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PRIMARY ACT.

55. The + - or, in other words, numbers are acts or functions. Zero is, consequently, the primary act. Zero is, therefore, no absolute nothing, but an act without substratum. Generally speaking there is, therefore, no nothing; the mathematical nothing is itself an act, consequently a something. The nothing is only postulate.

56. An act devoid of substratum is a spiritual act. Numbers are, accordingly, not positions and negations of an absolute nothing, but of a spiritual act.

57. The zero is an eternal act; numbers are repetitions of this eternal act, or its halting points, like the steps in progression. With zero the Eternal therefore originates directly, or both are only different expressions for one and the same act, according with the difference of the science wherein they are employed. Mathematics designates its primary act by the name of zero; Philosophy by that of Eternal. It is an error to believe that numbers were absolute nothings; they are acts and consequently realities. While numbers in a mathematical sense are positions and negations of Nothing, in the philosophical they are positions and negations of the Eternal. Everything which is real, posited, finite, has become this out of numbers; or, more strictly speaking, every Real is absolutely nothing else than a number. This must be the sense entertained of numbers in the Pythagorean doctrine, namely, that everything or the whole universe had arisen from numbers. This is not to be taken in merely a quantitative sense, as it has hitherto been erroneously, but in an intrinsic sense, as implying that all things are numbers themselves, or the acts of the Eternal. The essence in numbers is naught else than the Eternal. The Eternal only is or exists, and nothing else is when a number exists. There is, therefore, nothing real but the Eternal itself; for every Real, or everything that is, is only a number and only exists by virtue of a number. Every Singular is nothing for itself, but the Eternal is in it, or rather it is itself only the Eternal, though not the Eternal in itself, but affirmed or negatived. The existence of the Singular is not its own existence, but only that of the Eternal subjected to an arbitrary repetition; for the act of being and affirming are of one kind.

58. The continuance of Being is a continuous positing of the Eternal, or of nothing, a ceaseless process of becoming real in that which is not. There exists nothing but nothing, nothing but the Eternal, and all individual existence is only a fallacious existence. All individual things are monades, nothings, which have, however, become determined.

The Eternal must posit without cessation, for otherwise it would be an actual nothing, while in fact it is an act; but it must incessantly suppress also this position, else it would be only a finite act, or an act which had only one kind of direction, that of affirmation + + + +, and so on, which represents only the half of arithmetic. The totality of the Finite is, therefore, of eternal duration also: the Singular, however, issues forth and disappears like the numbers in arithmetic. The eternal duration of the Finite consists, however, only in ceaseless repetition. Such an Eternal is to be distinguished therefore from the Primary eternal, and is called the Infinite. The totality of finite things is not therefore eternal, but only infinite.

PRIMARY CONSCIOUSNESS.

59. Two tendencies are present in the primary act, both of which being inseparable are one in kind. It has the tendency to posit, and also to suppress, itself. The unity strives unto binary division or to antagonism, even as the 0 strives to produce + or -. While the primary act itself posits, it does this indeed out of its own strength, and that which it posits is also none other than itself; it itself posits i. e. actively; and is itself posited i. e. passively; it itself posits itself, is the self-position of itself; for + is nothing else than 0 self-posited. The positing and posited act are of one kind; the latter, however, is the Real, the Finite; the former the Ideal, the Eternal. Both are distinguished from each other through this only, that the Real is the posited, numbered, and consequently determined act; the ideal, however, the positing, consequently numbering and thus undetermined act. While, however, the + is nothing else than 0, it must necessarily bear a relation to it, and thus retrograde into the 0. This retrogression is an act in the reverse direction, or what is indicated in mathematics by negation. The - has been therefore necessarily granted with the +, else the + would not be represented as = to 0. The act of positing is therefore at the same time also an act of negation. So soon as the 0 is or exists, it is = + -. The realization of the Eternal is accordingly a complete antagonism of itself. For 0 is equal to + -, not simply = + or = to-.

60. The being of the Eternal is therefore a self-manifestation. Every Singular is nothing but a self-manifestation; since all numbers are only positions of zero or of +, which can never be without-. In every essence there are two, but the two are the one essence itself, which posits itself by division. The Positing of the Eternal in the sense in which it has been hitherto adopted, namely, as a realization of the same, is not merely an act of positing, not an indeterminate Positing, but an antagonism of itself. The zero is simply the indeterminate Positing, or the negative Positing; but the number, or the real is the antagonism of zero, the + -, or the self-manifestation. The 0 cannot be thought of for itself alone without the +; the latter, however, not without 0, as well as the-also not without 0; for it is the suppression of the posited 0, namely, the +. Every act of self-manifestation is therefore twofold, a manifestation (= +), but a manifestation of itself, consequently a retrogression into 0 (= -). Through negation the Finite becomes united with the Eternal. Every disappearance of the Finite is a retrogression into the Eternal; for it must return to whence it came. It has arisen out of nothing, is itself the existing nothing; it must therefore retrograde again into the nothing.

GOD.

61. The self-manifestation of the primary act is self-consciousness. The eternal self-consciousness is God.

62. The continued act of self-consciousness, or becoming self-conscious repeated, is called representation. God is therefore comprehended in ceaseless representation. Representations are single acts of self-consciousness. Single acts, however, are real things. All real things, however, are the world. The world therefore originates with the representations of the Eternal.

63. The representations are, however, manifested or attain only reality through expression. The world is therefore the language of God; the creation of the world the speaking of God. "God spake, and it was." It is not merely said, God thought and it was. Thought belongs merely to spirit; in so far, however, as it becomes apparent, it is a word, and the sum of all apparent thoughts is speech. This is the created, realized system of thought. The thought is only the idea of the world, but speech is the idea actualized.

64. As thought differs from speaking, so does God from the world. Our world consists in our apparent thoughts, namely, the words. The universe is the language of God. So far as the thoughts lie at the foundation of the words, it can be said, that our world were the play of our thoughts, and the actual world that of God's. The word has become world. Worldly things have no more reality for God, than our words or our language for us. We carry a world within us while we think; we posit or create a world without us while we speak. Thus God carries the world within himself while he thinks; he posits the same without himself or creates it, while he speaks. In so far as thought necessarily precedes speech, it may be said, that there would have been no world, if God had not thought. In the same sense it may be also said, that all things are nothing but representations, thoughts, ideas of God. So soon as God thinks and speaks is there a real thing. To speak and to create are one. All, that we perceive, are words, thoughts of God; we are ourselves nothing else than such words or thoughts of God, consequently his metatypes or images, in as far as we unite in ourselves the whole system of speech. There is therefore no being without self-consciousness. That only which thinks is (for itself); that which does not think is not for itself, but only for some other consciousness. The world differs from God as doth our speech from us. The self-consciousness of God is independent of the world, even as our self-consciousness is independent of our speech.

65. The divine laws are also the laws of the world; this has therefore been created and governed in accordance with eternal and immutable laws.

66. Physio-philosophy is the history of creation; the creation, however, is the language of God. The system of thought, however, lies necessarily at the foundation of the system of speech. Now the science of the laws of thought is called logic; physio-philosophy is therefore a divine doctrine of speech or a divine logic. The laws of speech instruct us in the genesis of language. Physio-philosophy is, therefore, the science of the genesis of the world, or Cosmogony.

FORM OF GOD—TRIUNITY.

67. As the complete principle of mathematics consists of three ideas, so also does the primary principle of nature, or the Eternal. The primary principle of mathematics is 0; so soon, however, as it is actual, is it + and-; or the primary idea resolves itself in being at once into two ideas, each of which resembles the other in essence, but differs from it in form. Thus it is here one and the same essence under three forms, or three are one. Now that which holds good of mathematical principles, must hold good also of the principles of nature. The primary act is manifested, or operates under three forms, which correspond to the 0, + and-.

These three ideas of the Eternal are all equivalent to each other, are the same primary act, each of them being whole and undivided, but each otherwise posited. The positing primary act is the whole Eternal; the posited is likewise the whole Eternal, and that which is subtractive, retrogressive, combining the two first, is also the whole Eternal. Although all three ideas are equivalent to each other, still the positing idea ranks first, the posited second, and the combining third; not as if they had first arisen successively (this is impossible, for they are coexistent, namely, before all time), nor as if they occupied different positions (for they are everywhere); but only according to their order and value. How one may be three and three one, is thus rendered comprehensible only by mathematics.

68. The first idea is the original, that therefore which is thoroughly independent, which having arisen from and being based upon itself, has consequently emerged from nothing else; in short, it is the eternal idea, like the mathematical 0 = Monas aoristos. Everything is possible with it; it can propose and solve all problems, knows therefore everything and creates everything. It is the generative, creative and paternal idea.

69. The two other ideas have emerged out of the first, although apparently equivalent to it; yea, they have themselves issued out of themselves. The second idea is, therefore, Dyas aoristos, and corresponds to the mathematical +; the third idea is the Trias aoristos, and corresponds to the mathematical-, so that by the three the primary trinity 0 + - is completed. The first idea labours or, what is more, rejoices from all eternity to convert itself into the two others. The action or the life of God consists in eternally manifesting itself, eternally contemplating itself in unity and duality, eternally dividing itself and still remaining one. The second idea has issued next from the first, and is therefore related to it as Son is to Father, when the ideas are viewed as personified. The third idea has emerged conjointly from the second and first, and forms therefore the spiritual union, the mutual love between both. It may be therefore simply called Ghost or Spirit, if it is thought of as personified.

70. Since every Singular, having been produced through the primary trinity, is only the expressed word of the primary trinity, so also must their qualities be recognizable in the same. The Singular is not simply therefore a position of one idea, but of all three. All things have issued out of the trinity. The essence of the universe consists in the trinity which is unity, and in the unity which is trinity; for it is a likeness of the primary trinity. Being, generally, is an act, and that, indeed, of a threefold nature. Apart from act or function there is no being. That, which is called nothing, is in itself an act, and there is, therefore, no absolute nothing. The nothing is only something relative to a particular being. Even the mathematical zero is not nothing, but an act. It is nothing only in reference to particular numbers. Numbering is a repetition of one and the same act. The forms or conditions of the primary act are Rest, Motion, and Extension or expansion.

a. PRIMARY REST. (First form of the Primary Act.)

71. The primary idea is the position simply without any relation, or any antagonism; it is the oscillating resting point in the universe, around which everything collects itself, and from which everything emerges; the Centrum ubique, circumferentia nusquam. The primary idea is the substratum of everything, which will come before us in the sequel of this work. Everything depends upon this primary essence; all action, motion, and form issues forth from it; or rather, in all phenomena naught else appears than the primary essence in different stages of position, just as in all numbers naught else appears but the zero. The primary idea is the absolute beginning. This primary idea is the non-representable, the never apparent and yet omnipresent, idea; but which is always withdrawing itself from our view when we imagine or believe that we gaze upon it; in short, the Spiritual, which declares itself in everything and yet always remains the same. The origin of all action may be termed the primary force.

b. MOTION, TIME. (Second form of the Primary Act.)

72. The primary idea operates only, while it posits; through positing, however, arises a succession of positing, or numbers; positing and successive positing are one. The function of the primary idea consists in an eternal repetition of the essence; the primary act is a continuous self-repeating act. Repetition of the primary act devoid of another substratum is Time. Time is none other than the eternal repetition of the positing of the Eternal, corresponding to the series of numbers + 1 + 1 + 1 + n. Time has not been created, but has emerged directly out of the primary act and its position; it is the function of God himself. Something has thus already originated, which appears to conduct us into the universe. Time is the first portal through which the operation of God passes over into the world. Time is the infinite succession of numbers or the mathematical nothings. The mathematising, numbering act is Time. Numbers, however, are Singulars or finitudes, which constitute the world.

73. Time is infinite, for it is the totality of positing; it is only the points or numbers in it that are the Finite.

74. All things are created in time; for time is the totality of Singulars. Time is no stationary quantity, which is always changing itself into something new during its progressive flux. It is not a continuous stream, but a repetition of one and the same act, namely, the primary act, like as it were to a rolling ball, which constantly returns upon itself. There is no endless, still less an eternal thing; for things are only positions of time. Time itself is, however, only repetition, and thus also a suppression of these positions. The vicissitude of things is in fact time; if there be no change, there is also no time. Time is an universal property of things. Exemption from time is only in the Eternal.

75. Time, not being itself the Finite, but creating it, is not itself a Real, but still an Ideal, a form only of the primary act, an idea, with which finite things have been directly posited. Time is the act of numbering; numbering is thinking; thinking is time. Our thinking is our time. In sleep there is no time for us. God's thought is God's time; God's time, however, is all time, consequently time of the world. Time is not of earthly but heavenly descent or origin. In so far a divine quality belongs to all finite things. They are divine, in so far as they are time; terrestrial, in so far as they are evanescent moments of time.

POLARITY.

76. Time is an action of the primary power; and all things are active only in so far as they are filled or inspired with the idea of time. The whole activity of things, all their forces arise out of the primary act or primary power, are only moments of the same. There are, however, no positive without negative numbers, consequently also no moments of time without suppression of the same. There is, therefore, no single force, but each is the position of + and-. A force consisting of two principles is called Polarity. Time is, therefore, the primary polarity, and polarity is manifested at the very instant in which the creation of the world is stirring.

77. Polarity is the first force which appears in the world. If time is eternal, polarity must also be eternal. There is no world, and in general nothing at all without polar force.

78. Every single thing is a duplicity.

79. The law of causality is a law of polarity. Causality is valid only in time, is only a series of numbers. Time itself has no causality. Causality is an act of generation. The sex is rooted in the first movement of the world.

MOTION.

80. Polarity may be viewed as a single positing of + -; if, however, this positing repeats itself, Motion originates, viz. when many + - + - are consecutively posited, and thus the principal poles separate from each other, as in an iron bar when magnetizing. Time is a polar positing of the primary act, and an endless repetition of this positing; through this originate individual things, whose succession is motion.

81. Primary motion is the result of primary polarity. All motion has originated from duplicity; consequently from the idea in a dynamic not a mechanical manner. A mechanical motion, which might be produced ad infinitum by mechanical impulses, is an absurdity. There is nowhere a purely mechanical motion; nothing, as it is at present in the word, has become so by impulse; an internal act, a polar tension lies at the bottom of all motion.

82. Motion itself, however, is not twofold in character; it is unity, but the result of duality. In time we have to distinguish the polar act of position, and the act of repeating this position, which is motion. Motion is the simple repetition of the polar, twofold act, or the ceaseless separation of poles; but, as in every polar line the two poles are in all cases together, so even is this mutual separation of poles only a repetition of polarity.

83. Motion also is not created, but has emerged directly from the Eternal, is the primary function itself repeated. Motion is the ever self-manifesting, consequently progressive God.

84. Motion is thought, which is manifested as speech. Thought polarizes the fingers. If the thought be powerful it moves them, and through them other bodies. Speech is only a thought that has passed over into motion. The world is the thought of God that has been translated into motion, the moved thought of God—thought spoken. It is here evident that the world is not simply the thought but the language of God; for there is no action without motion; consequently no thought without speech, and vice versâ.

85. There is no thing which were without motion, just as there is none without time. A Finite without everlasting motion is a contradiction. All rest in the world is only relative, is but a combined motion. There is only rest in the Eternal, in the nothing of nature.

86. The primary motion is only possible in a circle, because it fills every thing.

87. The motion of finite things by polarity may, in a wider sense, be called life; for life is motion in the circle. Polarity, however, is a constant retrogression into itself. Without life there is no being. Nothing is, simply by virtue of being, e. g. by its mere presence; but everything of which a being can be declared, is only, or manifests itself, by its polar motion or by life. Being and life are inseparable ideas. While God acts, he creates life.

88. Life is nothing new, that came first into the world, after it was created, but an Original, an idea, a moved thought of God, the primary act itself with all its consequences.

89. There is in the universe no vital force of its own; the individual things lie not there some time and await the polarizing breath, but they first become through the breath of God. The Causa existentiæ is life.

90. There is nothing properly dead in the world; that only is dead which is not, only the nothing. Something can only cease to live, when its motion ceases; this, however, ceases only when deprived of its polarity; the polarity dissolved, however, is zero. Thus individual things retreat into the Absolute, if they cease to live. Everything in the world is endowed with life; the world itself is alive, and continues only, maintains itself, by virtue of its life; just as an organic body maintains itself, only while it is constantly being generated anew by the vital process.

91. Every living thing is twofold in character. It is one persistent in itself, and one immersed in the universe. In everything, therefore, are two processes, one individualizing, vitalizing, and one universalizing, destructive. By the process of destruction, the finite thing seeks to become the universe itself; by the vitalizing process, however, the variety of the universe, and yet with that to remain a Singular. That only is truly living which represents the Eternal, and the whole multiplicity of the universe in the Singular.

92. The whole in the singular is called Individual. The individual is an example of computation, which admits only of being developed, from its comprehending the whole of arithmetic in itself. Nothing individual can persist eternally; it must eternally move itself, consequently fill up everything, displace everything, must become itself the universe.

MAN.

93. Time consists of single acts; i. e. the life or the absolute act does not work with one stroke, but an infinite number of times. All acts, therefore, taken together, all finite things in time, are equal to the primary act or the Eternal.

94. There are two totalities, a primary totality 0 + -, and a secondary, or the summing up of all numbers 0 + n-n; the former the eternal, the latter the finite totality, or the one the eternity, the other the infinity.

95. The more a thing has adopted into itself of the Manifold of the universe, by so much the more is it animated, by so much the more does it resemble the Eternal. It is conceivable, for a finite or living essence to unite all numbers or acts in itself, without, however, its being the very Eternal. It would, however, be obviously the most perfect finite essence, and, as a secondary totality, be the likeness of the primitive; the former the compound universality, the latter the identical.

96. Such an essence would be necessarily the highest and last, whereunto creation could attain; for more than the universe cannot be represented in one thing. With such an essence creation would be closed or would terminate.

97. Since the realization of the Eternal is a becoming self-conscious, so is the highest creature also a Self-conscious, but a Singular. Such a creature is the finite God, or God become corporeal. God is Monas indeterminata, the highest creature is Monas determinata, Totum determinatum. A finite self-conscious being we call Man. Man is an idea of God, but that in which God wholly, and in every single act becomes an object unto himself. Man is God represented by God in the infinity of time. God is a Man representing God in one act of self-consciousness, without time.

98. Man is God wholly manifested. God has become Man, zero has become + -. Man is the whole of arithmetic, compacted, however, out of all numbers; he can therefore produce numbers out of himself. Man is a complex of all that surrounds him, namely, of element, mineral, plant and animal.

99. The other things below man are also ideas of God, but none of these ideas is the whole representation of arithmetic. They are only parts of the divine conscience posited in time; but man is God, planted or posited uninjured in time. Man is the object in the self-consciousness of God; the creatures below man are, however, the objects only of the consciousness of God. Thus, if God places before and from himself only single qualities, there are worldly things; if, however, God in this crowd of representations attains to his own entire representation, then arises Man. God is = + 0-, Man = + [oo] 0-[oo], the animal is = + n 0-n. The animals are only represented in part. The subject of self-consciousness is = + 0-; the objects, however, are the numbers which are equivalent to this, being = [oo] + 3 + 2 + 1 + 0-1-2-3-[oo]. Thus if all numbers, all world-elements, together with their perfections, occur in consciousness = + 0-, there is a Man; if only single, and perhaps but few things, such as food, stones, &c. (with the entire exception of the celestial bodies), enter consciousness, there is an animal. They are represented only partly or in a portion of the universe, but man is represented wholly or in all its parts. Animals are fragments of man.

100. No creatures below Man can possess self-consciousness. They have, indeed, consciousness of their several acts and of their sensations, and possess memory; but as these several acts are only parts of the world, or of the great consciousness, and are not the Whole, they can never become objective unto themselves, never imagine. Animals are men, who never imagine. They are imaginative, but never of themselves wholly; they are therefore beings who never attain to consciousness concerning themselves. They are single accounts; Man is the whole of mathematics.

FREEDOM.

101. An action, which is not determined by some other action, is free. God is free, because apart from him there is none other action.

102. Man, as being an image of God, is likewise free; as being an image of the world he is devoid of freedom. Man is, therefore, in his primary commencement or principle free, but not in his end or object to be attained. In the resolution Man is free, in the execution he is not free. The mathematician can select at pleasure any proposition; but having selected it, must solve it in accordance with necessary laws and with definite numbers and figures. Man is a twofold being, compounded of freedom and necessity.

RETROSPECT.

103. Hitherto we have considered simply the arithmetical relations of the primary act and of the universe. We have shown, to wit, that all ideas fluctuate simply under the forms of numbers; that everything was comprised in the 0 + -. Time was only the active series of numbers; motion was the actual arithmetical calculation, namely, the process of reducing numbers to absolute identity, to zero.

104. Life is moreover only a mathematical problem, which, the higher it ascends, approaches so much the nearer to absolute zero in its attainment of the infinity of numbers, becomes so much the more endowed with life.

105. Arithmetic is the science of the second idea, or that of time and motion, or of life; it is, therefore, the first science; mathematics not only begins with it, but creation also, with the becoming of time and of life. Arithmetic is, accordingly, the truly absolute or divine science, and therefore everything in it is also directly certain, because everything in it resembles the Divine. Theology is arithmetic personified.

106. Hence it follows in the most perfect manner, that every science, if it would possess certainty, must resemble arithmetic. Now a science always implies a science treating of certain objects; all certain objects must, therefore, resemble the objects of arithmetic; or all objects, of whatever denomination, whether natural or spiritual, must correspond to arithmetical objects, consequently in idea be numbers, an actual arithmetical problem, as it were the numbers of motion, of life.

107. A natural thing is nothing but a self-moving number; an organic or living thing is a number moving itself out of itself, or spontaneously; an inorganic thing, however, is a number moved by another thing; now, as this other thing is also a real number, so then is every inorganic thing a number moved by another number, and thus ad infinitum. The movements in nature are only movements of numbers by numbers; even as arithmetical computation is none other than a movement of numbers by numbers, but with this difference, that in the latter this operates in an ideal manner, in the former after a real.

c. FORM, SPACE. (Third form, of the Primary Act.)

108. Viewed arithmetically every position is a number, geometrically, however, it is a point. What the 0 is in arithmetic, the point is in geometry; the one the arithmetical, the other the geometrical nothing. Both sciences commence with nothing and are only different views of nothing. The 0 is a temporal nothing (a number), the point a spatial nothing (a figure).

109. The first motion of numbers or of points is the motion of the primary number, the 0, or the primary act; and this motion depends upon the multiplicity of numbers or points, upon the disintegration of the identical primary number, upon the + -. The first motion of the primary act is an expansion of itself into multiplicity, whereby not merely sequence but an addition also is posited. The primary act is not simply positing, but also posited; as the former it is time, as the latter it is time posited universally. Time remaining stationary is Space. Space is not different in essence from time, but only according to position; it is only time resting, while this is moved, active space.

110. Space has first arisen out of time, as the third idea out of the second, but only ideally. It has arisen out of it, while, time being the act of positing, it is the posited; now as time posits from eternity, so is space also from eternity and in eternity. The eternity of space, however, depends not upon duration, but upon extension; it is unlimited.

111-112. Space is everywhere, as time is ever. Two spaces can no more exist than two times. There is only one Eternal. Time and space are, however, nothing special that has attained unto the Eternal, but the Eternal itself. They are also not two kinds of qualities subsisting near each other, but are one in kind. The series of numbers is infinite, thus universal; space is consequently universal.

113. Space is an idea like time, a form of God like time; it is the passive form, the extended 0 = + 0-.

114. All temporal things are also in space and limited. An unlimited thing extended through the whole of space is an absurdity. God's operation only is extended through the whole of space; it is space itself; when he willed to act, he became time; but when he was time, he became space.

115. Space has not been created, but has emerged out of the Eternal; it is nothing new in the universe, nothing next to God and present with him, but coexistent with God.

116. Single things must be both in space and in time; or a real thing first originates, where time and space cross each other at one point; they cross, however, everywhere, and therefore things are everywhere.

117. There is no void or empty space, no time and no place, were a Finite could not be; for time and space are virtually the manifesting primary act, the zero that has become thing.

POINT.

118. Time has begun with number, space with the point, with the spatial nothing, with the zero of space. This point necessarily posits itself "ad infinitum;" it extends itself also in all directions, and necessarily in equal distances. Such an extended point is the Sphere.

119. The sphere is nothing peculiar, nothing new in the thoughts of God, but only the point expanded, while this again is but a contracted sphere, just as the totality of numbers is an expanded 0, and this their contracted sphere.

120. Space is spherical, and, indeed, an infinite sphere. The sphere has been posited with space, and consequently from eternity; it is also an idea, and that, indeed, the total idea; for time and space have in it been posited together.

121. For God to become real, he must appear under the form of the sphere. There is no other form for God. God manifesting is an infinite sphere.

122. The sphere is, therefore, the most perfect form; for it is the primary, the divine form. Angular forms are imperfect. The more spherical a thing is in form, by so much the more perfect and divine is it. The Inorganic is angular, the Organic spherical.

123. The universe is a globe, and everything, which is a Total in the universe, is a globe.

LINE, LIGHT, MAGNETISM.

124. While the point expands, it is active; this active expansion is a simple repetition of the point, and this is a Line, which in the sphere, however, is a Radius. With time originates not merely a series of numbers, but together with it also the line. The line and time are of one kind, repeated positions of the nothing, of the point. It is consequently clear, how that time were a repeated positing of the Eternal itself: for the line is only a repeated self-positing of the point, of the nothing. God fluctuating in his eternity, and the point, are one in kind; but God acting is a line, being or existing a sphere, i. e. the point in the act of being.

125. The line is nothing new in creation, but time itself, when regarded more closely. God creates the line as little as he does time; but this originates unto him, while he moves, while he thinks. It is impossible to think without producing a line. The line is therefore from eternity, is a series of numbers.

126. The essence of the line does not consist in its two extremities being continued with equal significance into the Infinite; but in its radiality, i. e. that one extremity turned towards the centre has become central, converging, absolute; but the other turned towards the periphery has become divergent, finite, multiplicity. The primary line is a line produced with two antagonized characters. The central extremity is 0, the peripheral is the bisected zero = ±. This radial line gives us the antetype of a new polarity. The two extremities are not related as + and-towards each other, but as 0 and + -. At the instant, when a line originates in the universe, it is not a line merely, or an indefinite line that originates; but one that is definite at both extremities, polar, indeed, but after a determinate fashion. Nothing, not even a finite thing, exists in an indefinite manner.

127. There is no mathematically straight line in the world: all real lines are polar; they are all rooted in God by one extremity, by the other in finitude. The primary act becomes in its first operation not merely a posited nothing, a numerical series; not merely time, not merely an aoristic line, but a Linea determinata; in short, God can step forth into time only as radius. The Monas determinata is a Monas radialis, or a centroperipheric monas.

128. The essence of the primary antagonism is a centroperipheric antagonism. As centre is related to periphery, so is here one pole related to the other. Polar existence and central or peripheral existence are one. Primary polarity is centroperiphery. The primary line is constantly in a state of polar action, which is called tension; for it is always converging and diverging, at once central and peripheric. Every line originates, therefore, only by tension, and is only by it, yea, every line is nothing else than this tension.

129. A line, one extremity whereof strives towards the centre, the other to the periphery, the one to identity, the other to duality, will exhibit itself in the world as a line of Light, in the planet as a Magnetic line. Magnetism is centroperipheric antagonism, a radial line, 0—±, the action of the line being cleft at one extremity. Magnetism has its root in the beginning of creation. It is prophesied with time.

SURFACE, ELECTRICITY, OXYDATION.

130. The periphery is the boundary of the sphere, and is, consequently, a superficies or Surface. This, therefore, originates also directly with the positing of the Eternal.

131. As the primary line is not a purely polar, but a radial line, so is the primary surface not a level, but a curved or convex surface.

132. There is no level surface in the universe, no pure surfaces any more than pure lines. All surfaces are curved. For example, those of drops, of the heavenly bodies, of animals. The surface of a sphere is no Continuum; but consists properly of the divided peripheric and upright extremities of the radii; it is a ±.

133. The surface of a globe has no centre, no 0, like the radius; but is an absolute Dualized, a ± without 0.

134. This mode of operating of the primary act is manifested as electricity. Electricity is a merely peripheric antagonism, without centre, thus without union; an eternally Dissevered without rest. Electricity is thus also a special form, under which polarity makes its appearance, and is likewise rooted in the primary creation. There is, consequently, no thing which were not magnetic and electric.

135. The idea of a surface is constantly that of surrounding. It is not generated by a section of a globe, but by the completion, the circumferential limitation of the sphere. The essence of the sphere is boundary. Every surface is finite, is convex. In the divine position a surface never occurs, save on the boundary of the primary sphere.

136. As no thing can exist without a line, without a radius, so also none can be without surface, without circumscription. The single surface is identical with the Locus of the old philosophers. Every Finite is a closed whole, and that thing is of the most perfect kind which has the most perfect closure, surface, periphery (or skin).

137. The surface is also not different from the primary act, but a form of the primary act itself; or a boundary, which, however, nowhere remains stationary, but is always displaced by means of the eternal act. Therefore the world is at once unlimited and limited; the latter in reference to the closure of the surface, the former to the endless expansion of the same.

138. The periphery is the object in divine consciousness, the point which, posited without the centre, is thus one and the same, centre (subject) and periphery (object). It is everywhere the same point, the same 0, wherever it be posited. Hence the profound saying, "Mundus est Sphæra, cujus centrum ubique, circumferentia nusquam."

139. The surface stands in antagonism to the line, like periphery and centre; it stands perpendicular upon the radius, and can never pass parallel to linear action. Electricity ranks in eternal antagonism to magnetism.

SPHERE, HEAT, CHEMISTRY.

140. The line and surface are density, the representation of time and space; they have therefore like these originated out of nothing, namely, out of the point. The sphere is the expanded nothing. Nothing thus extended, or nothing posited, becomes a something, viz. line, surface, density, polarity. The line is a long nothing, the surface a hollow nothing, the sphere a dense nothing; in short, the something is a nothing which has received only predicates. All things are nothings with different forms. The point is = 0, the line = +, the surface = + -, the sphere = + 0-.

141. The internal motion of the globe, or the becoming of the globe, is manifested in the universe as Heat, in the planet as Chemistry.

ROTATION.

142. The primary sphere is rotating, for it has originated through motion; the motion of the sphere cannot, however, be progressive, for it fills everything. God is a rotating globe. The world is God rotating. All motion is circular, and there is everywhere no straight motion any more than there is a single line or straight surface. Everything is comprehended in ceaseless rotation. Without rotation there is no being and no life; for without it, there is no sphere, no space and no time.

143. The more perfectly circular the motion of a thing is, so much the more perfect is it. Straight motion is only the mechanical; such, however, exists not through itself. The more a body moves in a straight direction, the more mechanical and ignoble is it. Straight motion too yields only straight form.

GEOMETRY.

144. The sphere with its attributes is the totality of numbers, is thus a rotating number. The universe is the same. In arithmetic the quantity of divine positions is regarded; in the sphere, however, the direction of these positions, or of series of numbers.

145. The doctrine of the sphere is Geometry; for all forms are contained in the sphere. All geometrical proofs admit of being conducted through the sphere. Geometry has originated directly from arithmetic, or is arithmetic itself, with this difference, that the latter regards series of numbers as individualities, the former, however, as a whole. Arithmetic is a geometry seriebus discretis; geometry is an arithmetic seriebus continuis, a solidified arithmetic.

146. Geometry is a science of equal value with arithmetic; it is even as certain, because it has no other propositions; it is equally eternal, is the same realization of the primary act, the Deus geometrizans of the Pythagoreans. Everything to be certain must therefore resemble geometry, must be itself a position of geometry, only under other relations.

147. Geometry is more real, more finite, therefore also more apparent, and, as it were, more material than arithmetic. The ideas in it have become something determinate, have assumed form, while before they still fluctuated formless in arithmetic; here were they mere ghosts without veils, but in geometry they have received these veils. Time has received for its form, its body, the line; space, the surface; life, the globe, consequently the rotation for its form or body. It is to be here remarked, that ideas always become more real and more finite, always approximate nearer to actual manifestation, the lower they descend or the more they are considered individually. Geometry has not originated later than arithmetic, but is only a more individual view of ideas, arithmetic being more universal. Geometry is arithmetic with stationary numbers, = points. The Divine thus approximates to manifestation, to materiality, the more individual it becomes; and this is very natural, for it verily limits itself more and obtains always more predicates. The more a thing obtains predicates, by so much the more perfect is its finiteness. By geometry we are actually transferred into the universe, but only into the formal, in which it has, like a skeleton, been sketched for us solely upon a general plan; namely, as infinite extension, in which line and periphery, central and peripheric action, magnetism, electricity, and rotation, &c., have been prefigured.