pair of rays, up to the point where the two shorter f-rays intersect with the circumference of a small circle drawn around the center of the ellipse, and the two longer g-rays intersect with the circumference of a larger circle drawn around the center of the ellipse. These two outer circles, whose radii are of arbitrarily length, serve simply to intercept the vectors (directions) of the single tone-values and to distinguish them clearly from one another. All other points of the ellipse are constructed in the same way. The tone-logarithms here were simply chosen in order for the construction of the ellipse points to be as uniform as possible. If the reader has a good set of drawing instruments, then he can use all of index 16 for point-construction—a beautiful and extremely interesting project. In this case it would be best to use focal points 16 cm apart, and to double the logarithmic numbers.

Figure 174
Figure 174

Even if this construction of an ellipse from the equal sums of focal-point rays is nothing new and can be found in every elementary textbook, its construction from the reciprocal P-logarithms still gives us an important new realization. As one can see from the opposing direction of rays in the ratio progression of the outer and inner circles, the tones are arranged here in each pair of octave-reduced semicircles, and thus the directions of the ratios of the two circles are opposite to each other. From the viewpoint of akróasis, then, there are two polar directions of values concealed in the ellipse: a result that might alone justify harmonic analysis as a new addition to a deeper grasp of the nature of the ellipse.

Parabola, hyperbola, ellipse, and circle (in §33 we will discuss the harmonics of circular arrangements of the P) are of course conic sections, i.e. all these figures can be produced from certain sections of a cone, or of two cones tangent at their apexes. The above harmonic analyses, of which many more could be given, show that these conic sections are closely linked to the laws of tone-development, which supports the significance of the cone as a morphological prototype for our point of view. In pure mathematics, this significance has been known since Apollonius, renewed by Pascal, and discussed in De la Hire’s famous work Sectiones Conicae, 1585 (the reader should definitely seek out a copy of this beautiful volume at a library), right up to modern analytical and projective geometry. For those interested in geometric things and viewpoints, hardly anything is more wonderful than seeing the figures of these conic sections emerge from an almost arbitrary projection of points and lines, aided only by a ruler. For a practical introduction see also L. Locher-Ernst’s work, cited in §24c.

§27a. Ektypics

Mathematically speaking, ellipses, parabolas, and hyperbolas can be defined as the geometric location of all points for which the distance from a fixed point (the focal point) is in a constant relationship to the distance from a fixed straight line (the directrix). On this rest the projective qualities of conic sections and the possibility of constructing them by means of simple straight lines (the ruler).

In detail, as remarked above, these “curves of two straight lines” have many more specific harmonic attributes—for example, the octave relationship (1 : 2) of the areas of a rectangle divided by a parabola, the graphic representation of harmonic divisions in the form of hyperbolas, etc. One obtains the “natural logarithm” when one applies the surface-content enclosed by the hyperbola between the two coordinates (F. Klein: Elementarmathematik vom höheren Standpunkt aus, 1924, p. 161); thus, a close relationship also exists between the conic sections and the nature of the logarithm. The applications of the laws of the conic section are many, especially in the exact natural sciences. I will mention only the Boyle-Marriott Law, which connects the respective number-values of pressure and volume, and in which the hyperbola emerges as a graphic expression (and thus the pressure : volume ratio of the reciprocal partial-tone values 4 : 1/4, 2 : 1/2, 1 : 1, 1/2 : 2, etc. are expressed most beautifully). I am also reminded of the “parabolic” casting curves in mechanics, the properties of focal points, parabolas in optics, the countless “asymptotic” relationships, etc. Admittedly, these applications are mostly obscured by differential and integral calculus, though doubtless simplified mathematically—in other words, the morphological content of conic sections is outwardly diminished in favor of a practical calculation method, but remains the same in content.

Figure 175a
Figure 175a

Figure 175b
Figure 175b

Because of this, it is not astonishing when a figure such as a cone, from which all these laws flow as from the source of an almost inexhaustible spring of forms, is applied emblematically even in the most recent deliberations of natural philosophy, as a direct prototype for the “layers of the world” and for our “causal structure.” In Figures 175a and b I reproduce the diagrams from H. Weyl: Philosophie der Mathematik und Naturwissenschaft, 1927, pp. 65 and 71, which speak for themselves.

§27b. Bibliography

Thimus: Harmonikale Symbolik des Alterthums, 4th part. H. Kayser: Hörende Mensch, 65, 66, 126, and familiar geometry textbooks.

Related Pages

Sign up for email NewsLetter Download Latest NewsLetter
$0.00
$ (USD)
Institute of Cosmological Economics > ICE Forum index
T. G. Butaney
View our T. G. Butaney pages
View our T. G. Butaney pages
T. G. Butaney, a famous Indian astrologer, wrote 3 books on astrological financial market forecasting and horse racing prediction. His books were judged "The Best Money Minting Books on Speculation and Racing By Readers All Over The World", and explain Market Forecasting, Race Astrology & Numerology and Handicap Formulae.
Vibration by The Patterns
Vibration by The Patterns
Vibration by The Patterns
Volume 1 of Dr. Lorrie Bennet's 4 volume series. A course in Theoretical Wave Mechanics as an introduction and foundation to Gann's Law of Vibration. This volume lays foundations for all Gann and Baumring's higher teachings and is an essential prerequisite to move on to the deeper levels of Gann Theory presented in Vols. 2-4.
Gann Theory
Gann Theory
Gann Theory
We maintain the largest collection of secondary works on Gann Theory in the world, publishing many books written by top Gann experts and experienced Gann traders. We continually review work by other Gann experts, filtering out the highest quality material for inclusion in our catalog in order to satisfy the needs of our demanding clientele.
Hasbrouck Archives
View our Hasbrouck Space-Time Forecasting pages
View our Hasbrouck Space-Time Forecasting pages
Cutting edge Space and Solar Researchers, Muriel and Louis Hasbrouck's Space & Time Forecasting techniques are STILL more advanced than those of NASA or the current scientific community. They produced 50 years of Market Forecasts with a 90% accuracy rate and forecasted Space Weather, Earthquakes and Geomagnetic Storms.
Polarity Factor System
The Polarity Factor System - By Daniele Prandelli
The Polarity Factor System - By Daniele Prandelli
The Polarity Factor System, An Integrated Forecasting & Trading Strategy Inspired by W. D. Gann's Master Time Factor, by Daniele Prandelli conveys the strategy and tools that Prandelli uses to generate a consistent 10% a month trading. A proven system with Advanced Risk Management Rules & time turning points based on Gann's cycle theory.
Baumring Financial List
Baumring Financial List
Baumring Financial List
Dr. Baumring compiled long reading lists even more comprehensive than Gann's, comprising works having key elements directly applicable to Gann Theory and Cosmological Economics. Any student wanting to explore particular fields in depth will find Baumring’s lists to be indispensable, since they over important but unfamiliar topics.
Petrus Talemarianus
View our Petrus Talemarianus pages
View our Petrus Talemarianus pages
A masterpiece on the Golden Rule according to principles of Tantrism, Taoism, Kabala, and Pythagoreanism serving to fulfill the Laws of Universal Harmony and aiding accomplishment of the Great Work. It develops a system of correspondences in symbolic, geometric, mathematical and astronomical systems of architecture of the ancient world.
Gann Metaphysical
Gann Metaphysical Reading List
Gann Metaphysical Reading List
In the 1940’s Gann published a Recommended Reading list of about 90 books, each containing an essential part his system, which he sold to his students. n the 1980’s Dr. Baumring compiled about 70 of these titles, and we have collected the remainder, providing the only complete set available. We strongly recommend these works to all Gann students.
Initiation
Initiation
Initiation
We have many books on initiatory systems and the exploartion of human potential.
Theosophy
Theosophy
Theosophy
Theosophy, a school of esoteric thought developed my Helena Blavatsky in the late 1800’s presented a revival of many lost esoteric traditions. Many of Gann’s contemporaries were closely involved with Theosophy, and it influenced the Anthroposophy of Rudolf Steiner, the Arcane School and work of Alice Bailey and the teacher Krishnamurti.
Vedic Math
Vedic Math
Vedic Math
Vedic math is a system of math calculation allowing anyone to do mathematical calculations very quickly in one’s head. An advancement in mathematical calculation, with cosmological implications, Vedic math is a revolution in mathematics that anyone can master. Fast and accurate mental maths without a calculator!.
L. David Linsky
View our L. David Linsky pages
View our L. David Linsky pages
A New Discovery of a Mathematical Pattern in the Gold Market which forecasts Gold's turns with an 85-95% accuracy over 40 years. Scientific Proof of a Cyclical Pattern in the Gold Market providinges a 100 Year Forecast of Gold's Major Tops & Bottoms and Bull & Bear Market Campaigns out to 2100.
18.206.160.129
Disclaimer Privacy Policy Terms and Conditions

Guarded by Cerberus