RECTANGULAR AND TRIANGULAR
FORMATIONS IN HOROSCOPES
Dane Rudhyar & Leyla Rael
Only in astrological textbooks are planetary aspects separated from one another. Their natural habitat is rather in complex interrelatedness to one another in birth-charts integrating a myriad of aspects into more or less complex patterns. In fact, single aspects can never be fully understood out of the context of all the other aspects in a horoscope.
For example, we have seen that an opposition refers to the phase midway in a cyclic process when a change of gears has to take place, when one must 'wake up' and consciously participate in the rest of the process. As awareness develops, one becomes able to use, and responsible for how one uses, the activities or biopsychic functions. represented by the opposing planets. The nature of the planets involved in the opposition; the zodiacal signs, Sabian degrees and houses of the horoscope in which they are found; and even the salient points about the prenatal conjunction beginning the cycle of which the opposition is the culmination: all these indications give the astrologer valuable clues about what the conflict leading to birth in consciousness may involve.
The opposition itself, however, does not tell us anything about the best way to use or integrate into the overall life-pattern the growing awareness and objectivity, once awakened; it does not help us to understand the full significance and dynamic interrelationship between the opposition-symbolized factors and other facets of our lives and processes of unfoldment. The aspects linking the opposition into the rest of the chart that is, the aspects the two planets at either end of it make to other planets as well as the aspects linking the two hemispheres of the chart divided by the opposition: these are the keys to what can and most naturally should be done with or about the awareness, capacity or development symbolized by the opposition.
In order to begin to be able to interpret the complex and dynamic interrelationships between aspects, one of the first things the astrologer should do is to try to determine whether specific group patterns of planets and aspects exist in a particular chart. Groupings of aspects were not unknown in traditional astrology, but they were almost entirely limited to sequences of one kind of aspect. Of the latter, only the trine and square were used in practice. Thus, when two planets in trine to one another were also trine a third planet, three mutual trines or a 'grand trine' was the result. When four planets formed a series of squares, a 'cosmic' or 'perfect' cross was mentioned.
The main reason for considering these sequences of the same kind of aspects significant was that the grand trine emphasized one of the four elements (fire, earth, air or water), because the three planets were placed in zodiacal signs of the same element. While to most astrologers, a grand trine linking three planets is a very 'good' indication, there are astrologers who do not consider it too favorable, for they feel it tends to over-emphasize one of the four elements; it may also stress a rather dream-like approach to life lacking in dynamism and concreteness. Likewise, the perfect or 'grand' cross stressed one of the quadruplicities of zodiacal signs cardinal, fixed or mutable. Such a repetition of squares is usually considered very 'difficult,' yet some astrologers saw in it a sign of remarkable strength and capacity for action. Overall what was mainly considered important about these configurations the grand trine and perfect cross was the factor of the zodiac, not the strictly structural element, i.e., the geometrical pattern made by the planets regardless of the zodiacal signs, elements or qualities in which they were located, nor the dynamic element of their aspect interrelationship.
The meaning attributed to the familiar T-square (or T-cross) reflects this preoccupation with zodiacal factors and repeated aspects. The configuration was named for its two squares, not its opposition. And it is interpreted as a perfect cross from which one of the four factors Is missing. The 'empty' factor is therefore seen as a zone of release for the energies produced by the combination of three planets in two squares including three of the four zodiacal elements.
What usually is not emphasized in interpreting the two kinds of crosses, 'perfect' and T' and which is really a key to understanding all types of complex aspect patterns is the fact that these configurations are really combinations of two kinds of aspects, opposition and square, while the grand trine is composed of only one kind of aspect, the trine. The grand trine is thus unique. There is no other configuration (except a stellium, which does not fit into the same category of patterns as those we are discussing here) composed of only one kind of aspect. Once the linking of different kinds of aspects is recognized as significant, the possibility of giving specific meanings to combinations of them according to the particular aspects involved should become evident.
The three basic features of a primary planetary pattern are;
( 1) that combinations of two or more kinds of aspects display a clear-cut kind of symmetry,
(2) the configuration of aspects should be closed and complete, spanning 360°, and
(3) It should be a regular polygon capable of being inscribed in a circle.*
*One can, of course, consider significant and interpret aspect configurations spanning fewer than 360° for example, a trine, bisected into two sextiles, an opposition divided by a semi-square and sesquiquadrate. We Would rather, however, consider these secondary, not primary, configurations. Nevertheless, in particular charts, especially those of an overall hemispheric type, such secondary patterns may form the basic structure of the horoscope.
This last-mentioned criterion results from the fact that in astrology every moving factor is related to and given meaning in relation to a whole circumference or cycle, whether the 360° of the zodiac, or of the wheel of houses, or the 360° span from conjunction to conjunction between planetary pairs.
Patterns meeting the above criteria can be divided into two basic categories: four-sided and three-sided figures, i.e., rectangles and triangles, the square or perfect cross being only one specific case of rectangle, and the grand trine being only one particular instance of triangle. In the following, we will cover the basic figures, but especially if non-regular polygons covering the whole 360° (such as trapezoids) are considered, the variations are practically endless.
Because the perfect square includes both square and opposition aspects, it can be seen as the foundation of all regular, closed configurations in which two or more types of aspects are interwoven. Indeed, geometrically speaking, as already mentioned, the square figure is only a special kind of rectangle a rectangle whose four sides are equal and whose diagonals cut each other at 90° angles.
The accompanying figure shows how, if we keep the vertical line (theoretically the meridian of the birth-chart or the line of the solstices) as a basis, we can draw any number of rectangular patterns. In the square, the four sides and four angles are equal. As we decrease the length of one side, the length of the complementary side increases until, at the limit, the rectangle becomes concentrated, as it were, into the vertical line.
We are thus dealing with a series of rectangular patterns, the two extreme possibilities of which are the square and the line astrologically, the grand cross and the opposition (or multiple opposition). In between these two cases, we find a theoretically infinite number of possibilities for rectangular patterns. The grand cross becomes a kind of ideal or archetypal rectangle. Actually, only those rectangles which link aspects should be considered in astrology, and six basic kinds can be distinguished.
This series of rectangles can be established very simply by considering this angular relationship between the two diagonals or oppositions. In the perfect square, the diagonals make two equal angles of 90° each. The relation is thus 1:1. When, the oppositions are connected by trines and sextiles, the diagonals form angles of 120° and 60° to one another; the two angles are m 1:2 relation. A relation 1:3 is found in a rectangle linking semi-squares (45°) and sesquiquadrates (135°). Arelation l:4occurs when semiquintiles or deciles (36°) and bi-quintiles (144°) are related. When the angular distance between the two diagonals or oppositions are 30° and 150°, we find aspects of semi-sextile and quincunx, and the ratio between the two oppositions is 1:5. We can also add a rectangle in which the aspects between the two diagonals are quintiles (72°) and tri-deciles or sesqui-quintiles (108°); the ratio between two such related diagonals would be expressed as 2:3.
The series of four rectangles 1:2,1:3,1:4, 1:5 (not counting the square or 1:1 ratio and the quintile or 2:3 ratio) parallels the series of rectangles upon which the shapes used in Greek design and architecture were based, according to the principle of 'dynamic symmetry' rediscovered some years ago by the American scholar J. Hambidge. Indeed, since the days of Pythagoras, the rectangle was the very symbol and signature of Greek philosophy and culture the symbolic key to the mysteries of Man and the universe.
The fundamental factor which all astrological rectangles have in common is the presence of two oppositions as diagonals. It is this factor which must be stressed in interpreting all rectangles including the grand cross or perfect square. What changes and gives each specific type of rectangle its particular meaning and significance is the relationship between the two diagonals, the aspects integrating the four ends of the two oppositions. In fact, whenever two oppositions are found, what the astrologer should find out and consider immediately is the way in which they are related to one another. The nature of the aspects linking the four planets involved in the two oppositions of a rectangle indicate what a person must meet and pass through in order to achieve the kind of awareness and objectivity presented by the oppositions, and how that awareness and ability to function, once it is awakened and made manifest, can and must integrated into the person's life and the life of the community.
In more psychological terms, the opposition refers to a polarization of two biopsychic functions and to the awareness and ability to consciously participate in further developmental processes that can and should be actualized on the basis of the tension of the polarization. An opposition or multiple opposition alone is a theoretical possibility never met in practice. It is in some ways reminiscent of what happened to Burden's ass the donkey who, standing equidistant from two equal bales of hay, starved to death because there was no reason to go toward one pile rather than the other. This is a situation in the abstract (for both the donkey and the astrologer) because in practice one never encounters only an opposition or multiple opposition; other factors are always involved. The opposition poses a challenge to develop awareness, to break free of unconscious compulsion. How in relation to what other activities and functions besides the two opposing ones that awareness most naturally develops, what spurs it, what can or should be done with or about it once it blossoms, can best be seen in other aspects. In terms of rectangular patterns, these are represented by the aspects linking the four ends of the diagonal oppositions.
At the opposite end of the rectangle-spectrum from the theoretical multiple opposition is the grand cross. The simplest way to approach a study of it is to consider the case of the zodiacal pattern constituted by the line of the two equinoxes (Aries 1° and Libra 1°) and solstices (Cancer 1° and Capricorn IS). This is what we might call the archetype of all perfect squares or grand crosses, the basic illustration of all quadrature.
Such a quadrature rests on the pattern of the seasons, which in human experience is the origin of man's structured sense of time in relation to all life processes. The daily flow of life-experiences would have no definiteness, no larger pattern, no frame of reference if it were not for seasonal changes. Through contrasts and well-defined changes, the flow of life begins to assume a form, a rhythm, a sequential meaning and character of order. As a result, human beings sense that there are laws of change, that time has a periodical structure that, therefore, predictability is possible. All this makes civilization, science, philosophy and, underlying them all, astrology possible. The square figure is indeed the symbol of all foundations of concrete, masterful living.
Traditional astrology has unfortunately over-stressed the destructive meaning of both the opposition and the square. Thus, oppositions are popularly supposed to refer only to dilemmas, conflicts between opposite points of view and the breaking asunder of opposing factors. Squares are thought of as aspects of violence related to the shattering of things, to tragedy, etc. These meanings are only partly correct which is to say that they are also partly wrong, for they are accurate only insofar as the negative expression of planetary relationships is concerned.
As we have seen from several points of view the opposition positively speaking, signifies the need and ability to be objective to happenings and experiences. It is the basic symbol of consciousness, or awareness, 'and it need not, especially when linked With other aspects, refer to the kind of situation in which Burden's donkey found himself. As to the destruction associated with squares, it is directed toward obsolete structures be they behavior patterns, dependencies or crystallized dogmas, ramshackle tenements or outmoded social institutions which no longer serve healthy functions, or toward objects and situations which must be removed and cleared away before greater things can take place.
A perfect square configuration in a birth-chart represents & tight linking of two kinds of consciousness-building processes (oppositions) which produces four 90° aspects (squares) and leads to a very thorough and exhaustive type of clearing-up activity. What is actually meant by this 'linking of two kinds of consciousness-building processes'?
In the seasonal cross of the year, spring activities symbolically oppose fall activities that is, the birth (or rebirth) of living organisms is seen to be in dynamic contrast to organic disintegration and death. Out of this contrast, human beings come to gain a consciousness of the impermanence of all that lives, a consciousness of change. In the opposition between the summer solstice and the winter solstice, human beings learn, on the contrary, to deal with the relatively permanent factors in life: family, a home, a personality community, a state, a civilization.
These two kinds of consciousness taken together the consciousness of the inevitable periodicity of life and death and the consciousness of the possibility of building long-lasting structures refer to the very foundation of all human realizations and endeavors, the very basis of human reality. By integrating these two kinds of awareness, man functions as a civilized, morally responsible, cooperative being.
Therefore, the essential meaning of the grand cross configuration is the need and capacity to develop a type of integration of awareness (opposition) and activity (square) which is only possible if there is also the readiness to give up all lesser allegiances and the attachment to whatever each planet at the four corners of the perfect square represents. The type of integration possible with a perfect square depends almost entirely upon whether the individual is able, at crucial turning points, to let go of whatever he or she is attached to. If the person does not let go, the perfect square can become the kind of wheel of torture on which medieval criminals were quartered. If one becomes objective to and free of the separative pulls and unconscious compulsions of the opposing planets (i.e., of the bio-psychological functions and drives they represent), then one can be a deeply and powerfully integrated person. The key will inevitably be knowing when to forge ahead and when to detach.
The character of the squares involved, whether they are 'waxing' or 'waning', involutionary or evolutionary, can give significant clues to the kind of challenge of action and/or letting go that has to met and the best way to meet it. Whether the configuration falls in angular, succeedent or cadent houses also points to the life-areas through which the consciousness-raising process and subsequent integration through action is most likely to take place. Of course, ether the cross is found in cardinal, fixed or mutable signs is of single importance?
A grand cross in angular houses and fixed signs is found in the horoscope of Albert Schweitzer. The oppositions are between fourth-house Pluto and tenth-house Mars; first-house Saturn and seventh-house Uranus. There is an additional opposition between a third-house Moon/Neptune conjunction and ninth-house Jupiter, and it forms a T-square to the first-house Sun/Mercury conjunction. While we are primarily interested in the grand cross, it is practically impossible to ignore these other aspects of the chart.
The grand cross itself primarily refers to the need for radical transformation on two levels: the level of Mars (personal desire and capacity to mobilize energy and act) and the tenth house (public life, 'vocation' or calling); and the level of Saturn (the sense of form or structure, authority, one's relation to one's ancestral tradition and culture) and the first house (individual selfhood). With Pluto in the fourth house, the deepest, most fundamental 'tone' urging transformation welled up from Schweitzer's deepest roots: his ancestral Christian-European tradition. Since Saturn is in the first house, all the issues of this ancestral tradition became focused, for Schweitzer, in his own individuality.
This was made very clear by Schweitzer himself when, at a great turning point in his life he realized that he had not the inward right to take as a matter of course my happy youth, my good health, and my power of work. Out of the depths of my feeling of happiness there grew up gradually with me an understanding of the saying of Jesus that we must not treat our lives as being for ourselves alone. Whoever is spared personal pain must feel himself called to help in diminishing the pain of others. We must all carry our share of the misery which lies upon the world.*
*My Life and Thought, pp. 81-82.
Thus, the Pluto/Mars opposition challenged a complete impersonalization of the level at which passions, desires and the search for well-being and achievement operate. True to its fulfillment, and the fulfillment of the Saturn/Uranus opposition, Schweitzer broke away from his ancestral culture by going to Africa, to live among and heal the natives there. He did not merely break away in hateful rebellion; he infused the best of his ancestral tradition with luminous meaning by taking the atonement of its sins upon himself. Since the Saturn/Uranus opposition spans the first and seventh houses, it also presumably refers to Schweitzer's marriage to a Jewish woman a definite departure from normal Christian-European patterns at the time, and another indication of his 'marriage' to those historically dispossessed and persecuted in the name of Christianity.
The seeming serenity of Schweitzer's later years is, however, belied by the picture of him his birth-chart presents: a man with tremendous conflicts and a Saturnian sense of form, but also with passionate intensity (Mars in Scorpio) and explosive energies swayed by deep and even dark Images (Pluto in the fourth house). Schweitzer's peace had tragic roots indeed, and it was not easily won. He believed that every man's personality is a mystery that no other person should seek to probe or intrude upon. Indeed, his own words suggest that this mystery may not even be a thing for the individual to fathom himself. True to the grand-square (and T-square, a total of six squares) in his chart, the mystery should be acted out rather than passively known or observed. For Schweitzer, only in action does the mysterious whole of personality reveal itself and become conscious in affirmations of life and emanations of spiritual light.
The pressures of such high expectations of oneself could have been too great for a lesser man to bear. Yet Schweitzer bore and fulfilled them heroically. His great love for all life, the stability of his formalistic mind sustained by the majestic, ordered music of Bach (of which he was acknowledged the greatest interpreter) made him overcome within himself what he had felt as the sins and foreseen as the disintegration of his European culture. His way of overcoming was to heal the sick and, in fulfillment of the highest symbolism of any Cross, to atone as an individual for the sins of the many. Such an interpretation of Schweitzer's life and chart becomes the more inspiring and accessible for each of us when we realize that from a process-oriented point of view, his grand cross formed when the faster-moving Mars and Saturn came around to oppose and square the relatively slower-moving, historically significant Pluto/Uranus square.
While the life of Albert Schweitzer certainly points to the socially and spiritually constructive possibilities of a grand square, the case of the Russian dancer, Nijinsky, had a less happy outcome. In his chart the two oppositions at right angles to one another are in angular houses and mutable signs. Mercury at the nadir opposes retrograde Saturn at the Midheaven. A rising, separating Moon/Mars conjunction opposes to exteriorize the historically most significant, forming Neptune/Pluto conjunction in the seventh house. Despite his great renown and artistic ability, emotional confusion and tragedies in unorthodox interpersonal relationships led to mental instability and ultimate institutionalization.
If instead of a perfect square, we consider the other rectangle configurations, we also find two lines of opposition, but their relationship is of a different order. Between these two lines there is not the sharp contrast as between the diagonals of the perfect square. A rectangle points in a certain direction the more so, the greater difference between the lengths of the sides. It does not challenge, like the perfect square, a general, complete kind of actional integration a challenge which, if not successfully met, often leads to a general confusion or tragic sense of failure or frustration. It presents a a challenge for a particular kind of integration.
This is why the rectangular shape has been used in many temples and chambers of initiation. These buildings were built to symbolize the process of transition from one stage of personal-spiritual unfoldment to the next the fulfillment of a great goal. Seen in the vertical plane, a rectangle becomes a door, something to pass through, to enter a new realm. Practically speaking, in a birth-chart, its orientation in relation to the angles and other horoscopic axes is most significant. Most fundamentally, the two oppositions of a rectangle pose the 'problem'; the aspects relating the four ends of the diagonals of the rectangle indicate the best manner in which what is represented by the oppositions can be integrated and the overall life-task met.
Actually, what occurs in practice is that a client comes to an astrologer with a basic life-situation or problem. When looking at the birth-chart, the astrologer identifies the basis of the problem with one or both of the oppositions. This lets the astrologer know what underlies the problem in the client's life. The aspects linking the two oppositions reveal the best way the client can meet and integrate the situation into his or her overall development.
One of the most practically constructive and spiritually harmonious possibilities of any rectangle is indicated when the two oppositions are linked by sextiles and trines. (1) Where fully active, this 'harmonic rectangle' points to the potential development of a character strongly organized in an attempt to take an important step in personal growth and/or spiritual development. The configuration tends to bring the polarized elements symbolized by the opposing planets into a unity because a strong sense of organization (sextile) and a cohesive, purposeful vision (trine) are potential in the personality. Whatever tensions arise in the life or personality that are symbolized by the opposing planets do not necessarily 'go away.' But they can be laid on the altar,' as it were, or channeled toward the concrete completion of a significant life-task.
Examples of 'harmonic' or 'mystic' rectangles abound, A most significant case is that of Dag Hammarskjold, the late Nobel prize-winning Secretary-General of the United Nations. The two diagonals of the rectangle are formed by oppositions between Mercury and Saturn, and a Moon/Neptune conjunction opposing Uranus. They are integrated by sextiles between Mercury and Moon/Neptune, and between Saturn and Uranus, while Saturn and Moon/Neptune are trine, as are Mercury and Uranus. To reach integrations of often violently clashing opposites in the field of international interests was the pattern-setting Secretary-General's purpose and, often, ability. In active practice, his vision (trine) of global integration was tested and brought down, as it were, to the level of practical, political organization (sextile).
Stressing the more 'mystic' aspect of the configuration is the chart of Paul Foster Case, the occultist especially regarded for his work and still-in-print book on the Tarot. In his chart, Mars/Neptune and Mercury/Moon oppositions structure the rectangle. The sextiles are between Mercury (which is also conjunct Uranus) and Mars, and the Moon and Neptune. The trines are between Mercury and Neptune, and the Moon and Mars. The total integration evokes the potentiality for developing an innovative mind which is mystically inclined and open to inspiration from 'higher levels.' The involvement of Mars suggests also the capacity to mobilize resources and act to fulfill the higher Vision.
Another kind of powerful integration is shown in the horoscope of the late Director (some would say despot) of the F. B. I., J. Edgar Hoover. Here Mars opposes Saturn, while Mercury opposes Jupiter, making the personal level of operation (Mars and Mercury) the conduit for sociocultural images and imperatives (Jupiter and Saturn).
The sextiles are between Mercury and Saturn (a clear, well-structured yet conservative mind) and Mars and Jupiter (the ability to organize a power-base and expand it). Jupiter and Saturn, and Mercury and Mars are trine. Hoover knew where he stood in relation to social issues, and he knew how to impress his vision on his surroundings. A formidable combination indeed!
The complex chart of Henry Ford again presents a fitting example. Born at the time of a Full Moon, his natal soli-lunar opposition is linked by sextile and trine to the longer-lasting opposition between Saturn and Neptune, a fitting symbol of the dissolution of social structures at the threshold of the industrial era which Ford, the inventor of assembly-line manufacture, helped usher in.
When two oppositions are linked by semi-squares and sesqui-quadrates.a particularly dynamic potentiality results. To our knowledge, this figure has never been named, but it could be called an 'octilinear rectangle' since it is based on division of the circle by Eight. Here, in a concentrated form, arise all the issues we discussed in relation to the semi-square and sesquiquadrate. Through meeting them, whatever is polarized by the two oppositions can become integrated and manifest as a workable way of life or world-view. Whatever is started in life should bring about very focused and concrete results, particularly if the sesquiquadrate operates in its positive aspect as an enthusiastic 'outreaching' (square + semi-square) and the challenge of the semi-square (dissemination of one's vision in order to fulfill the needs of the public one serves) is fulfilled.
An octilinear rectangle is found in the horoscope of Ram Das, in which the Venus/Neptune opposition and the Saturn/Pluto opposition are integrated by semi-squares between Pluto and Neptune, and Venus and Saturn. Venus and Pluto, and Saturn and Neptune, are thus sesquiquadrate. The need to break down and regenerate ossified social structures, authority images, etc. is stirred into operation by the use of value-transforming psychedelic drugs and mystical experiences or spiritual discipleship. The surrender of self, or at least the radical transformation of one's sense of self-worth, is also challenged by the Venus/Neptune opposition. Neptune is made the more focal in this configuration, since it is at the 'point' of what we have called a "Finger of the World" a triangle whose base is a square, the two ends of which are both sesquisquare a third planet. The square is between an almost exact conjunction of Sun and Uranus, and Saturn. Since Neptune is in the third house, the challenge is indeed to transform and transcend a culture- and religion-conditioned sense of everyday reality and to deepen the mind by, at least at first, unfocusing its 'hold' on such a taken-for-granted sense of what is 'real.' Jupiter, the planet of social participation and religious images, rises (septile the focal Neptune and conjunct Pluto which is semi-square Neptune), and the Sun/Uranus conjunction is in the eleventh house of social transformationall told, a powerful challenge to lead and participate in transformative processes as a result of personal experience.
In general, the rectangle linking two oppositions by semi-squares and sesquiquadrates can be particularly productive of effective integration if the individual is thorough and persistent enough actually to put across and carry out the vision, uncompromisingly and at the same time trying to take into account the needs of the biospheric, psychological and social environment. Much, of course, depends on the actual planets involved and whether the semi-squares and sesquiquadrates between them are 'waxing' or 'waning,' thus involutionary or evolutionary. If this type of rectangle links planets Mars, Uranus, Pluto and/or the Sun, the dynamic intensity of configuration would be particularly stressed.
While neither the semi-square nor the sesquiquadrate is part of the arithmetically derived involutionary series, after we have understood the principles underlying the three interwoven aspects of all cyclic processes (involution, devolution, evolution), we can place these aspects in the waxing half of a cycle. The semi-square falls at the middle of phase 2 between the semi-sextile and sextile; the sesquisquare falls at the midpoint of phase 5 between the trine and the quincunx. Each of these aspects, when waxing, can be understood to be the point at which the process of the particular phase in which it is found reaches its culmination and maximum intensity. In the sense of cycles-within-cycles, as midpoints of phases these aspects are analogous to oppositions (or division by Two) of the phases in which they are found. They thus refer to a possible point of release orobjectification of what needs to occur during that phase.
The figure joining two oppositions by semi-sextiles and inconjuncts or quincunxes has no name. It indicates that what the oppositions represent can best become integrated through everyday work and close, personal bi-polar relationships, possibly in which self-improvement and serving the needs of one's partner would be stressed. Zodiacally, what is emphasized in such a configuration is usually the relationship between succeeding 'masculine' and 'feminine' signs although if the opposition aspects are not exact, the semi-sextiles may link the ends and beginnings of the same signs. Only small orbs should be allowed when one considers such a rectangle. The orbs can be a little larger in the case of harmonic rectangles, but not larger than six degrees in most cases.
An example of a rectangle involving semi-sextiles and inconjuncts is found in the horoscope of George Sand, the flamboyant 19th-century romantic novelist and feminist prototype. The oppositions are between second-house Mars and Neptune in the eighth house of sexual relationships, and between the first-house Moon and Jupiter in the seventh house. The rectangle is thus concentrated in the houses referring to personal expression and interpersonal relationships and marriage. Sand's romances, scandalous for her time, were well-publicized, especially her liaison with the composer Chopin. Through theih and through meeting the personal crises they engendered, she was able to transcend the cultural imperatives and taboos of her day. In the process, and through her ardent dedication to her craft, she set an example of independence admired and emulated even by contemporary women.
Other rectangles based on the quintile occur when the ends of two oppositions are related by semi-quintiles or deciles (36°) and bi-quintiles (144°), or when the oppositions occur at 72° intervals (quintile) and the other sides of the rectangle are 1&1/2 quintiles or 108° (tri-decile or sesqui-quintile) in length. These rectangles of the quintile variety stress the potentiality of creativity in one form or another. But we should recognize that creativity may manifest in many more ways than those We usually consider, for example, in the arts. In an expanded sense, creativity refers to the capacity of an individual to transform the environment in some manner, material or social, so that the person leaves an individual mark upon it. Creativity can thus refer to any activity through which an individual effectively projects upon any kind of material at hand or upon the way of life of his or her community the manner of thinking, the vision or ideal, the typical form of behavior which expresses his or her individuality.
An example of a rectangle structured by semi-quintiles and bi-quintiles is found in the horoscope of Krishamurti. Here, Venus and the Moon are in opposition, as are the Sun and Uranus. The Moon and Uranus are semi-quintile, as are the Sun and Venus; and the Sun and Moon and Venus and Uranus are therefore bi-quintile.
In concluding this necessarily abridged study of rectangular configurations, we should note some important general points. First, some rectangles may not fall into the categories we have described, but may nevertheless seem significant on their own merits. For example, the chart of Clyde Barrowof Bonnie and Clyde fame displays the integration of two oppositions (Mercury and Jupiter and Uranus and Neptune) by septiles (Mercury/Uranus and Jupiter/Neptune) and trines (Mercury/Neptune and Jupiter/ Uranus). A similar configuration is found in the chart of the 19th-century occultist and author of The Secret Doctrine, H. P. Blavatsky. In her horoscope, the Moon (fourth-house) opposes Pluto (tenth-house) and the sun opposes Jupiter (which is conjunct Uranus). The septiles are between the second-house Sun and the Moon, and between the eighth-house Jupiter and Pluto. The Sun and Pluto are trine, as are the Moon and the Jupiter/Uranus conjunction. Another atypical case is the birth-chart of India's Prime Minister Indira Gandhi, in which two oppositions are integrated by a variety of aspects. Here, two oppositions (Saturn/Uranus and Venus/Pluto) are linked by a 153° quincunx (Venus/Saturn), a 35° semi-quintile (Venus/Uranus), a sesquiquadrate (Pluto/Uranus) and a novile (Pluto/Saturn) . Required in fulfilling all such patterns is a highly original integration of what is presented by the oppositions, and it must include the essential meanings of all the aspects in evidence.
The generalization underlying the interpretation of all types of rectangles is therefore that the way in which the oppositions are related is the key. While in order to qualify as a 'classifiable' rectangle, aspects should be standard, recognized ones, not too far 'out of orb,' other non-symmetrical patterns linking a variety of aspects must also be recognized to exist as subsets of classifiable configurations. The purpose for classifying astrological phenomena resides not so much in creating pigeon-holes into which subsequent examples can be made to fit, as in creating in the student's mind a sense of pattern a sense of a continuum of patterns having not only identifiable categories, but underlying principles of formation as well. Once the basic principles are grasped, the student should be able to generalize his or her experience to creatively interpret patterns falling in the cracks between established categories.
Geometrically speaking, the equilateral triangle is the most stable of all forms. The astrological grand trine normally links the three aspects of each of the four elements. It presents every mode of existence in its essentially threefold nature. It is unique in all astrological configurations in that it is composed of only one kind of aspect and just as the grand cross is the archetype of all rectangular patterns in astrology, the grand trine occupies the same position in relation to triangular configurations.
The equilateral triangle symbolizes in most religions perfection of being i.e., God as the supreme foundation of all existence. In that sense, it is the symbol of both a static and transcendent condition. It contains no opposition aspect; therefore, it is essentially subjective. It simply is, without conflicts, what it is. However, if an expansive planet like Jupiter dominates a grand trine, this 'what it is' may keep enlarging itself until some internal pressure or external boundary causes it to explode or to become objectively manifest within a form which may produce conflicts or tension. In a particular chart, not only are the actual planets joined by the grand trine significant; what may be as important is the way in which the grand trine is integrated (by what other aspects) into the overall pattern of the chart. Since a grand trine refers to a fullness of vision, or something complete as an ideal at the level of ideas or archetypes, when it is integrated into the chart via an opposition, what is complete at the level of ideas has a more obvious or pointed possibility or necessity for concretization in the world or in the life and personality of the individual.
When one point of a grand trine is involved in an opposition, the opposition's other end almost inevitably falls at the midpoint of one of the trines, forming sextiles to the other two planets in the trine: a 'kite' formation. In such a pattern, vision or understanding and purpose (trines) find the possibility of outward manifestation in objective form (oppositions and sextiles) through organizational genius and the capacity for planning and enlightened management in which needs and answers to needs are brought together. The functional activities represented by the planet at the midpoint of the bisected trine should be those through which is focused and released what the entire configuration represents.
There are other symmetrical triangular configurations spanning the complete 360° of the circle which have not the stability of the grand trine because they are triangles one side of which is smaller than the other two, which are of equal size. The planet forming the apex of the triangle is at the inverse midpoint of two planets in aspect forming the triangle's base. This is also the case in the grand trine, but multiplied and entirely mutual, as each planet is at the inverse midpoint of the arc connecting the other two. On one hand, this contributes to the cohesiveness of the grand trine, but it also serves to keep its focus more or less diffuse and unmanifest (unless, of course, it is involved in a kite or with other focalized aspects integrating it into the overall pattern of a particular chart). The planet at the apex of the non-equilateral triangle can act as a kind of dynamic release or 'seeding' point for whatever is represented by the planets and aspect forming the triangle's base. The most important aspects in the configuration, however, are not necessarily the two pointing toward the apex. Depending upon the overall Gestalt of a particular chart, the foundation-aspect the base of the triangle (no matter in which direction the pattern points)could be considered the most significant operation which is 'trying,' as it were, to manifest through the other two equal aspects in one way or another.*
One of of these types of triangular configurations has been studied by some astrologers and variously called the configuration' or 'Yod' or 'Finger of God.' This configuration produced when two planets in sextile to one another each form quincunxes to a third planet at the inverse midpoint of the sextile. To single out such a pattern as particularly important, however, without taking into consideration the others of the series of which it is part and the principles according to which all acquire significance seems to lack a basic understanding of astrological procedure as well as common sense. For another triangle is formed when a quintile and two bi-quintiles are similarly linked as in the so-called Y-configuration, and we have already mentioned the instance of a square linking two sesquiquadrates.
Granted such aspects as quintiles, bi-quintiles and sesquiquadrates are more difficult to spot in charts drawn in terms of zodiacal longitude, but that should not be sufficient reason for failing to recognize the principles of organization underlying major configurations in which such unfamiliar aspects may be found. At the limit of the series of symmetrical triangular configurations we find the so-called T-square, which is really a triangle in that it links three planets, one at the inverse midpoint of the aspect formed by the other two. In this case, the base of the triangle is the opposition, while the equal sides are composed of squares. The triangle whose base is an opposition is not a very 'tall' triangle, but it nevertheless fulfills the criteria of triangularity fulfilled by the other three.
All these symmetrical triangular configurations in which the a three related planets are not equidistant i.e., not constituting a grand trine have one thing in common. They refer to a state of dynamic equilibrium which is calling for some sort of resolution. On the one hand, the planet at the apex of the triangle can in many cases be interpreted to provide a possible outlet to release and relieve whatever tension is involved in the relationship between the two planets forming the triangle's base. But release and relief are not the same as resolution. For all these triangular configurations represent a dynamic trend toward a fourth point which is not necessarily occupied by a physical planet (although in a particular chart it may be).
The 'empty point,' as it were, pulls to itself the combined biopsychic energy of whatever is represented by the three planets in triangular configuration. This point is the point in opposition to the apex of the triangle. When aspects are not exact, this point may or may not coincide exactly with the midpoint of the aspect forming the base of the triangle. In such a case, an area rather than a point may be considered. In either case, the accompanying figure illustrates the 'direction' of each of the configurations toward what we will call the 'tension point.'
In the so-called 'Yod' configuration (which, of course, can be upside-down, horizontal or diagonal in a chart), the 'tension point' is opposite the planet to which the quincunxes point thus at the midpoint of the triangles sextile base. The same principle applies to the so-called T-square. The 'tension point' is the zodiacal degree which, "occupied by a fourth planet, would transform the T-square into a perfect or grand cross. This is why the T-square acts like and is indeed a triangular, rather than rectangular configuration.
To avoid confusion, we shall repeat here that the grand trine stands apart because it is completely unique, balanced and self-sufficient. In and of itself, it is a configuration devoid of tension. It does not indicate any drive toward anything. It simply is what it is in fullness of being, and for this reason symbolizes spirit or divine perfection. In all other triangular configurations, the fact that one planet, the apex, is equidistant from two other planets in significant relationship to one another indicates a certain amount of tension between the apex-planet and the base-planets. The nature of the tension and the way it seeks resolution (and not merely relief!) varies, of course, with the nature of the particular aspects involved. Needless to say, perhaps, the house positions of the planets, and the zodiacal signs in which they are found, are also of the utmost significance.
Perhaps the best way of interpreting this triangular situation in general is to say that in the so-called Y-configuration whether it involves quincunxes, bi-quintiles, sesquiquadrates or squares - one planet is related to two others by equidistant paths. Thus, symbolically speaking, a possible choice is shown to exist between two ways of life, two approaches to a definite situation symbolized by the planets and aspect forming the triangle's base. We could clarify the matter and refer it to zodiacal symbolism by saying that at the inverse midpoint of two planets in sextile in, say, Virgo and Scorpio, a third planet is quincunx them both in Aries. This can be interpreted to mean that, while Aries seeks its complement in Libra (the empty point at the midpoint of the sextile), it can seek it in two ways: the Virgo way or the Scorpio way. This configuration involving Aries-Virgo-Scorpio has, as it were, Libra as its goal; it is in a state of tension toward Libra. But there are two possible approaches toward resolving the tension: the Virgo approach (purity, discipleship, work, service or retraining) or the Scorpio approach (union through feelings, cooperation or commerce, root-identification, sexuality, etc.).
We could go further and say that the whole configuration is poised, so to speak, toward relationship and relatedness release or relief may be found in Aries (self-motivation or self-centeredness), but not necessarily resolution of the whole question of relationship implied in the configuration in its entirety.
Again the houses of the birth-chart and the actual planets involved as well as the way in which a triangular pattern is oriented in terms of the cross of horizon and meridian, and linked to other elements of the chart and the chart's overall Gestalt are of the utmost significance.
Examples of significant triangular patterns abound, both in general practice and in horoscopes we have already used as examples. We can look again at the birth-charts of Mohandas Gandhi, Albert Einstein, Albert Schweitzer, Werner Erhard and Ram Das, and find significant T-squares or triangles whose bases are oppositions. Gandhi's horoscope in particular shows the T-square as a species of triangle, for in it both a T-square and a grand trine 'point to' or hang off the tenth-house Moon. Both the Saturn/Neptune trine and the Venus/Mars vs. Jupiter/Pluto opposition seek release through the Moon and the field of Gandhi's public life. A vision of transformed social structures (Saturn trine Neptune) illumines, as it were, the Mahatma's struggle with sexuality and marriage at the personal level, and both seek expression through the charismatic persona represented by the tenth-house Leo Moon. Resolution of both configurations thus coincides in the horoscope's fourth house the field of experience related to a person's ancestral 'roots' and the kind of in-depth personality integration that can occur when their sustaining power is effectively and appropriately tapped.
Einstein's ninth-house Jupiter/third-house Uranus opposition is bisected by Pluto in the twelfth house a fitting symbol of the socially transformative, Plutonian catharsis released through Einstein's work. But the configuration's 'direction of resolution' points toward the sixth house, the area from about 25° Scorpio to 2° Sagittarius. In terms we presented earlier, while Taurus (Pluto) seeks its complement in Scorpio, it can seek it in two ways: the Aquarius (Jupiter) way or, specifically in Einstein's chart, the Virgo (Uranus) way. The Jupiter/Aquarius 'path' presumably refers in Einstein's life to his international (ninth house) and social fame and involvement, as well as to the development of his humanitarian sense and relationship to his ancestral Jewish religion. Since Jupiter is in waning square to Pluto, Einstein was challenged to let go of inherited, obsolete structures determining the level at which he operated in these areas. He was born a German Jew, gave up his German citizenship at an early age to become a neutral and, to him, more humanistic, less militaristic Swiss; and while he was asked to become President of the State of Israel after Chaim Weitzman's death, he also had to arrive at his own, more open and universal attitude to his Jewish tradition and consequent status as a Jew.
On the other hand, Uranus is seen in 'waxing* square to Pluto, thus challenging Einstein to become a definite vehicle for establishing through his life what was released as & transforming, universalizing impulse at the Pluto/Uranus conjunction before his birth (in the last two degrees of Aries in 1850-51). The Virgo (Uranus) path thus refers to what was released through Einstein's innovative mind (third house-Uranus) and to his utter dedication to the difficult, and thankless, task he undertook after he had already made his reputation as a 'genius.' Along this path he had to meet many deep personal crises (Virgo and the sixth house), not the least of which was facing what he termed the "biggest mistake" of his life: signing a letter to President Roosevelt urging the U.S. to commit a considerable amount of its already-taxed-by-wartime resources to the development of an atomic bomb before, it was feared, the Germans did.
Although the configuration's point of resolution lies in Einstein's sixth house, Einstein never truly resolved or satisfactorily answered the great philosophical questions engendered by his early work in relativity. While younger physicists readily adopted the statistical, probability-based world-view of quantum mechanics, Einstein nevertheless determinedly maintained that "God does not play dice with the universe." He sought an encompassing alternative to quantum mechanics to no avail throughout the remainder of his life. He never adapted to the role of a public figure, either, and in true twelfth house fashion increasingly withdrew to his study at home and at Princeton University.
In Werner Erhard's chart, the Sun opposes a retrograde (naturally!) Saturn in the tenth house, and both are squared by the seventh house Moon. This is a configuration involving the most basic of factors, challenging individualization and independent emergence through marriage and close personal relationship conditioned by a strong Mother-Image all conditioned by what must have been a difficult or in some way lacking father-son relationship. But here marriage releases the psychic tension involved in the 'wake up and individualize' Sun/Saturn opposition. Resolution comes only through first-house personal integration and being, through perhaps undergoing a 'test of isolation'* by separating oneself from the taken- for-granted patterns of one's time, adopting and maintaining an unpopular stance.
*Cf. An Astrological Triptych: The Way Through, "Twelve basic challenges and tests of individual existence," by Dane Rudhyar (ASI Publishers, New York; 1978).
The T-square in Ram Das's chart also involves the Moon at the 'short end.' The Moon is in the sixth house of retraining, spiritual discipleship and personal crises of readjustment, while the bisected opposition is between tenth·house Venus and third-house Neptune. Public life is again involved, but resolution comes through the twelfth house through the universalization, indeed ritual-like illumination, of all day-to-day activities, and by carrying the self-sacrificing burden of participating in and leading a large-scale social movement.
The T-square in Albert Schweitzer's chart is between Jupiter and Neptune (in opposition to one another) and Mercury (square to both). The Jupiter/Neptune opposition points to to the need to transform and make entirely inclusive the sense of social participation. Moreover, it symbolizes the necessity of making religion more than a merely cultural, taken-for-granted activity. The challenge is to make religion a truly spiritual pursuit, whose great Images live in and through one's open and transformed being. Mercury (in Capricorn and in superior conjunction with the Sun) Schweitzer's formalistic mind potentially provides an outlet for expressing what is symbolized by. this Jupiter/Neptune opposition. Both Mercury and the Sun are on a degree symbolizing a "total commitment to a transcendent goal." Yet the configuration's resolution points toward Cancer and the seventh house, toward "the focalization of complex inner potentialities in harmonic and concrete relationship" (Cancer 24°). Schweitzer apparently had such a relationship, not only with his wife, but also with his original and highly focused image of the person of Jesus, who became for Schweitzer a living presence and true exemplar.
Another triangle, a grand trine, is also present in Schweitzer's chart. If links Venus, the Moon and Uranus. Since Saturn is opposite Uranus, and is therefore at the 'resolution point' of the trine between Venus and the Moon, a 'kite' formation results. The integrative 'vision' symbolized by the grand trine can thus be exteriorized via Saturn's power of organization.
Grand trines are also found in the horoscopes of Jimmy Carter, Herman Melville (cf. Chapter 2), and the two charts in which two grand trines interpenetrated to form Star? of David. Carter's grand trine involves ninth-house Pluto, fifth-house Uranus and first-house Moon a perhaps 'fateful' personal involvement in expressing a vision of large-scale, cathartic social processes. In carter's case, however, Saturn rises before the Moon, and the Moon is just separating from its prenatal conjunction with Saturn. Expression of the Pluto/Uranus trine (rooted in the same Pluto/Uranus conjunction as Einstein's Pluto/Uranus square) is therefore heavily influenced by Saturn i.e., by the Father-Image and conservative, perhaps taken-for-granted or dogmatic social imperatives and taboos.
We have already found triangles formed by a square and two sesquiquadrates what we have called a "Finger of the World" and we point again to the horoscopes of Werner Erhard and Ram Das, and also to the chart of Henry Ford. Erhard's Moon/Saturn square points with two sesquiquadrates to second-house Pluto, which is also conjunct the Moon's South Node. The great question posed by any focal second-house indication is always how best to use one's resources, whatever they may be. Here, an amassing of wealth or public renown can be seen as a way of releasing the biopsychic tension involved in the Moon/Saturn square. The resolution of the configuration points, however, to the eighth house, the field in which an individual's resources are shared with others.
A similar house-situation is found in the birth-chart of Henry Ford, whose sesquiquadrate triangle 'points' to the Moon in the second house (at the cusp of the third). The square is a waxing one between Venus and Uranus a challenge to transform one's sense of values and one's capacity to give form to one's ideas. Ford's industrial innovations and the automobiles they mass-produced surely brought him much in the way of monetary gain, and helped to make of him an autocratic empire-builder. While the configuration's resolution points to Leo and the eighth-house/ninth-house cusp. Ford's
Sun is there (he was born at Full Moon) and whatever resolution there may have been seems rather to have fueled the already fully formed Leonine ego. Nevertheless, Ford, in true Full Moon fashion, stood as a real-life exemplar in his case, of the Horatio Alger 'myth' of a man who, through his own initiative (and perhaps ruthlessness) managed to go from (almost) rags to riches, accomplishing much of social significance along the way.
The triangle in Ram Das's chart links the square between eighth-house Saturn and eleventh-house Sun/Uranus to the third-house Neptune. The use of drugs or a yearning for unorthodox or mystical experiences can be interpreted as a release from the biopsychic tensions of an overly rigid, traditional background restricting satisfying and transformative interpersonal and social relationships. The resolution of the configuration points to the place occupied by tenth-house Venus. The Sabian Symbol for Venus's degree (coincidentally the same degree as Werner Erhard's Saturn) pictures a large cross "illumined by a shaft of light. . . lies on rocks surrounded by sea mist." The degree challenges focused individualization (the cross)\ out of the undifferentiated psychic and collective 'sea,' and indicates that a "spiritual blessing" (the shaft of light) will strengthen those "who, happen what may, stand uncompromisingly for their own truth."
A triangle involving two quincunxes and a sextile is found in the horoscope of George Sand. Saturn and Neptune in the seventh and eighth houses are sextile, and both are quincunx the first-house Moon. The Saturn/Neptune sextile is waning, beginning in the Saturn/Neptune cycle the final phases of a process symbolically transforming the Father-Image and heralding the acceptance of broader social archetypes. A new integration, on the basis of transformed relationships, is possible and challenged here. The midpoint of the sextile (the point opposite the Moon) coincides with Jupiter at 27° Libra. While the symbolic references to relationships are obvious here, Jupiter's Sabian degree emphasizes the ability to "transcend the conflicts and pressures of the personal life. "Ms. Sand's personal life especially where relationships were concernedwas indeed subject to conflicts and pressures, both inner and outer. She was indeed forced, and at least partially able, to become objective to and transcend them.
Another triangle involving a sextile and two quincunxes appears in the chart of Werner Erhard. As in the case of George Sand, a waning sextile between Saturn and Uranus forms the configuration's base. Mercury in Libra in the 5th house opposes the midpoint of the 10th/12th house sextile. Release of the sextile challenging reorganization at the level of the Father-Image and of social archetypes is through creative mental activity and communication (5th house Mercury) and interpersonal relationships (Libra). With Saturn and Uranus in such a relationship, it is interesting to note the eclectic nature of the est training and particularly how much of the American New Thought movement from earlier this century has been incorporated into it. The configuration's resolution, however, is symbolized by the early degrees of Aries in the 11th house a challenge to pioneering social transformation. Since the 11th house follows the 10th, it also poses the question. What will a successful individual do wither about his success, and as well with the rebellious attitude or feeling of deep discontent that made him act as a reformer or revolutionary to begin with?
Such concepts could be developed much further and a whole book written about rectangular and triangular aspect patterns. But enough may have been said to indicate how the basic ideas might be extended and applied to particular situations. We have interspersed what we hope will be useful examples throughout the text, but if they are to prove valuable, they should be studied in depth along with complete biographical information for the persons whose charts have been used.
The study of simple rectangular and triangular configurations is only a basic step toward the visualization and interpretation of the whole pattern made by all ten planets of a birth-chart. As a foundation, it does help to develop one's mind to see and think in terms of the whole chart, rather than according to the merely analytical procedure, which is satisfied to list aspects and planetary positions as separate factors and somehow to see what they might add up to. Both methods are nevertheless valid when used together as they always should be the former to present a whole view of the individual person and his or her potentialities, the latter to clarify the many detailed features of the personality in everyday life.
1. I believe that I was the first astrologer to study and Interpret this configuration. It is mentioned in my book The Astrology of Personality (1934-35). At first I called it a 'mystic rectangle' because its shape seems to have been used in initiation chambers and temples of older civilizations; altars In these structures had also been constructed on its proportions. Later on I realized the inadequacy of the term, that it was confusing, especially considering the way it has been used and abused of late. I then began to call it a 'harmonic rectangle.'
Some astrologers, perhaps not agreeing with my claim that such a rectangle had an integrative or harmonic character, have spoken of it, years later, as the X-configuration. This, is, of course, in line with such terms as perfect cross and T-square and we shall see in a moment that some astrologers have also spoken of a Y-configuration, which I consider as a species of tri angle. The question here besides the fact that all such 'X's' are not integrated by sextiles and trines is perhaps whether you like the alphabet better than geometry, but it may go deeper. In speaking of rectangles and triangles, I am envisioning shapes in which dynamic centers (the planets) constantly interact. What is important is the interaction between these centers, and the geometrical concept expresses this fact better than the alphabetic formulation especially since letters such as T, X and Y are not found in all languages. Today one should think universally, not in terms of national cultures and alphabets!DR