Mystics

"And thus far historians produce the perfection of this science. But Euclid was not much junior to these, who collected elements, and constructed many of those things which were invented by Eudoxus; and perfected many which were discovered by Theætetus. Besides, he reduced to invincible demonstrations, such things as were exhibited by others with a weaker arm. But he lived in the times of the first Ptolemy: for Archimedes mentions Euclid, in his first book, and also in others. Besides, they relate that Euclid was asked by Ptolomy, whether there was any shorter way to the attainment of geometry than by his elementary institution, and that he answered, there was no other royal path which led to geometry. Euclid, therefore, was junior to the familiars of Plato, but more ancient than Eratosthenes and Archimedes (for these lived at one and the same time, according to the tradition of Eratosthenes) but he was of the Platonic sect, and familiar with its philosophy: and from hence he appointed the constitution of those figures which are called Platonic, as the end of his elementary institutions."

"Again, Amyclas the Heracleotean, one of Plato's familiars, and Menæchmus, the disciple, indeed, of Eudoxus, but conversant with Plato, and his brother Dinostratus, rendered the whole of geometry as yet more perfect. But Theudius, the Magnian, appears to have excelled, as well in mathematical disciplines, as in the rest of philosophy. For he constructed elements egregiously, and rendered many particulars more universal. Besides, Cyzicinus the Athenian, flourished at the same period, and became illustrious in other mathematical disciplines, but especially in geometry. These, therefore, resorted by turns to the Academy, and employed themselves in proposing common questions."

"A full history of Greek geometry and astronomy during this period written by Eudemus, a pupil of Aristotle, has been lost. It was well known to Proclus, who, in his commentaries on Euclid, gives a brief account of it. This abstract constitutes our most reliable information. We shall quote it frequently under the name of Eudemian Summary."

"It is well known that the commentary of Proclus on Eucl. Book I is one of the two main sources of information as to the history of Greek geometry which we possess, the other being the Collection of Pappus."

"For this, to draw a right line from every point, to every point, follows the definition, which says, that a line is the flux of a point, and a right line an indeclinable and inflexible flow."

"Let us now explain the origin of geometry, as existing in the present age of the world. For the demoniacal Aristotle observes, that the same opinions often subsist among men, according to certain orderly revolutions of the world: and that sciences did not receive their first constitution in our times, nor in those periods which are known to us from historical tradition, but have appeared and vanished again in other revolutions of the universe; nor is it possible to say how often this has happened in past ages, and will again take place in the future circulations of time. But, because the origin of arts and sciences is to be considered according to the present revolution of the universe, we must affirm, in conformity with the most general tradition, that geometry was first invented by the Egyptians, deriving its origin from the mensuration of their fields: since this, indeed, was necessary to them, on account of the inundation of the Nile washing away the boundaries of land belonging to each. Nor ought It to seem wonderful, that the invention of this as well as of other sciences, should receive its commencement from convenience and opportunity. Since whatever is carried in the circle of generation proceeds from the imperfect to the perfect."

"The mathematician speculates the causes of a certain sensible effect, without considering its actual existence; for the contemplation of universals excludes the knowledge of particulars; and he whose intellectual eye is fixed on that which is general and comprehensive, will think but little of that which is sensible and singular."

"A transition, therefore, is not undeservedly made from sense to consideration, and from this to the nobler energies of intellect. Hence, as the certain knowledge of numbers received its origin among the Phœnicians, on account of merchandise and commerce, so geometry was found out among the Egyptians from the distribution of land. When Thales, therefore, first went into Egypt, he transferred this knowledge from thence into Greece: and he invented many things himself, and communicated to his successors the principles of many. Some of which were, indeed, more universal, but others extended to sensibles."

"If we listen to those who like to record antiquities, we shall find them attributing this theorem to Pythagoras and saying that he sacrificed an ox on its discovery. For my part, though I marvel at those who first noted the truth of this theorem, I admire more the author of the Elements for the very lucid proof by which he made it fast."

"The Platonic doctrine of Ideas has been, in all ages, the derision of the vulgar, and the admiration of the wife. Indeed, if we consider that ideas are the most sublime objects of speculation, and that their nature is no less bright in itself, than difficult to investigate, this opposition in the conduct of mankind will be natural and necessary; for, from our connection with a material nature, our intellectual eye, previous to the irradiations of science, is as ill adapted to objects the most splendid of all, "as the eyes of bats to the light of day.""

"But after these, Pythagoras changed that philosophy, which is conversant about geometry itself, into the form of a liberal doctrine, considering its principles in a more exalted manner; and investigating its theorems immaterially and intellectually; who likewise invented a treatise of such things as cannot be explained in geometry, and discovered the constitution of the mundane figures."

"This, therefore, is mathematics: she reminds you of the invisible form of the soul; she gives life to her own discoveries; she awakens the mind and purifies the intellect; she brings light to our intrinsic ideas; she abolishes oblivion and ignorance which are ours by birth."

"She was dead, but her very death heightened that word "supernatural"; it was what she, not being, was."

"It is told that those who first brought out the irrationals from concealment into the open perished in shipwreck, to a man. For the unutterable and the formless must needs be concealed. And those who uncovered and touched this image of life were instantaneously destroyed and shall remain forever exposed to the play of the eternal waves."

"Christianity and life ought to be one."

"There were no Calvinists or Dominics or Augustines. The man who was most like those great ones was a Dane, a contemporary of Hans Andersen, but though Hans Andersen achieved world-wide repute at once, Soren Kierkegaard had to wait for his through some seventy years. It has taken Christendom that long to catch him up; it took fifty years to catch up St. Thomas, and it has not caught up Dante yet. He coordinated experiences in a new manner; say, using the old word, that he caused alien and opposite experience to coinhere. ... No doubt as soon as Kierkegaard becomes fashionable he will be explained. His imagination will be made to depend on his personal history, and his sayings will be so moderated in our minds that they will soon become not his saying but ours. It is a very terrible thing to consider how often this has happened with the great, and how often we are contented to understand what we have neatly supposed that they have said."

"Not much younger than these (sc. Hermotimus of Colophon and Philippus of Mende) is Euclid, who put together the Elements, collecting many of Eudoxus' theorems, perfecting many of Theaetetus', and also bringing to irrefragable demonstration the things which were only somewhat loosely proved by his predecessors. This man lived in the time of the first Ptolemy. For Archimedes, who came immediately after the first (Ptolemy), makes mention of Euclid: and, further, they say that Ptolemy once asked him if there was in geometry any shorter way than that of the elements, and he answered that there was no royal road to geometry. He is then younger than pupils of Plato but older than Eratosthenes and Archimedes; for the latter were contemporary with one another, as Eratosthenes somewhere says."

"Deep, deeper than we believe, lie the roots of sin; it is in the good that they exist; it is in the good that they thrive and send up sap and produce the black fruit of hell."

"If one is anxious to write about God, one ought to be anxious to write well."

"After Pythagoras, Anaxagoras the Clazomenian succeeded, who undertook many things pertaining to geometry. And Oenopides the Chian, was somewhat junior to Anaxagoras, and whom Plato mentions in his Rivals, as one who obtained mathematical glory. To these succeeded Hippocrates, the Chian, who invented the quadrature of the lunula, and Theodorus the Cyrenean, both of them eminent in geometrical knowledge. For the first of these, Hippocrates composed geometrical elements: but Plato, who was posterior to these, caused as well geometry itself, as the other mathematical disciplines, to receive a remarkable addition, on account of the great study he bestowed in their investigation. This he himself manifests, and his books, replete with mathematical discourses, evince: to which we may add, that he every where excites whatever in them is wonderful, and extends to philosophy. But in his time also lived Leodamas the Thasian, Architas the Tarentine, and Theætetus the Athenian; by whom theorems were increased, and advanced to a more skilful constitution. But Neoclides was junior to Leodamas, and his disciple was Leon; who added many things to those thought of by former geometricians. So that Leon also constructed elements more accurate, both on account of their multitude, and on account of the use which they exhibit: and besides this, he discovered a method of determining when a problem, whose investigation is sought for, is possible, and when it is impossible."

"The telephone bell was ringing wildly, but without result, since there was no-one in the room but the corpse."

"An hour's conversation on literature between two ardent minds with a common devotion to a neglected poet is a miraculous road to intimacy."

"He said: "If I thought more of myself?" "You wouldn't have much difficulty in finding it," she answered. "Let's walk." He didn't understand the first phrase, but he turned and went by her side, silent while he heard the words. Much difficulty in finding what? in finding it? the it that could be found if he thought of himself more; that was what he had said or she had said, whichever had said that the thing was to be found, as if Adela had said it, Adela in her real self, by no means the self that went with Hugh; no, but the true, the true Adela who was apart and his; for that was the difficulty all the while, that she was truly his, and wouldn't be, but if he thought more of her truly being, and not of her being untruly away, on whatever way, for the way that went away was not the way she truly went, but if they did away with the way she went away, then Hugh could be untrue and she true, then he would know themselves, two, true and two, on the way he was going, and the peace in himself, and the scent of her in him, and the her, meant for him, in him; that was the she he knew, and he must think the more of himself."

"But Eudoxus the Cnidian, who was somewhat junior to Leon, and the companion of Plato, first of all rendered the multitude of those theorems which are called universals more abundant; and to three proportions added three others; and things relative to a section, which received their commencement from Plato, he diffused into a richer multitude, employing also resolutions in the prosecution of these."

"About the time of Anaxagoras, but isolated from the Ionic school, flourished Œnopides of Chios. Proclus ascribes to him the solution of the following problems: From a point without, to draw a perpendicular to a given line, and to draw an angle on a line equal to a given angle. That a man could gain a reputation by solving problems so elementary as these, indicates that geometry was still in its infancy, and that the Greeks had not yet gotten far beyond the Egyptian constructions."

"A scholiast on Euclid, thought to be Proclus, says that Eudoxus practically invented the whole of Euclid's fifth book."

"Pappus... is the author of a Commentary on the Almagest, a Commentary on Euclid's Elements, a Commentary on the Analemma of Diodorus,—a writer of whom nothing is known. All these works are lost. Proclus, probably quoting from the Commentary on Euclid, says that Pappus objected to the statement that an angle equal to a right angle is always itself a right angle."

"The term 'axiom' was used by Proclus, but not by Euclid. He speaks, instead, of 'common notions'—common either to all men or to all sciences."

"The regular solids were studied so extensively by the Platonists that they received the name of Platonic figures The statement of Proclus that the whole aim of Euclid in writing the Elements was to arrive at the construction of the regular solids is obviously wrong The fourteenth and fifteenth books treating of solid geometry are apocryphal."

"Extracts... made by Proclus indicate that Ptolemy did not regard the parallel-axiom of Euclid as self-evident, and that Ptolemy was the first of the long line of geometers from ancient time down to our own who toiled in the vain attempt to prove it."

"Omraam Mikhaël Aïvanhov, OmraamWiki, 2 February 2019"

"In 1923 he enrolled at the University in Sofia: After receiving diplomas in philosophy, psychology, and education, Mikhael continued to frequent the university. Stimulated by curiosity, he moved freely from one faculty to another, exploring the different disciplines, following courses in medicine, chemistry, and physics. He spent so many years at the university that his friends nicknamed him ‘the eternal student’."

"Sometimes I receive letters from brothers and sisters saying, ‘Oh Master, we would so like to be like you. You are an example for us.’ But I say that you should take the sun as your example, as I do. I look to the sun, and I point toward it to encourage you to go in that direction. Do not stop at me; go right past me to the sun, immerse yourself in its life, its warmth and its light, so that you can become like it. As for me, think of me as being a signpost that shows you the path you should take. So, do not stop at the signpost. When you travel along a road, and you see a sign that says Paris or Frejus, you do not stop there and hug it saying, ‘How I love you, dear signpost. How I love your beautiful lettering, and how well you point out the direction I should take!’ No, you keep traveling until you reach Paris or Frejus."

"When he entered the conference room, in front of his listeners, there was an indescribable aura around him. Some days he was inhabited by a mysterious presence: perfectly still, his eyes closed, he spoke in a sober and concise manner; at other times he spoke with great force, like a prophet charged with shaking his contemporaries out of their ruts. But most of the time, he spoke like a father talks to his children, most simply. He knew how to laugh frankly with a spontaneity that testified to a deep joie de vivre. On the material level, there is a will that never knows how to act against others. He is a refined soul, filled with a sacred and impersonal love. He is an intelligence recognized by all his listeners as being particularly luminous and penetrating, possessing extraordinary powers of analysis and synthesis. What is more, he thinks what is divine, he feels it and he executes it."

"On the surface it may seem that wars are caused by economic and political questions, but in fact they are caused by our wholesale slaughter of animals. The laws of justice are inexorable, and human beings are going to have to pay with their own blood … We kill animals, but nature is an organic whole, and by killing animals we are, as it were, affecting certain glands in that organism. When this happens, the balance of the organism is disrupted, and it is not surprising that before long war breaks out among men. Yes, human beings have slaughtered millions of animals for their meat, without realizing that on the invisible plane those animals are linked to other human beings, and it is they who will now have to share the fate of the animals. When we slaughter animals we are slaughtering human beings. Everybody agrees that it is time to establish the reign of peace in the world, that there must be no more wars. Yes, but war will go on just as long as we continue to slaughter animals, because by destroying them we are destroying ourselves."

"The idea of ​​brotherhood for which we are working is still like a newborn child. I speak to the entire universe about this child who wants to grow up, learn to walk, learn. I know all her needs, my constant concern is to ensure its subsistence and its growth, I have no other job, and I have to be so vigilant! This idea of ​​fraternity, it is she and she alone who has the power to make peace reign in the world. I have come among you so that an ideal of fraternal life can be realized here which will serve as an example for the future... to bring a model of collective, fraternal life, where each individual will consciously accept a kind of magnificent servitude in order to access another freedom, truer, deeper, that of his Higher Being."

"Now is the time to live an experience that humans have not yet attempted and that will free them from their illusions, isolation and helplessness. For the work I envision, I want people who are rich in heart and soul. We must no longer be content to talk about love, peace and fraternity, we must live them by learning to meet and make exchanges in areas where the values ​​advocated by society no longer count so much. Come and support my work, lend your strength, give an example of fraternal spirit. You claim to love your country, but what are you doing so that everyone can live there fraternally? You don't yet know how contagious your example could become."

"Everything was linked, coherent in the life of Brother Mikhaël. I could never discover a rift between his collective life, his words and his behavior. He never advised others of something that he himself did not put into practice in the privacy of his existence."

"According to Aivanhov one of the fundamental truths of initiatic science is that in the “subtle” world (the so-called “higher world”) all elements that make up reality, are linked and connected to each other in a specific way. Therefore, the realization of the Kingdom of God on our planet becomes an almost spontaneous and natural reality, if everybody makes efforts to realize this divine Kingdom within themselves, which then could bring about the... Golden Age. In order to describe the best way of how each individual can come closer to this significant ideal, Aivanhov reveals the eternal principles of initiatic science and defines the cosmic laws which reign both in the universe as well as in man; in the macrocosm as well as in the microcosm. At the same time, he also describes the constant exchange between “that which is above and that which is below”. A basis for this method is the conviction that human beings cannot attain the tangible realization of such a high ideal through faith alone, but that they also need knowledge about how ‘reality’ is organized. This knowledge will help to understand how the arrival of the Golden Age remains no longer a utopia, but becomes a certainty."

"When I was meditating, I tried to perceive the universe as an immense symphony ... One day, I felt myself carried away in space, very far away, and suddenly I heard that the whole universe was singing ... no human music can compare to what I heard ... This music is not heard with the physical ears, but with the soul, with spirit ... This experience that I had so early in my life has remained like a seal in my soul and has pushed me to seek harmony always and everywhere."

"Ὁ αὐτὸς ἀββᾶς Μακάριος͵ ἐν Αἰγύπτῳ ὢν͵ εὗ ρεν ἄνθρωπον ἔχοντα κτῆνος καὶ συλοῦντα τὰς χρείας αὐτοῦ· καὶ αὐτὸς ὡς ξένος παραστὰς τῷ συλοῦντι͵ συνεγέμου τὸ κτῆνος͵ καὶ μετὰ πολλῆς ἡσυχίας προέπεμπεν αὐτὸν͵ λέγων͵ ὅτι Οὐδὲν εἰσηνέγκαμεν εἰς τὸν κόσμον͵ δῆλον ὅτι οὐδὲ ἐξενεγκεῖν τι δυνάμεθα. Ὁ Κύριος ἔδωκεν· ὡς αὐτὸς ἠθέλη σεν͵ οὕτως καὶ ἐγένετο. Εὐλογητὸς Κύριος ἐπὶ πᾶσιν"

"As anyone who watches a bird flying may wish that he himself could fly, yet still he cannot fly, being without wings, so also a man may have the will to be pure, to be without blame and spotless, to be always without evil and in communion with God, yet he does not truly have the power. To fly into the divine air and enjoy the liberty of the Holy Spirit (2 Cor 3:18) may be one's desire, but, if he does not have wings given him, he cannot. Let us pray to God that he give us "the wings of a dove" (Ps 55:7) of the Holy Spirit so we may fly to him and find rest and that he may separate and take away from our soul and body such an evil wind, namely, sin itself, inhabiting the members of our soul and body. For this he alone is able to do."

"A man watches a bird flying, and wishes to fly himself, but he cannot, because he has no wings. Even so the will is present with a man to be pure, and blameless, and without spot, and to have no wickedness in him, but to be always with God; but he has not the power. To fly into the air of God and the liberty of the Holy Ghost may be his wish, but unless wings are given him, he cannot. Let us then beseech God to bestow upon us the wings of a dove, even of the Holy Ghost, that we may fly to Him and be at rest, and that He would separate and make to cease from our souls and bodies, that evil wind, which is the sin that dwelleth in the members of our souls and bodies. None but He can do it."

"Most people, they have these near-death experiences. They go through a tunnel and they meet a bright light at the end of the tunnel. That bright light is actually their higher self, or the soul, which people reconnect with after they die, after you leave the physical body. In our Sufi practice we aspire to die before we die, to reconnect with that bright light, the higher self, while we’re still in a physical body."

"What is wisdom? If you are a mystic you become totally empty and you are given whatever you need. For example, there is a plane where all the knowledge is, and you can go there. You can get whatever you need."

"God despises the powerful and the mighty, the likes of Herod, Caiaphas, and Annas, and he accepts for his service the small, like Mary, Zechariah, and Elizabeth. For that is God's way of working , and down to the present day he does not act otherwise."

"Oh, dearest brothers, of what else does this Gospel of Luke remind us? Only that faith with all its sources, presents us with impossible things, which the tender ones believe will never come to pass in reality. The whole insane, fantastic world sets and the world says with a little forked tongue: 'Yes, one can indeed preach the Gospel, fear God alone, and yet also hold in honour the unreasonable rulers, even though they strive against all justic and do not accept God's word. Oh, for God's sake, one should be obedient to them in all things, those Good Junkers.' Yes welcome, you [i.e. Martin Luther ] defender of the godless! How fine, how very fine it must be to be so able to serve with praise two masters who strive against one another, as the advisers of the rulers truly do! Oh, how skillful clever reason thinks it is! In its hypocrisy, it uses love of neighbor to dress up and ornament itself in the most imposing manner."

"Man must smash to bits his stolen, contrived Christian faith through powerful, enormous suffering of the heart, through an amazement that cannot be rejected. Through this, man becomes very small and despicable in his own eyes."

"The spirit of the strength and fear of God be with you , you pitiable community. After the libelous writing [of Luther] have made you partly fearful - and also most impudent - it is exceedingly necessary for me to counter the rising evil with a demonstration of Christian mastery. At the present time, this mastery cannot be shown except through an exposition of holy Scripture, especially the teachings of the spirit of Christ, and through a comprehensive comparison of all the secrets and judgement of God. For all knowledge contains within itself its diametrical opposite."

"Freely and boldly I declare that I have never heard a single donkey-cunt doctor of theology, in the smallest of his divisions and points, even whisper, to say nothing of speaking loudly, and points, even whisper, to say nothing of speaking loudly, about the order (established in God and all his creatures)."