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nine. through a given point draw a right line, such that perpendiculars on it from two given points on opposite sides may be equal to each other. |
what thou doest can no one do to thee again. lo, there is no requital. |
if four lines (ab, four hundred, ef, gh) be proportional, and any pair of similar rectilineal figures (abk, four hundred fifty) be similarly described on the first and second, and also any pair (ei, gj) on the third and fourth, these figures are |
but the proceeding seemed sufficiently imperious and arbitrary, indeed rather a spiteful and insulting ostentation of power, than that the possession of the fortress would be of any great importance. |
they abandon me throughout; all i write is rude; polish and beauty are wanting: i cannot set things off to any advantage; my handling adds nothing to the matter; for which reason i must have it forcible, very full, and that has lustre of its own. |
aristobulus says, he had not a fund of above seventy talents for their pay, nor had he more than thirty days' provision, if we may believe duris; onesicritus tells us, he was two hundred talents in debt. |
one who pulls away a pillar from under a roof or one who removes a stone from a wineskin in the water is the accidental cause of motion): and in the same way the real cause of the motion of a ball rebounding from a wall is not the wall but the thrower. |
the conception of the philosopher, or the philosopher and lover in one, as a sort of madman, may be compared with the republic and theaetetus, in both of which the philosopher is regarded as a stranger and monster upon the earth. |
anything else might be in a state of rest, but there is no reason why it should not be its nature to be moved. the earth is not carried along, and would not be carried along if it were infinite, provided it is held together by the centre. |
o listen to him; other men like thee have thankless children and are choleric, but yielding to persuasion's gentle spell they let their savage mood be exorcised. |
nine. the right line joining the middle points of opposite sides of a quadrilateral, and the right line joining the middle points of its diagonals, are concurrent. |
this last cause then is prior: and so generally. |
the "image" (according to his materialistically coloured psychology) which, when it is a strong motion, is called sense, passes, as it becomes weaker or decays, into imagination, and gives rise, by its various complications and associations with others, |
there are also opposite maxims and habits of pleasure which flatter and attract the soul, but do not influence those of us who have any sense of right, and they continue to obey and honour the maxims of their fathers. |
but salius enters, and, exclaiming loud for justice, deafens and disturbs the crowd; urges his cause may in the court be heard; and pleads the prize is wrongfully conferr'd. |
prop. one hundred.-theorem (simson). if the first of four magnitudes be the same multiple of the second which the third is of the fourth, the first is to the second as the third is to the fourth. |
for i wish that you should appear implicated in this fault, so that if i myself should appear unable to support the weight of such a subject, you may bear the blame of having imposed such a burden on me, and i only that of having undertaken it. |
hold office for twenty years, and would therefore have an oligarchical rather than a democratic character. |
three. you ask me what i think we had better make use of to help us to support this ennui. |
i know a man of authority, bred up to letters, who has confessed to me to have been brought back from the errors of unbelief by sebond's arguments. |
these distinctions will be drawn more carefully later. on the present occasion it was necessary to refer to them: what has now been stated obscurely will then be made more clear. |
therefore the triangles abc, def, have the three sides of one respectively equal to the three sides of the other. hence i. viii. the angle abc is equal to def. |
we call that a thing easy to be done, which can be done without great labour, or expense, or annoyance, or perhaps without any labour, expense, or annoyance at all, and in the shortest possible time. |
thankfulness, and that they behoved to sacrifice to empedocles as to one who had become a god. |
five. whatsoever it be that happens unto thee, it is that which from all time was appointed unto thee. |
i have already told you the types of song and dance which they should follow: and 'some things,' as the poet well says, 'you will devise for yourself--others, god will suggest to you.' |
it is evident also that the denial corresponding to a single affirmation is itself single; for the denial must deny just that which the affirmation affirms concerning the same subject, and must correspond with the affirmation both in the universal or |
the question, what is place? presents many difficulties. an examination of all the relevant facts seems to lead to divergent conclusions. |
he knew that he was not to sack the city neither with nor without himself, for his mother had often told him this when he had sat alone with her, and she had informed him of the counsels of great jove. |
accomplished in a finite time. moreover it is the same with coming to rest as with motion. and so it is impossible for one and the same thing to be infinitely in process of becoming or of perishing. |
moreover it is said that with reference to these events the argives and eginetans made it a custom among themselves in both countries seventy two to have the brooches made half as large again as the size which was then established in use, and that their |
pleasure by the difficulty, by desire, and a certain kind of glory, and was of tiberius's mind, who in his amours was as much taken with modesty and birth as any other quality, and of the courtesan flora's humour, who never lent herself to less than a |
moreover, according to them, things are seen through air and water and other transparent bodies, because such bodies possess pores, invisible indeed owing to their minuteness, but close-set and arranged in rows: and the more transparent the body, the more |
substrata are receptive of 'contrarieties' of some kind. so much, then, as an answer to the questions (i) whether coming-to-be 'is' or 'is not'-i.e. |
def. i.-if two right lines in the same plane be such that, when produced indefinitely, they do not meet at any finite distance, they are said to be parallel. |
prop. twenty five.-problem. to describe a rectilineal figure equal to a given one (a), and similar to another given one (bcd). |
chap. nineteen. the duke ai asked, saying, 'what should be done in order to secure the submission of the people?' confucius replied, 'advance the upright and set aside the crooked, then the people will submit. |
this, those of the volscians who had long envied his reputation, and could not endure to see the influence he had with the people laid hold of, as the first matter of complaint against him. |
the inner curve is the one to take, not only in running races and in the contests of the circus, but also in the race of life; even literary pursuits, the most becoming thing for a gentleman to spend money upon, are only justifiable as long as they are |
she, of herself, too, dreaded his inconstancy, and hated his cruelty; and, therefore, conspiring with her three brothers, tisiphonus, pytholaus, and lycophron, made the following attempt upon him. |
each thing that comes to be comes from a similar body, and there is a coming to be of all things, though not, it is true, at the same time. hence there must also be an origin of coming to be. |
oedipus. o bid me not (as guest i claim this grace) expose my shame. |
he flew and flew over many a weary wave, but when at last he got to the island which was his journey's end, he left the sea and went on by land till he came to the cave where the nymph calypso lived. |
the whole, however, has become larger. and this increase is due (a) on the one hand to the accession of something, which is called 'food' and is said to be 'contrary' to flesh, but (b) on the other hand to the transformation of this food into the same |
for the case n four, which is the only figure of this class except the pentagon for which a construction has been given, see note at the end of this work. |
but as if on purpose to punish him in his pride, before they parted from him, messengers came with news of the complete slaughter of one of the spartan divisions by iphicrates, a greater disaster than had befallen them for many years; and that the more |
in these qualities the greeks rank themistocles and jason of pherae above all others. |
and this hope was nursed by ancient tradition, which had found expression from time to time in the celebrated lines of seneca and in many other places. |
a less magnitude in less time; for the divisions of time and of magnitude will be the same. and if either is infinite, so is the other, and the one is so in the same way as the other; i.e. |
this, indeed, would be as good as saying that the heavens are infinite, which we have shown to be impossible. |
quadi. the gothini, to their additional disgrace, work iron mines. |
match either for friend or enemy, he ought not therefore to strike, stab, or slay his friends. |
object which produces it is called bright and flashing. |
infinite, he degenerates into pedantry and smacks a little of scholastic prattle. |
various ways in which you hellenes may be useful to me you yourself have mentioned, but there is one still greater. |
cor. three.-similar portions of similar figures bear the same ratio to each other as the wholes of the figures. |
one is, that he contradicts himself; for, but just now, he could not imagine anything good unless the senses were in a manner tickled with some pleasure; but now he says that to be free from pain is the highest pleasure. |
for whereas marrow and bone and flesh and sinews are composed of the four elements, and the blood, though after another manner, is likewise formed out of them, most diseases originate in the way which i have described; but the worst of all owe their |
the eleatic isolation of being and the megarian or cynic isolation of individuals are placed in the same class by plato (soph.); and the same principle which is the symbol of motion to one mind is the symbol of rest to another. |
socrates: seeing then that men become good and useful to states, not only because they have knowledge, but because they have right opinion, and that neither knowledge nor right opinion is given to man by nature or acquired by him--(do you imagine either |
if four hundred, four hundred be the internal and external bisectors of the angle one hundred of the triangle acb, the three rectangles ad.db, ac.cb, ad.bd are proportional to the squares of ad, ac, ad; and are-(one) in arithmetical progression if the |
five hundred fifty two. the national spirit contains nature-necessity, and stands in external existence ( four hundred twenty three): the ethical substance, potentially infinite, is actually a particular and limited substance ( five hundred forty nine, |
this is the meeting-point of rousseau's educational with his political theory. his view as a whole can be studied only by taking together the social contract and the emile as explained by the letters on the mount and other works. |
movent causes a motion away from itself more violent than the natural locomotion of the thing moved, which continues its course so long as it is controlled by the motion imparted to it. |
"if they are individual and not universal, (a) real things will be just of the same number as the elements, and (b) the elements will not be knowable. |
then halius, prytanis, alcander fall- engag'd against the foes who scal'd the wall: but, whom they fear'd without, they found within. at last, tho' late, by lynceus he was seen. |
as soon as our people are inside and in safety, close the strong gates for i fear lest that terrible man should come bounding inside along with the others." |
incentives of devotion are more effectual than those of avarice. q. maximus buried his son when he was a consul, and one thousand. cato his when praetor elect, and fifty. |
by the former, objects are given to us; by the latter, thought. so far as the faculty of sense may contain representations a priori, which form the conditions under which objects are given, in so far it belongs to transcendental philosophy. |
up to boredom. this is a precise proof that existence in itself has no value, since boredom is merely the feeling of the emptiness of life. |
and the latter is supposed to be placed, first horizontally, and then vertically.). or if the mirror be turned vertically, then the concavity makes the countenance appear to be all upside down, and the lower rays are driven upwards and the upper downwards. |
you ought to speak of other states in the plural number; not one of them is a city, but many cities, as they say in the game. |
ludicrous applications of them. he does not, like heracleitus, get into a rage with homer and archilochus (heracl.), but uses their words and expressions as vehicles of a higher truth; not on a system like theagenes of rhegium or metrodorus, or in later |
and to this i say, that the various and contrary choices that men make in the world do not argue that they do not all pursue good; but that the same thing is not good to every man alike. |
moreover, there can always be something between points (for all lines are intermediate between points), whereas it is not necessary that there should possibly be anything between units: for there can be nothing between the numbers one and two. |
rough, then only harsh. those of them which are of an abstergent nature, and purge the whole surface of the tongue, if they do it in excess, and so encroach as to consume some part of the flesh itself, like potash and soda, are all termed bitter. |
he esteemed these endeavors of socrates as most truly a means which the gods made use of for the care and preservation of youth, and began to think meanly of himself, and to admire him; to be pleased with his kindness, and to stand in awe of his virtue; |
but since there cannot be anything prior to the first principle of all things, the principle cannot be the principle and yet be an attribute of something else. |
the winning of honor, is but the revealing of a man's virtue and worth, without disadvantage. for some in their actions, do woo and effect honor and reputation, which sort of men, are commonly much talked of, but inwardly little admired. |
we must, for instance, point out that a man is the only one, or the first, or almost the only one who has done something, or that he has done it better than any one else; all these distinctions are honourable. |
"that my mind may not eternally be intent upon my ills." --ovid., trist., iv. i, four. |
"omne adeo genus in terris, hominumque, ferarumque, et genus aequoreum, pecudes, pictaeque volucres, in furias ignemque ruunt." |
external world. and now there is no longer any difficulty in understanding the creation of images in mirrors and all smooth and bright surfaces. |
education and the fashions of his country, any absurdity for innate principles; and by long poring on the same objects, so dim his sight as to take monsters lodged in his own brain for the images of the deity, and the workmanship of his hands. |
notwithstanding all this, hermippus tells us that he had no hand in the ordinance; that iphitus made it, and lycurgus came only as a spectator, and that by mere accident too. |
eighteen.thirty six.) elijah saith to god, "i have done all these thy words," in stead of "i have done all these things at thy word," or commandement: and (jer. |
passive quality in virtue of which a thing is said to be acted on or to be incapable of being acted on. |
thirteen. within ten days, if so happen, thou shalt be esteemed a god of them, who now if thou shalt return to the dogmata and to the honouring of reason, will esteem of thee no better than of a mere brute, and of an ape. |
for the passingaway of either 'element' produces either the other or the matter. |
it is thus that the poets who have represented tiresias the augur as a wise man and blind never exhibit him as bewailing his blindness. |
persons, as it will be a double temptation to the enemy to fight with greater resolution where so great booty and so rich spoils are to be obtained; and this very thing has been observed in former times, notably to encourage the romans against the |
can be made, for they will simply come and take by force what we have. so much more have we to fear from this neighbour than from another. |
(yet in another way of putting it this is not necessary, as one of the contraries will serve to effect the change by its successive absence and presence.) |
it is true indeed that, in the case of any individual thing that has a becoming, locomotion must be the last of its motions: for after its becoming it first experiences alteration and increase, and locomotion is a motion that belongs to such things only |
for wee cannot understand, that one power hath power over another power; and that one power can have right or command over another: for subjection, command, right, and power are accidents, not of powers, but of persons: one power may be subordinate to |
"health first, beauty next, wealth third," in the words of the old song, or how would you rank them? |
utile ei videbatur plurimum posse alterius invidia; id quam iniustum in patriam et quam turpe esset, non videbat. |
thus spake the trodden one, and zarathustra rejoiced at his words and their refined reverential style. "who art thou?" asked he, and gave him his hand, "there is much to clear up and elucidate between us, but already methinketh pure clear day is dawning." |
another class live above this mark to the beauty of the symbol, as the poet and artist and the naturalist and man of science. a third class live above the beauty of the symbol to the beauty of the thing signified; these are wise men. |
i think, that the state ought to tolerate every principle of philosophy; nor is there an instance, that any government has suffered in its political interests by such indulgence. |
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