People From Alexandria

"Can we then hold the poverty-in-wealth of the money-grubbing usurers to be of any account? They may seem to be kings with purses full of gold, but they never even in their dreams have had a glimpse of the wealth that has eyes to see."

"If they are unwilling to give, they should at least lend with all readiness and alacrity, not with the prospect of receiving anything back except the principal. … In place of the interest which they determine not to accept they receive a further bonus of the fairest and most precious things that human life has to give, mercy neighborliness, charity, magnanimity, a good report and good fame. And what acquisition can rival these? Nay, even the great king will appear as the poorest of men if compared with a single virtue. For his wealth is soulless, buried deep in store-houses and recesses of the earth, but the wealth of virtue lies in the sovereign part of the soul, and the purest part of existence."

"The health of the soul is to have its faculties, reason, high spirit and desire happily tempered, with the reason in command and reining in the other two, like restive horses. The special name of this health is temperance, that is σωφροσύνη or “thought-preserving,” for it creates a preservation of one of our powers, namely that of wise-thinking."

"We must mention the higher, nobler wealth, which does not belong to all, but to truly noble and divinely gifted men. This wealth is bestowed by wisdom through the doctrines and principles of ethic, logic and physic, and from these spring the virtues, which rid the soul of its proneness to extravagance, and engender the love of contentment and frugality, which will assimilate it to God. For God has no wants, He needs nothing, being in Himself all-sufficient to Himself, while the fool has many wants, ever thirsting for what is not there, longing to gratify his greedy and insatiable desire, which he fans into a blaze like a fire and brings both great and small within its reach. But the man of worth has few wants, standing midway between mortality and immortality."

"But some, making no account of the wealth of nature, pursue the wealth of vain opinions. They choose to lean on one who lacks rather than one who has the gift of sight, and with this defective guidance to their steps must of necessity fall."

"If one adds anything small or great to the queen of virtues, piety, or on the other hand takes something from it, in either case he will change and transform its nature. Addition will beget superstition and subtraction will beget impiety."

"There is no sweeter delight than that the soul should be charged through and through with justice, exercising itself in her eternal principles and doctrines and leaving no vacant place into which injustice can make its way."

"The natural gravitation of the body pulls down with it those of little mind, strangling and overwhelming them with the multitude of the fleshly elements. Blessed are they to whom it is given to resist with superior strength the weight that would pull them down, taught by the guiding lines of right instruction to leap upward from earth and earth-bound things into the ether and the revolving heavens."

"The road that leads to pleasure is downhill and very easy, with the result that one does not walk but is dragged along; the other which leads to self-control is uphill, toilsome no doubt but profitable exceedingly. The one carries us away, forced lower and lower as it drives us down its steep incline, till it flings us off on to the level ground at its foot; the other leads heavenwards the immortal who have not fainted on the way and have had the strength to endure the roughness of the hard ascent."

"Moses … takes one form of desire, that one whose field of activity is the belly, and admonishes and disciplines it as the first step, holding that the other forms will cease to run riot as before and will be restrained by having learnt that their senior and as it were the leader of their company is obedient to the laws of temperance."

"The holy Moses … discarded passion in general and detesting it, as most vile in itself and in its effects, denounced especially desire as a battery of destruction to the soul, which must be done away with or brought into obedience to the governance of reason, and then all things will be permeated through and through with peace and good order, those perfect forms of the good which bring the full perfection of happy living."

"Moses … denied to the members of the sacred commonwealth unrestricted liberty to use and partake of the other kinds of food. All the animals of land, sea or air whose flesh is the finest and fattest, thus titillating and exciting the malignant foe pleasure, he sternly forbade them to eat, knowing that they set a trap for the most slavish of the senses, the taste, and produce gluttony, an evil very dangerous both to soul and body."

"It would be a sign of great simplicity to think that the world was created in six days, or indeed at all in time; [...] Time is a thing posterior to the world. Therefore it would be correctly said that the world was not created in time, but that time had its existence in consequence of the world. For it is the motion of the heaven that has displayed the nature of time."

"A Judge must bear in mind that when he tries a case he is himself on trial."

"Are you making war upon us, because you anticipate that we will not endure such indignity, but that we will fight on behalf of our laws, and die in defence of our national customs? For you cannot possibly have been ignorant of what was likely to result from your attempt to introduce these innovations respecting our temple."

"Nothing will a man rue more than refusal to listen to the wise."

"We have a very clear evidence of freedom in the equality recognized by all the good in addressing each other."

"One may well wonder at the short-sightedness of those who ignore the characteristics which so clearly distinguish different things and declare that the laws of Solon and Lycurgus are all-sufficient to secure the greatest of republics, Athens and Sparta, because their sovereign authority is loyally accepted by those who enjoy that citizenship, yet deny that right reason, which is the fountain head of all other law, can impart freedom to the wise, who obey all that it prescribes or forbids."

"Those in whom anger or desire or any other passion, or again any insidious vice holds sway, are entirely enslaved, while all whose life is regulated by law are free. And right reason is an infallible law engraved not by this mortal or that and, therefore, perishable as he, nor on parchment slabs, and, therefore, soulless as they, but by immortal nature on the immortal mind, never to perish."

"The legislator of the Jews in a bolder spirit went to a further extreme and in the practice of his “naked” philosophy, as they call it, ventured to speak of him who was possessed by love of the divine."

"But you say, “by obedience to another he loses his liberty.” How then is it that children suffer the orders of their father and mother, and pupils the injunctions of their instructors?"

"Homer often calls kings “shepherds of the people,” but nature more accurately applies the title to the good, since kings are more often in the position of the sheep than of the shepherd. They are led by strong drink and good looks and by baked meats and savory dishes and the dainties produced by cooks and confectioners, to say nothing of their craving for silver and gold and grander ambitions."

"The good man … has learnt to set at naught the injunctions laid upon him by those most lawless rulers of the soul, inspired as he is by his ardent yearning for the freedom whose peculiar heritage it is that it obeys no orders and works no will but its own."

"If one looks with a penetrating eye into the facts, he will clearly perceive that no two things are so closely akin as independence of action and freedom, because the bad man has a multitude of encumbrances, such as love of money or reputation and pleasure, while the good man has none at all. He stands defiant and triumphant."

"He who has God alone for his leader, he alone is free."

"Ὅπερ ἔδει δεῖξαι."

"There is irrefutable evidence that a substantial portion of the material recorded in the Elements was known before Euclid, and there is nothing either in the style or in the plan of the treatise to suggest that it was intended as a collection of original contributions. Thus, on the whole... the chief objective... was to put system and rigour into the work of his predecessors."

"The Greeks elaborated several theories of vision. According to the Pythagoreans, Democritus, and others vision is caused by the projection of particles from the object seen, into the pupil of the eye. On the other hand Empedocles, the Platonists, and Euclid held the strange doctrine of ocular beams, according to which the eye itself sends out something which causes sight as soon as it meets something else emanated by the object."

"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."

"With the completion of Euclid's Elements... For the first time in history masses of isolated discoveries were unified and correlated by a single guided principle, that of rigid deduction from explicitly stated assumptions. ...If the Pythagorean dream of a mathematized science is to be realized, all of the sciences must eventually submit to the discipline that geometry accepted from Euclid."

"The laws of nature are but the mathematical thoughts of God."

"Δός αὐτῷ τριώβολον, ἐπειδὴ δεῖ αὐτῷ ἐξ ὧν μανθάνει κερδαίνειν."

"Non est regia [inquit Euclides] ad Geometriam via."

"μὴ εἶναι βασιλικὴν ἀτραπὸν ἐπί γεωμετρίαν."

"Πρῶτος ἀριθμός ἐστιν ὁ μονάδι μόνῃ μετρούμενος."

"Καὶ τὸ ὅλον τοῦ μέρους μεῖζον [ἐστιν]."

"ὅπερ ἔδει ποιῆσαι."

"Inasmuch as many things, while appearing to rest on truth and to follow from scientific principles, really tend to lead one astray from the principles and deceive the more superficial minds, he has handed down methods for the discriminative understanding of these things as well, by the use of which methods we shall be able to give beginners in this study practice in the discovery of paralogisms and to avoid being misled. This treatise, by which he puts this machinery in our hands, he entitled (the book) of Pseudaria, enumerating in order their various kinds, exercising our intelligence in each case by theorems of all sorts, setting the true side by side with the false, and combining the refutation of error with practical illustration. This book then is by way of cathartic and exercise, while the Elements contain the irrefragable and complete guide to the actual scientific investigation of the subjects of geometry."

"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."

"Those who have written the history of geometry have thus far carried the development of this science. Not much later than these is Euclid, who wrote the 'Elements,' arranged much of Eudoxus' work, completed much of Theaetetus's and brought to irrefragable proof propositions which had been less strictly proved by his predecessors."

"Euclid alone has looked on Beauty bare."

"Euclid is said to have written the Elements of Music. Two treatises are attributed to Euclid in... the Musici, the... Sectio canonis (the theory of the intervals) and the... (introduction to harmony). The first, resting on the Pythagorean theory of music, is mathematical and clearly and well written, the style and the form of the propositions agreeing well with what we find in the Elements. Its genuineness is confirmed not only by internal evidence... Euclid is twice mentioned by name, in the commentary on Ptolemy's Harmonica published by Wallis... The second treatise is not Euclid's..."

"The history of Alexandrian mathematics begins with the Elements of Euclid and closes with the Algebra of Diophantus, both of which are founded on the discoveries of several preceding centuries."

"Euclid... gave his famous definition of a point: "A point is that which has no parts, or which has no magnitude." …A point has no existence by itself. It exists only as a part of the pattern of relationships which constitute the geometry of Euclid. This is what one means when one says that a point is a mathematical abstraction. The question, What is a point? has no satisfactory answer. Euclid's definition certainly does not answer it. The right way to ask the question is: How does the concept of a point fit into the logical structure of Euclid's geometry? ...It cannot be answered by a definition."

"There never has been, and till we see it we never shall believe that there can be, a system of geometry worthy of the name, which has any material departures (we do not speak of corrections or extensions or developments) from the plan laid down by Euclid."

"The fact is that if you talk to the people who actually knew him, who worked for him, who were his customers, they have a completely different view from people who sit in ivory towers and take pot shots at him."

"[In 1997, Porter was the UK editor of Vanity Fair] Our concern was that if we settled, the evidence about his [Mohamed Al-Fayed's] abuse and surveillance would never be available to her. So it was vital that she understood that all Fayed’s properties were wired for audio and video, and that she could never be sure of having a private conversation on his premises, let alone being able to undress without being watched. Through intermediaries, we made our fears known. Diana's friend Rosa Monckton and her husband Dominic Lawson also repeatedly warned Diana. I have no idea whether she paid attention. By the end of July 1997, no agreement was reached."

"For evidence of his vengefulness, look no further than his exposure of Neil Hamilton and the other MPs embroiled in the cash-for-questions scandal, and his subsequent pursuit of Jonathan Aitken. This was not a principled stand against corruption, for he was the self-confessed corrupter. It was, rather, an act of straightforward revenge, during which it became plain that he had kept all the necessary documentation to prove his allegations."

"According to former employees, Fayed regularly walked the store [Harrods] on the lookout for young, attractive women to work in his office. Some were asked to go to Paris with him. Good-looking women were given gifts and cash bonuses almost before they understood that they were being compromised. "Come to Papa," he would say. "Give Papa a hug." Those who rebuffed him would often be subjected to crude, humiliating comments about their appearance or dress. A dozen ex-employees I spoke with said that Fayed would chase secretaries around the office and sometimes try to stuff money down women's blouses."

"When Francesca Bettermann was hired, she had to take an H.I.V. test—women working close to the chairman had to undergo full internal exams and be grilled on their entire gynecological histories—and her handwriting was analyzed."