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 Title: Lecture: The Alphabet
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 the feeling that the geometrical, thought concretely, was the music of
 Title: Mathematics and Occultism
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 of geometrical forms and arithmetical relations of numbers, then he is
 prototype, because the geometrical proportions of the World are the
 Title: Lecture: The Souls Progress through Repeated Earth Lives
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 Title: Mission of FolkSouls (1929): Lecture 3
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 In order to arrive at geometrical, mathematical knowledge it is not
 Title: Mission of FolkSouls (1929): Lecture 5
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 been expressed in quite a special way by means of a geometrical
 figure. If you go through all geometrical figures, you will find none
 Title: Lecture: The Inexpressible Name, Spirits of Space and Time.
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 furthest of all along the path of mathematicalgeometrical knowledge.
 mathematicalgeometrical sphere, the less transparent things become.
 Title: Lecture: The Universe
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 arranged geometrically, also the eyes, which are focused
 geometrically. We may therefore say: insofar as man faces
 Title: Errors in Spiritual Investigation
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 existed a kind of belief, a certain mathematicalgeometrical belief
 Title: Lecture: The Position of Anthroposophy among the Sciences
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 formed geometrically within space; we feel thereby that we are on
 geometrical illustration; I could give others also.) Neither
 between triangular and rectangular shapes, do not see geometrical
 Title: Lecture: Anthroposophy and the Visual Arts
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 — we apply it, of course, geometrically, using, in the first
 planes that they determine). In this way we obtain a geometrical
 as the basis, in man, of the three geometrical spacedimensions. What
 Title: Lecture: Knowledge Pervaded with the Experience of Love
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 way in which mathematical or geometrical figures confront him in
 Title: Mission/FolkSouls (1970): 3. The inner Life of the Folk Spirits. Formation of the Races.
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 metallic triangles in your box of geometrical instruments. If you
 geometrical and mathematical knowledge sensedata are superfluous;
 Title: Mission/FolkSouls (1970): 5. Manifestation of the Hierarchies in the Elements of Nature.
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 special way by means of a geometrical figure. Amongst geometrical
 Title: Lecture: Wonders of the World: Lecture 3
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 geometrical figure. If we ponder deeply this figure we find that it
 Title: Tension Between East and West: Lecture 2: Psychology
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 otherwise experience in the case of a geometrical problem. If
 comprehended — as we comprehend geometrical concepts,
 Title: Tension Between East and West: Lecture 8: The Problem (AsiaEurope)
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 but in a geometrical progression. Meanwhile, the particular
 Title: Purpose of the Goetheanum and Anthroposophy
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 even to have these geometrical concepts, that are really to be
 Title: Karma of Vocation: Lecture VIII
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 stipend for him. Then, after he had pursued his geometrical
 Title: Necessity for Spiritual Knowledge: Lecture 2
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 Title: Supersensible Knowledge: Lecture VI: Education in the Light of Spiritual Science
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 structure, using finished geometrical shapes. That is why
 Title: The Building at Dornach (Bn/GA 289): Lecture I: The Goetheanum
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 the geometricaldynamic can alone rightly hold a place in the art of
 the merely mathematicalgeometricaldynamic column formation has been
 the geometricalmechanicaldynamic weightbearing and carrying, is the
 Title: Esoteric Cosmology: Lecture XII: The Devachanic World (continued)
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 The geometrical and symbolic figures employed as the sacred signs of
 Title: First Lecture (First Scientific LectureCourse)
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 rather less. Thus, what we have to say concerning geometrical form is
 Title: Second Lecture (First Scientific LectureCourse)
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 kinematical, geometrical and arithmetical truths, — truths we
 Title: Ninth Lecture (First Scientific LectureCourse)
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 purely geometrical or kinematical, and as I pointed out, this also
 Title: Tenth Lecture (First Scientific LectureCourse)
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 geometrical and kinematical — calculable waves in an unknown
 somehow compelled to bring more movement into our geometrical and
 hold of in a fully valid way with geometrical ideas derived from a
 geometrical or kinematical ideas are related to what appears to us
 Physics — we calculate and draw them in geometrical figures.
 origin of all our phoronomical — arithmetical, geometrical
 calculating, or drawing it geometrically, or analyzing the forms of
 intelligent beings and on the other hand the geometrical,
 the geometrical, the arithmetical ideas — rise up from the
 organ in the metabolism. Our geometrical ideas above all spring
 And if you now apply these geometrical ideas (I will say
 “geometrical” henceforth to represent the arithmetical
 real object. So too, what in your geometrical and phoronomical
 phenomena of warmth) — by means of geometrical, arithmetical
 originate. For this, our arithmetical, algebraical and geometrical
 Plainsailing arithmetical and geometrical methods proving
 Title: Man/Being/Spirit/Soul: Lecture III: The Science of the Spirit and Modern Questions
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 we can comprehend as exactly as mathematical or geometrical
 Title: Origins of Natural Science: Lecture III
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 mathematical or geometrical system, they would thereby achieve
 geometry, and who uses his analytical formulas and geometrical concepts
 from? Or, Where do we get our whole geometrical system?
 depths of soul where geometrical thought has its base. Man takes his
 that merely because of his being human the geometrical elements
 mathematical, methodical lines, not specifically geometrical lines,
 This is because, inwardly experienced, the blood absorbs all geometrical
 the mathematical and geometrical experience to its own movement. It
 each geometrical figure. Modern man feels no blood experience; he
 Title: Origins of Natural Science: Lecture IV
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 the formrelated or geometrical elements of mathematics, the
 world conception in which the triangle or another geometrical form
 surface of a given body or to its path of movement. Geometrical and
 fourteenth century. Thinking geometrically about space, man did not
 Title: Origins of Natural Science: Lecture VI
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 pertains to shape, to geometrical and numerical characteristics, to
 form, motion and geometrical qualities; and he further assumed that
 These images are the mathematical geometrical, and arithmetical
 Title: Warmth Course: Lecture III
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 considered equally well as a purely arithmetical or geometrical fact.
 of an ordinary geometrical line, we find it cannot be done. Now this
 Title: Warmth Course: Lecture V
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 geometrical concepts, we enter the unknown region where the will
 Title: Lecture: Mission of Michael: Lecture IV: The Culture of the Mysteries and the Michael Impulse.
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 we are aware of the mathematical and geometrical concepts. The middle
 Title: Lecture: The Proclamations to the Magi and the Shepherds
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 kind of knowledge resembling our geometrical or mathematical sciences.
 geometrical and arithmetical sciences were once imparted to mature
 Title: Lecture: Secrets/Threshold: Lecture IV
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 circle. People were constantly trying to prove geometrically how the
 a treatise, for it has been proved conclusively that the geometrical
 Title: Inner Impulses: Lecture VII
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 calculate it and treat it geometrically as is taught today in
 external picture, the purely geometrical picture. The other picture
 the other hand, man dreamt of geometrical lines in space; he dreamed
 Title: Rosicrucianism/Initiation: Lecture II: Hidden Centres of the Mysteries in the Middle Ages
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 geometrical figures, the corners and sides of which he named with the
 Title: Rosicrucianism/Initiation: Lecture III: The Time of Transition
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 Title: Rosicrucianism/Initiation: Lecture V: Occult Schools in the 18th and First Half of the 19th Century
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 by which he teaches them consist in certain geometrical forms, let us
 Title: Education: Lecture IX: Arithmetic, Geometry, History
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 but supersensibly, they continue to calculate or to draw geometrical
 Title: Practical Course/Teachers: Lecture X: Arranging the Lesson up to the Fourteenth Year
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 Here, too, the time has come when, using geometrical forms, we
 Title: Study of Man: Lecture III
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 concrete life — purely out of his geometrical, mathematical
 you draw geometrical figures, you perform in conjunction with the
 to the lines of geometrical solids: the cube, the octahedron, the
 other geometrical solids lies a remarkable harmony with the
 dies, and it is only reflected back in the geometrical images which
 Title: Study of Man: Lecture VIII
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 being actually executes geometrical forms in the cosmos and then
 Title: True/False Paths: Lecture Eight: Potential Aberrations in Spiritual Investigation
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 purely mathematically and geometrically. We must say: the medium is
 Title: True/False Paths: Lecture Eight: Potential Aberrations in Spiritual Investigation
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 purely mathematically and geometrically. We must say: the medium is
 Title: Art/Mystery Wisdom: Lecture Eight
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 merely from the geometricalmathematical point of view and
 Title: Metaporphoses/Soul One: Lecture 1: The Mission of Spiritual Science
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 with all sorts of geometrical figures, triangles, polygons and so on. Anyone
 Title: Anthroposophy Science: Lecture II
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 Title: Anthroposophy Science: Lecture III
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 is there when we dwell in geometrical, arithmetical, or
 than geometrical constructs or numerical relationships. He
 with geometrical and arithmetical pictures, and feel that
 geometrically. In the realm of our senses we actually
 Title: Anthroposophy Science: Lecture V
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 geometrical forms. It is important to grasp this because when
 geometrical forms, and we enter — at least to some
 degree — the geometrical forms themselves. This becomes
 is easily understood from a geometrical point of view), and
 does show us that we can enter into the geometrical forms,
 Title: Boundaries of Natural Science: Lecture III
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 the Rule of Pythagoras or any other geometrical axiom, but the existence
 the geometrical forms to a sense of wonder at the harmony that underlies
 Title: Boundaries of Natural Science: Lecture VI
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 can only in mathematical, geometrical, analyticmechanical thinking. When
 Title: The Building at Dornach: Lecture IV
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 from the geometrical aspects. There are four columns embraced
 shows by a dome. But this geometrical aspect is only part of
 feel this motif, we do not feel the geometrical
 Title: Fruits/Anthroposophy: Lecture 5: From Sense Perception to Spirit Imaging
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 is there in the soul in the same way as mathematical, geometrical forms
 Title: Fruits/Anthroposophy: Lecture 6: From Imaginative Knowledge to Inspirational Knowledge
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 not only of geometrical but also of qualitative involutions, to get
 Title: Child's Changing Consciousness: Lecture I
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 experience with their bodies what is shown in geometrical
 Title: Cosmic Prehistory: Lecture I: The Threefoldness of Space and the Unity of Time
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 experienced the three dimensions concretely, not abstractly or geometrically
 Title: Community Life: Address 2: The GoeschSprengel Situation  Part 2
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 days ago on various mathematical and geometrical ideas.
 Title: Answers to Big Questions: Lecture XV: What Has Astronomy to Say about the Origin of the World?
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 once in certain respect only a kind of geometrical calculation
 Title: Riddles of the World: Lecture II: Our International Situation. War, Peace and Spiritual Science
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 population geometrically. This causes a struggle for existence,
 Title: Riddles of the World: Lecture XVI: German Theosophists at the Beginning of the Nineteenth Century
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 knowledge in geometrical forms, and Novalis, who illumined the
 Title: Knowledge of Soul and Spirit: Lecture I: The Mission of Occult Science in Our Time
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 inside. Thus, it is with all geometrical and all mathematical
 Title: Theosophy/Rosicrucian: Lecture I: The New Form of Wisdom
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 apart from its history, just as geometrical truths exist independently
 Title: Impulses of Utility: Lecture I: Western and Eastern Culture, H. P. Blavatsky
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 has the tendency to impel men forward geometrically and only to
 increases in geometrical progression, And so for him there
 Title: Karmic Relationships, Volume I: Lecture XI
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 finds in teaching posts, a man at whose geometrical imagination and
 Title: Karmic Relationships, Volume I: Lecture XII
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 a strong capacity to be alive to the geometrical constitution of his
 Title: Karmic Relationships, V: Lecture IV
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 him because I myself loved geometrical construction and because he
 all the exclusiveness belonging to geometrical thinking. His mind was
 Title: Karmic Relationships, VII: Lecture Five
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 thought that the ability to construct figures from geometrical
 may be. and then evolves the geometrical figures. And now the
 Title: Supersensible Knowledge: Lecture I: Supersensible Knowledge: Anthroposophy as a Demand of the Age
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 geometrical or arithmetical problem. This can be done in the
 Title: Gospel of John: Lecture I: The Doctrine of the Logos
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 presented the most rudimentary geometrical facts? They study
 these geometrical facts quite apart from this Euclidian book,
 geometrical knowledge? Something very extraordinary would
 Title: Gospel of John: Lecture X: The Effect of the Christ Impulse Within Mankind
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 mathematical and geometrical truths. These cannot be put to
 Title: Things Past and Present: Lecture V: Comenius and the Temple of PanSophia
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 is presented in itself in this geometrical structure which he
 clairvoyantly in geometrical forms around the human being.
 Title: Things Past and Present: Lecture VIII: Thomas More and His Utopia
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 consisted of right angles and other geometrical shapes; this
 Title: Fundamental Social: Lecture 1: The Transforming of Instinctive into Conscious Impulses
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 and the increase in population in geometrical, progression. I
 4, 5. Then we shall have the corresponding geometrical ratio,
 Title: Karmic Relationships, VI: Lecture V
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 characteristics as well, but his geometrical talent provided no
 Title: Man: Hieroglyph: Lecture Ten
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 geometrical figure, we can employ neither a circle nor an ellipse; for
 geometrical figure which is to correspond with man's daily round in a
 Title: Cosmosophy 1: Lecture V
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 mathematical, geometrical way, we find that we can think out
 purely geometricalmechanical physics and so on, we draw out
 Title: Cosmosophy 1: Lecture X
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 Title: Man/World of Stars: Lecture I: The SpiritSeed of Man's Physical Organism
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 everywhere. The orientation is not geometrical like the
 Title: Occult Movement: Lecture Two: Mediumistic Methods
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 Title: History of Art: Lecture XII: Greek and Early Christian Art, Symbolic Signs, the Mystery of Gold
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 pulled in, how they can be expanded as geometrical figures.
 geometrical and figurative motifs, above in a similar fashion
 Title: Esoteric Development: Lecture III: Supersensible Knowledge: Anthroposophy as a Demand of the Age
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 undertakes to solve a geometrical or arithmetical problem. This can
 Title: Esoteric Development: Lecture VII: The Great Initiates
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 It is the same with the geometrical truths that we accept. But
 Title: History of Art: Lecture II: Leonardo, Michelangelo and Raphael
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 figures who, partly by meditation, partly by arithmetical, geometrical
 Title: Esoteric Lessons Part II: Berlin, 31511
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 geometrical figures in general. One should do this by writing these
 Title: The Situation of the World
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 accordance with geometrical progression. This produces a
 Title: Education as a Social Problem: Lecture VI: The Inexpressible Name, Spirits of Space and Time, Conquering Egotism
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 mathematicalgeometrical the more untransparent do matters
 Title: Influence of Spiritual Beings Upon Man: Lecture IX
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 all truths, the arithmetical, geometrical, are found inwardly, and yet
 Title: Presence of the Dead: Lecture Four: The Presence of the Dead in our Life
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 geometrical forms. GrecoRoman architecture is like a marriage of
 Title: Astronomy Course: Lecture I
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 geometrical conception of threedimensional space; — to
 Title: Astronomy Course: Lecture III
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 phenomena in their mathematical and geometrical aspect alone.
 Title: Astronomy Course: Lecture IV
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 approximately by mathematical or at any rate geometrical
 geometrical way, representing it in forms similar to purely
 geometrical figures. Here we are following up a reality which
 like purely geometrical forms. Thus in effect, in employing
 in a geometrical form what presents itself in Embryology; not
 some inherent law, similar to the laws underlying geometrical
 same thing may not happen with geometrical form as with
 incommensurable number. Now let us ask: How do geometrical
 geometrical forms as a means of illustration; the facts can
 no longer be grasped with geometrical forms? Just as we must
 clothed in geometrical (or again arithmetical, algebraic,
 Title: Astronomy Course: Lecture V
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 are expressed by our Astronomy in geometrical forms and
 continue merely to draw geometrical lines, tracing the
 can never fully compass it was geometrical figures or
 in the place of mere geometrical designs in order to
 geometrically. As I said yesterday, in studying the celestial
 Title: Astronomy Course: Lecture VIII
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 Title: Astronomy Course: Lecture IX
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 from what can be grasped in geometrical form to what is
 Title: Astronomy Course: Lecture X
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 that I wanted not only to solve this geometrical problem,
 geometrical forms involved, so that they relate to mechanics
 Title: Astronomy Course: Lecture XV
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 Title: Astronomy Course: Lecture XVI
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 movement are called curves), i.e. the true geometrical
 geometrical thinking and now the outer reality accords with
 Title: Astronomy Course: Lecture XVII
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 as I said before, you are really dealing with geometrical
 the relevant geometrical positions which are to be found in
 geometrical loci all that is really given. So too you must
 Title: Astronomy Course: Lecture XVIII
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 geometrical figures the phenomena elude us. Time and again
 presented in seemingly mathematical and geometrical guise.
 Title: Origin and Destination of Humanity: Lecture XVI: The Great Initiates
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 times and places. The same applies to the geometrical truths which we
 Title: Apocalypse of John: Introductory Lecture
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 scholastic form the mathematical and geometrical facts that
 Title: Lecture: Wonders of the World: Lecture 3
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 geometrical figure. If we ponder deeply this figure we find that it
 Title: Search for the New Isis: Lecture I: A Christmas Lecture
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 mere mathematical and geometrical pictures, if we can raise
 Title: Search for the New Isis: Lecture III: The Magi and the Shepherds: The New Isis
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 inwards and becomes the dry, geometricalmathematical, mechanistic
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