Diophantus

“ Hypatia, the daughter of Theon the mathematician, 25 was initiated in her father’s studies; her learned comments have elucidated the geometry of Apollonius and Diophantus, and she publicly taught, both at Athens and Alexandria, the philosophy of Plato and Aristotle. In the bloom of beauty, and in the maturity of wisdom, the modest maid refused her lovers and instructed her disciples; the persons most illustrious for their rank or merit were impatient to visit the female philosopher ”

“ These anticipations of Cardan are the more truly wonderful, when we consider that the symbolical language of algebra, that powerful instrument not only in expediting the processes of thought, but in suggesting general truths to the mind, was nearly unknown in his age. Diophantus, Fra Luca, and Cardan make use occasionally of letters to express indefinite quantities, besides the res or cosa, sometimes written shortly, for the assumed unknown number, of an equation. But letters were not yet substituted for known quantities; ”

“ It is quite natural that those whose birth is of base metal which will not bear scrutiny should tend to be weak-spirited and abject. The poet is quite right in saying: |C|
It slaves a man, stout-hearted though he be,
To know his mother or his father base. It is no doubt equally the case that persons of distinguished parentage become full of pride and self-assertion. Thus Themistocles’ son, Diophantus, is reported to have said on many occasions and to many persons that he had only to wish for a thing and the Athenian people voted for it. ”

“ On the other hand he is quoted by Theon of Alexandria (who observed an eclipse at Alexandria in a.d. 365) ; and his work was the subject of a commentary by Theon’s daughter Hypatia (d. 415) . The Arithmetica, the greatest treatise on which the fame of Diophantus rests, purports to be in thirteen Books, but none of the Greek MSS. which have survived contain more than six (though one has the same text in seven Books) . ”

“ Greek: "h". pasa apat"."..↑ "on account of the Peace". i.e. of the negotiations for the Peace, before it was finally arranged.↑ "all that they wished". viz. the restoration of the Temple of Delphi to their kinsmen, the Dorians of Mount Parnassus.↑ "four whole months". in reality, three months and a few days.↑ "Phocian people". i.e. those who were left in Phocis, as distinct from the exiles just referred to.↑ "of Diophantus". In 352, when Philip had been repulsed by Onomarchus, Diophantus proposed that public thanksgivings should be held (see Introd. to First Philippic) .↑ "of Callisthenes". ”

“ Who first went forth, Daiphantus most did ease.
They gone, Daiphantus to his standish highs!
Thinks, in his writs Vitullia's beauties were:
But what he wrote, his Muse not justifies,
Bids him take time! "Love badly writes in fear!
Her worthy praise, if he would truly write,
Her kisses' nectar must the same indite."
"Art, and sweet Nature! Let your influence drop
From me like rain! Yes, yes, in golden showers!
(Whose end is Virtue, let him never stop!) ”

“ Philopœmen on this occasion did all he could to keep Diophanes quiet and to make him sensible that as the times went, while Antiochus and the Romans were disputing their pretensions with vast armies in the heart of Greece, it concerned a man in his position to keep a watchful eye over them, and dissembling, and putting up with any less important grievances, to preserve all quiet at home. Diophanes would not be ruled, but joined with Titus, and both together falling into Laconia, marched directly to Sparta. ”

“ But anon, it could not be hid from Palladius that Diaphantus was grown weary of his abode in Arcadia, seeing the court could not be visited, but was prohibited to all men save certain shepherdish people. And one day, when Kalander had invited them to the hunting of a goodly stag, Diaphantus was missed, after death had been sent to the poor beast with a crossbow, and on returning to the house, Palladius, greatly marvelling, lighted on a letter written by Pyrocles before he went a-hunting, in which he said that violence of love led to his absence. ”

“ He would listen in fancy, as he had so often listened in reality, to the eloquence of antagonistic orators, he would balance the possible arguments for severity or clemency, he would conceive himself present at the moment when one uplifted hand might incline the scale of life or death, and he would feel the thrill of relief with which those who supported Diodotus found that Athens was saved at the eleventh hour—saved, if the bearers of the respite, rowing night and day, could reach Lesbos in time—from the infamy of devoting a population to the sword. ”

“ But though Diogenes was as ridiculous a dog as one would meet with on a summer's day; a blundering, ill-favoured, clumsy, bullet-headed dog, continually acting on a wrong idea that there was an enemy in the neighbourhood, whom it was meritorious to bark at; and though he was far from good-tempered, and certainly was not clever, and had hair all over his eyes, and a comic nose, and an inconsistent tail, and a gruff voice; he was dearer to Florence, in virtue of that parting remembrance of him, and that request that he might be taken care of, than the most valuable and beautiful of his kind. ”

“ DIO. Aye, but he's speaking to the dead, you knave, Who cannot hear us though we call them thrice. AESCH. And how do you make your prologues? EUR. You shall hear; And if you find one single thing said twice, Or any useless padding, spit upon me. DIO. Well, fire away: I'm all agog to hear Your very accurate and faultless prologues. EUR. A happy man was Oedipus at first— AESCH. Not so, by Zeus; a most unhappy man. Who, not yet born nor yet conceived, Apollo Foretold would be his father's murderer. How could he be a happy man at first. EUR. Then he became the wretchedest of men. ”

“ In a treatise in which he discussed the nature of the Gods he contended for the unity of the Deity, and asserted that man is unable to know him by any sensible representation, since he is unlike any being on earth; and demonstrated the sufficiency of virtue for happiness, by the doctrine that outward events are regulated by God so as to benefit the wise and good.
Diogenes, a native of Sinope in Pontus, who was born b.c. 412, was one of his few disciples; he came at an early age to Athens, and became notorious for the most frantic excesses of moroseness and self-denial. ”

“ I tell you when I see Their plays, and hear those jokes, I come away More than a twelvemonth older than I went. XAN. O thrice unlucky neck of mine, which now Is getting crushed, yet must not crack its joke! DIO. Now is not this fine pampered insolence When I myself, Dionysus, son of—Pipkin, Toil on afoot, and let this fellow ride, Taking no trouble, and no burden bearing? XAN. What, don't I bear? DIO. How can you when you're riding? XAN. Why, I bear these. DIO. How? XAN. Most unwillingly. DIO. Does not the donkey bear the load you're bearing? XAN. Not what I bear myself: by Zeus, not he. ”

“ Faint not, Daiphantus! Wise men love not so well!
"Like heaven's artist, the astronomer,
Gazing on stars, oft to the earth doth fall:
So I, Daiphantus, now Lover's Harbinger,
Am quite condemned to Love's funeral!
Who falls by women, by them oft doth rise;
Ladies have lips to kiss, as well as eyes!"
But tush, thou fool! thou lov'st all thou seest.
Who once thou lovest, thou should'st change her never!
Constant in love, Daiphantus, see thou beest!
If thou hope comfort, Love but once, and ever! ”

“ She held the theory that if Diogenes had stayed at home and attended to business, instead of prowling around Athens with a smelly lantern, he would have been visited by any number of honest men. Everything comes to him who waits might be a trite proverb, but experience had taught her that it was a true one. ”

“ Dion.
"Oh," cried Daphne, shuddering, "never! We couldn't even by daylight, and now it is almost dark."
"Anyway," said Dion, "we're safer being lost here than anywhere else in
Athens. It's where the Gods live. Maybe they'll take care of us."
"We might sacrifice something on an altar," said Daphne, "and pray, the way Father does."
"We haven't a thing to sacrifice," answered Dion. "We haven't anything to eat even for ourselves." ”

“ Whereas it is notorious that most of our Professors never lay out a Farthing either in Pen, Ink, or Paper. Others are for deriving them from Diogenes, because several of the leading Men of the Sect have a great deal of the cynical Humour in them, and delight much in Sun-shine. But then again, Diogenes was content to have his constant Habitation in a narrow Tub; whilst our Philosophers are so far from being of his Opinion, that it's Death to them to be confined within the Limits of a good handsome convenient Chamber but for half an Hour. ”

“ The crowd, because they could obscure their identity at the contest and by their numbers, gained the greater boldness, raised a loud cry at the horse-race on the birthday of Diadumenianus, which fell on the fourteenth of September: they uttered many lamentations, asserting that they alone of all mankind were destitute of a leader, destitute of a king; and they invoked the name of Jupiter, declaring that he alone should be their leader and uttering aloud these words: "As a master thou wert angry, as a father take pity on us." ”

“ But Diomedes, clear of vision, spies her out and drives his pointed spear against her hand, grazing the palm of it. Out leaps the ichor, life-stream of the blessed gods, and the goddess shrieking drops her burden and flees from the jeering Diomede;—nay, mounts even to Olympus where, sobbing in the [Pg 290] arms of her mother, Dione, she finds solace of her pain, and straightway turns to hopes of vengeance. Æneas, meantime, is wrapped by Phœbus Apollo in a dusky cloud and borne aloft to that god's temple, where Diana and Latona heal him. ”

“ Now consider whether Diogenes did not above all other men profess this belief, since he freely exposed his body to hardships so that he might make it stronger than it was by nature. He allowed himself to act only as the light of reason shows us that we ought to act; and the perturbations that attack the soul and are derived from the body, to which this envelope of ours often constrains us for its sake to pay too much attention, he did not take into account at all. ”

“ The creator has gone to rest and the world is silent.
The white walls of the temple were dull-green as though under water. All was dead; only on the great altar of the Sun a perpetual fire was burning and the sun disc of Aton above it—the highest point of the whole huge edifice—glowed with a dull-red glow as though a ray of an invisible sun were reflected in it.
Dio saw the king in the distance, but she did not recognise him at once. He was sitting on the altar steps in a curiously cramped attitude, with his chin resting against his knees and his face buried in his hands. ”

“ For Diogenes possessed nothing that is usually offered, incense or libations or money to buy them with. But if he held right opinions about the gods, that in itself was enough. For he worshipped them with his whole soul, thus offering them as I think the most precious of his possessions, the dedication of his soul through his thoughts. Let not the Cynic be shameless, but led by reason let him first make subservient to himself the emotional part of his soul so that he may entirely do away with it and not even be aware that he is superior to pleasures. ”

“ In the meantime, Gnatho set about composing a long and amorous discourse upon Daphnis. Dionysophanes, whose hairs were already beginning to turn grey, was a tall, handsome man, who need not have shrunk from rivalry with many a young man: in addition to this, he was richer than most men, and none were more virtuous. On the first day of his arrival, he offered sacrifice to all the Gods who preside over husbandry, to Demeter, Dionysus, Pan, and the Nymphs, and gave a feast to all the household. ”

“ The Milky Way like a cloud rent in two stretched from one end of the desert to the other; the Pleiades glowed and the seven stars of Tuart, the Hippopotamus, glittered with a cold brilliance.
The king uncovered his face and looked at Dio. His face was as still as the sleeping desert and the starry heavens above. But Dio shuddered: she recalled the Sphinx with the face of Akhnaton; if a man had been tortured for a thousand years in hell and then came to earth again, he would have such a face. ”

“ When some one asked that he might have back his cloak, "If it was a gift," replied Diogenes, "I possess it; while, if it was a loan, I am using it." A supposititious son having told him that he had gold in the pocket of his dress, "True," said he, "and therefore you sleep with it under your pillow." 63. On being asked what he had gained from philosophy, he replied, "This at least, if nothing else – to be prepared for every fortune." Asked where he came from, he said, "I am a citizen of the world." [37] Certain parents were sacrificing to the gods, that a son might be born to them. ”

“ Since I see thee, most excellent Diognetus, exceedingly desirous to learn the mode of worshipping God prevalent among the Christians, and inquiring very carefully and earnestly concerning them, what God they trust in, and what form of religion they observe, [1] so as all to look down upon the world itself, and despise death, while they neither esteem those to be gods that are reckoned such by the Greeks, nor hold to the superstition of the Jews; and what is the affection which they cherish among themselves ”