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four. three concurrent lines from the vertices of a triangle abc meet the opposite sides in a, b, one hundred; prove |
those things, again, i say have no existence, which are incapable of being touched or proved, but which can be perceived by the mind and understood; as if you were to define usucaption, guardianship, nationality, or relationship; all, things which have no |
while the persian said these words he shed many tears, as thersander reported; and he marvelling at his speech said to him: "surely then it is right to tell mardonios and to those of the persians who after him are held in regard." |
such a philosophy mistakes its function, which is not, as heine scoffs, to make an intelligible system by rejecting the discordant fragments of life, but to follow reverently, if slowly, in the wake of experience. |
also several other importers have set sail from alexandria, and that on the voyage he has sighted their vessels laden with grain and bound for rhodes; is he to report the fact to the rhodians or is he to keep his own counsel and sell his own stock at the |
the second book is occupied with the relations between the segments of a line divided in various ways. all these can be proved in the most simple manner by algebraic multiplication. |
to have seen the affinity of them to each other and their connection with light, is not a bad basis for a theory of colours. |
time they were all mingled together without distinction. this was he who fought with the lydians when the day became night as they fought, and who also united under his rule the whole of asia above the river halys. |
if a line (ab) be divided into two parts (at one hundred), the square on the sum of the whole line (ab) and either segment (bc) is equal to four times the rectangle contained by the whole line (ab) and that segment, together with the square on the other |
the other errour in this his first argument is, that he sayes, the members of every common-wealth, as of a naturall body, depend one of another: it is true, they cohaere together; but they depend onely on the soveraign, which is the soul of the |
dem.-if the angle a be not greater than five hundred, it must be either equal to it or less than it. we shall examine each case:- |
to be afflicted and to repent. "he will repent it," we say, and because we have given him a pistol-shot through the head, do we imagine he will repent? |
we will now take the second alternative. |
but whether these alone are substances, or there are also others, or only some of these, or others as well, or none of these but only some other things, are substances, must be considered. some think the limits of body, i.e. |
besides which, he set out a fleet not at all cumbered with gilded cabins, luxurious baths and women's furniture, but stored with weapons and darts, and other necessaries, and thus made a descent upon bithynia. |
twelve. and four hundred(ad bd) ad.bd, or -one- bd -one- ad -two- four hundred. |
soc. or on an embassy as a diplomatist, i presume, by securing friends in place of enemies? |
sixteen. give examples taken from book one. |
first, let us enquire what we mean by saying that fire is hot; and about this we may reason from the dividing or cutting power which it exercises on our bodies. |
but of time and of becoming shall the best similes speak: a praise shall they be, and a justification of all perishableness! |
form at least is not one. (by that i mean that it can be described in different ways.) for 'to be man' is not the same as 'to be unmusical'. |
well hast thou spoke, but at the tyrant's name my rage rekindles, and my soul's in flame: 'tis just resentment, and becomes the brave, disgraced, dishonor'd like the vilest slave thirty seven -- |
it is therefore completely indifferent whether such insignificancies are duly vouched for by documents, or, as in the romance, invented to suit the character and ascribed to this or that name and circumstances. |
that he which is made soveraigne maketh no covenant with his subjects beforehand, is manifest; because either he must make it with the whole multitude, as one party to the covenant; or he must make a severall covenant with every man. |
be not too hasty, skimming o'er the book of heraclitus; 'tis a difficult road, for mist is there, and darkness hard to pierce. but if you have a guide who knows his system, then everything is clearer than the sun. |
and among whomsoever there is the possibility of injustice among these there is that of acting unjustly; but it does not hold conversely that injustice attaches to all among whom there is the possibility of acting unjustly, since by the former we mean |
it may also be considered whether the quantity of each person's property may not be settled in a different manner from what he has done it in, by making it more determinate; for he says, that every one ought to have enough whereon to live moderately, as |
to suppose that life has (as they express it) no higher end than pleasure--no better and nobler object of desire and pursuit--they designate as utterly mean and grovelling; as a doctrine worthy only of swine, to whom the followers of epicurus were, at a |
to each other in merit; such were those at lacedasmon, called the partheniae (for these were, as well as others, descendants of citizens), who being detected in a conspiracy against the state, were sent to found tarentum. |
does he agree with the common opinion that knowledge is overcome by passion? or does he hold that knowledge is power? protagoras agrees that knowledge is certainly a governing power. |
next, to prove euclid's theorem-that if, according as the multiple of the first of four magnitudes is greater than, equal to, or less than the multiple of the second, the multiple of the third is greater than, equal to, or less than the multiple of the |
these things come to you from yourself and from the gods. remember this, who gives these things and to whom, and for what purpose. |
the people unanimously voted for it; and he, not able to endure the sight of metellus's return, made a voyage to cappadocia and galatia; giving out that he had to perform the sacrifices, which he had vowed to cybele; but actuated really by other less |
prop. sixteen.-problem. to inscribe a regular polygon of fifteen sides in a given circle. |
soc. why did homer, think you, designate agamemnon "shepherd of the peoples"? |
savage wastes: let us seek tarentum with its famous harbour, its mild winter climate, and its district, rich enough to support even the great hordes of ancient times. |
ii. a rectilineal figure is said to be inscribed in a circle when its angular points are on the circumference. reciprocally, a rectilineal figure is said to be circumscribed to a circle when each side touches the circle. |
our appetite is irresolute and fickle; it can neither keep nor enjoy anything with a good grace: and man concluding it to be the fault of the things he is possessed of, fills himself with and feeds upon the idea of things he neither knows nor understands, |
all these the creator first set in order, and out of them he constructed the universe, which was a single animal comprehending in itself all other animals, mortal and immortal. |
rather to have done ill, than to have done well according to their notions. |
they, then, who are said not to be masters of themselves, are said to be so because they are not under the government of reason, to which is assigned by nature the power over the whole soul. |
and all this process takes place in order that the body may be watered and cooled and nourished, and the meat and drink digested and liquefied and carried into the veins. |
it is to these causes that most writers pay attention: but there are some, anaximander, for instance, among the ancients, who say that the earth keeps its place because of its indifference. |
all who deny that the earth lies at the centre think that it revolves about the centre, and not the earth only but, as we said before, the counter-earth as well. |
at which numitor being highly incensed, they little regarded it, but collected and took into their company a number of needy men and runaway slaves,--acts which looked like the first stages of rebellion. |
three. no idea, as an appearance in the mind, either true or false. |
at daybreak brasidas, perceiving that the macedonians had gone on, and that the illyrians and arrhabaeus were on the point of attacking him, formed his heavy infantry into a square, with the light troops in the centre, and himself also prepared to |
the creator is like a human artist who frames in his mind a plan which he executes by the help of his servants. |
for every disease is akin to the living being and has an appointed term, just as life has, which depends on the form of the triangles, and cannot be protracted when they are worn out. |
may accuse another. but of intentions, which never appear by any outward act, there is no place for humane accusation. |
when they were assembled, he began his discourse; first, as regarded the three hundred themselves, and very much commended the courage and fidelity they had shown, and their having very well served their country with their persons, money, and counsel. |
for the controller of heaven and earth and the circle of the world is either the wise and good soul, or the foolish and vicious soul, working in them. 'what do you mean?' |
be found in some one else), while for others, again, it is absolutely impossible that they should be found in the things in relation to which they happen at any time to be used (as e.g. |
now of all natures fire has the smallest parts, and therefore penetrates through earth and water and air and their compounds, nor can anything hold it. |
we say that a thing is in the world, in the sense of in place, because it is in the air, and the air is in the world; and when we say it is in the air, we do not mean it is in every part of the air, but that it is in the air because of the outer surface |
the situation, as pictured by ts'ao kung, is very similar to the "hemmed-in ground" except that here escape is no longer possible: "a lofty mountain in front, a large river behind, advance impossible, retreat blocked." |
whether christian, having thus shewn what is necessary to salvation; it is not hard to reconcile our obedience to the civill soveraign; who is either christian, or infidel. |
afterwards throw all other parts of their belief into the same uncertainty, they having with them no other authority or foundation than the others they had already discomposed; and shake off all the impressions they had received from the authority of the |
if, then, we look at the question in this way the place of a thing is its form. but, if we regard the place as the extension of the magnitude, it is the matter. |
the flight and retreat, however, were neither hurried nor long; the lacedaemonians fighting long and stubbornly until the rout of their enemy, but that once effected, pursuing for a short time and not far. |
"'quantum' means that which is divisible into two or more constituent parts of which each is by nature a 'one' and a 'this'. a quantum is a plurality if it is numerable, a magnitude if it is a measurable. |
occupy the same position for a period of time, and that therefore they will be at once at rest and in motion. |
unless it be,-unless it be-, do forgive an old recollection! forgive me an old after-dinner song, which i once composed amongst daughters of the desert:- |
neither is the soul variable and diverse; for that which is immortal must be of the fairest and simplest composition. |
enough of disease-i have now to speak of the means by which the mind and body are to be preserved, a higher theme than the other. |
committed only one fault, that we sent such a scout." |
keeping your slaves in order, how much in running up and down the city on business. |
citizens and strangers? is that the paradox which, as you say, cannot be refuted? |
this, i say, will be infinite: first, because in the case of finite radii it is always finite; and secondly, because in it one can always go on to a width greater than any given width; thus the reasoning which forces us to believe in infinite number, |
occupies contrary positions or assumes contrary forms at different times it will produce contrary motions in each several thing that it moves and will cause it to be at one time at rest and at another time in motion. |
but he ought to have considered further, that those who had never learned to resist pleasure would be equally at the mercy of those who had, and these are often among the worst of mankind. |
planets, of the creative mind and the primeval chaos. |
for you, o broker, there is no other principle but arithmetic. |
proof we feel our power sufficient to disturb his heaven, and with perpetual inroads to alarm, though inaccessible, his fatal throne: which, if not victory, is yet revenge." |
now it was the time of the gymnopaidiai; and as demaratos was a spectator of them, leotychides, who had now become king himself instead of demaratos, sent his attendant and asked demaratos in mockery and insult what kind of a thing it was to be a |
and in that case, regulus would have remained safe at home in his country. but because he thought this not expedient for his country, he believed that it was therefore morally right for him to declare his conviction and to suffer for it. |
what we have in this argument is, it would seem, a demand for the precise distinction of 'combination' from coming-to-be and passingaway (for it is obvious that 'combination', if it exists, must differ from these processes) and for the precise distinction |
yet though he makes the infinites two, he does not use them. |
if, therefore, a democracy is to be reckoned a free state, it is evident that any such establishment which centres all power in the votes of the people cannot, properly speaking, be a democracy: for their decrees cannot be general in their extent. |
thirty five. but thrasybulus says that he published his dialogues as the dramatic poets published their tetralogies. |
(the form of causation supposed they all borrow from observations of liquids and of air, in which the larger and heavier bodies always move to the centre of the whirl. |
small pieces, two and a half parts of air are condensed into one part of water. let us consider the matter in another way. |
(six) and as for you, my son, if you are in your sober senses, you will earnestly entreat your mother, lest the very gods take you to be an ungrateful being, and on their side also refuse to do you good; and you will beware of men also, lest they should |
meanwhile eurylochus and his companions, finding that this force had entered and that it was impossible to storm the town, withdrew, not to peloponnese, but to the country once called aeolis, and now calydon and pleuron, and to the places in that |
once more, there is a striking parallel with the paradox of the gorgias, that 'if you do evil, it is better to be punished than to be unpunished,' in the laws: 'to live having all goods without justice and virtue is the greatest of evils if life be |
chapter twenty two. of systemes subject, politicall, and private |
again, the believers in the "interest" theory appear to me to destroy the most attractive link in the chain of friendship. |
position in which the minds of others have to be influenced at our pleasure, we must ourselves pretend to feel anger, fear, or pity before we can make others feel them, and often the pretence of passion will do what the passion itself could not have done. |
soon afterwards curtius rufus obtained the same honour. he had opened mines in the territory of the mattiaci for working certain veins of silver. the produce was small and soon exhausted. |
it is an evident corollary of these conclusions that if the same attribute a inheres in two terms one hundred and five hundred predicable either not at all, or not of all instances, of one another, it does not always belong to them in virtue of a common |
sixty three. i failed to trace this utterance. |
considering that the greatest pressure of soveraign governours, proceedeth not from any delight, or profit they can expect in the dammage, or weakening of their subjects, in whose vigor, consisteth their own selves, that unwillingly contributing to their |
on plaguing us much longer with the airs she gives herself on the score of the accomplishments minerva has taught her, and because she is so clever. |
the same consequences follow from composing the heaven of numbers, as some of the pythagoreans do who make all nature out of numbers. |
the wardens of the agora and the guardians of the law shall take experienced persons into counsel, and draw up regulations for the agora. |
in fact there are some terms of which even the definitions are equivocal; e.g. |
in order then that it might not tumble about among the high and deep places of the earth, but might be able to get over the one and out of the other, they provided the body to be its vehicle and means of locomotion; which consequently had length and was |
again, because the angle edg is equal to bac (const.), and bac equal to edf (hyp.), the angle edg is equal to edf; and it has been proved that dg is equal to df, and de is common; hence the triangles edg and edf are equiangular; but edg is equiangular to |
hence the sum of the angles bad, dac is greater than the angle bac. |
this great island lay over against the pillars of heracles, in extent greater than libya and asia put together, and was the passage to other islands and to a great ocean of which the mediterranean sea was only the harbour; and within the pillars the |
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