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if we say that the movent in such cases moves something else at the same time, that the thrower e.g. |
fixed, the inner the wandering stars. the soul of the world was diffused everywhere from the centre to the circumference. |
they are for the most part confined to a corner of earth, and see but a little way beyond their own home or place of abode; they 'do not lift up their eyes to the hills'; they are not awake when the dawn appears. |
they find society and friendship augmented by it; and besides, can there possibly be allowed a more orderly and regular diversion than what is performed m the sight of every one, and very often in the presence of the supreme magistrate himself? |
republic are these ancient athenians. let us divide the subject among us, and all endeavour according to our ability gracefully to execute the task which you have imposed upon us. |
when hector heard this he was glad, and went about among the trojan ranks holding his spear by the middle to keep them back, and they all sat down at his bidding: but the achaeans still aimed at him with stones and arrows, till agamemnon shouted to them |
cor. one.-the normal is the least line that may be drawn from a given point to a given plane; and of all others that may be drawn to it, the lines of any system making equal angles with the normal are equal to each other. |
for that which spreads itself out widely is fine, and a thing composed of small parts is so spread out. in the end, then, they distinguish the various other substances from the element by the greatness and smallness of their parts. |
twenty eight. if from any point in the circumference of the circle, circumscribed about a regular polygon of n sides, lines be drawn to its angular points, the sum of their squares is equal to n times the square of the radius. |
socrates: then restraint or chastisement is better for the soul than intemperance or the absence of control, which you were just now preferring? |
he is not satisfied with the result, and would like to renew the enquiry with the help of protagoras in a different order, asking (one) what virtue is, and (two) whether virtue can be taught. |
to wonder is opposed contempt, which generally arises from the fact that, because we see someone wondering at, loving, or fearing something, or because something, at first sight, appears to be like things, which we ourselves wonder at, love, fear, c., we |
let us take first the virtue of a man--he should know how to administer the state, and in the administration of it to benefit his friends and harm his enemies; and he must also be careful not to suffer harm himself. |
'it may be said of yu-chung and i-yi, that, while they hid themselves in their seclusion, they gave a license to their words; but, in their persons, they succeeded in preserving their purity, and, in their retirement, they acted according to the exigency |
forty five proergazomenon : a conjectural emendation of prosergazomenon . |
observation.-the great difficulty which beginners find in this proposition is due to the fact that the two triangles acf, abg overlap each other. |
in order to live in accord with nature, it is necessary to know what nature is; and to this end a threefold division of philosophy is made-into physics , dealing with the universe and its laws, the problems of divine government and teleology; logic , |
phocion told him, if he intended him to go against them as enemies, that force was insignificant; if as to friends and allies, one vessel was sufficient. |
the lover, and some enters into his soul, and some when he is filled flows out again; and as a breeze or an echo rebounds from the smooth rocks and returns whence it came, so does the stream of beauty, passing through the eyes which are the windows of the |
from potential to actual substance) is coming-to-be, a change in the sphere of magnitude is growth and one in the sphere of quality is 'alteration'-both growth and 'alteration' being changes from what is-potentially to what is-actually magnitude and |
five. if a line be divided into any number of parts, the continued product of all the parts is a maximum, and the sum of their squares is a minimum when all the parts are equal. |
to which i answer,-the equality of any other returning appearances might be known by the same way that that of days was known, or presumed to be so at first; which was only by judging of them by the train of ideas which had passed in men's minds in the |
one hundred seventy four. above these towards the south wind in the region of wild beasts dwell the garamantians, one hundred fifty seven who fly from every man and avoid the company of all; and they neither possess any weapon of war, nor know how to |
against the noblest kingdom and city of those which are among the hellenes, and the best men." to xerxes that which was said seemed to be utterly incredible, and he asked again a second time in what manner being so few they would fight with his host. |
at the taking of the town, the tyrant fled into the citadel, and was there besieged by curio, who had that charge given him. |
principle in them. and when external impressions enter in, they are really conquered, though they seem to conquer. |
one. the line that bisects the vertical angle of an isosceles triangle bisects the base perpendicularly. |
o eve, some further change awaits us nigh, which heaven, by these mute signs in nature, shows forerunners of his purpose; or to warn us, haply too secure, of our discharge from penalty, because from death released some days: how long, and what till then |
six. and sosicrates, in his successions, relates that he, having being asked by leon, the tyrant of the phliasians, who he was, replied, "a philosopher." and adds, that he used to compare life to a festival. |
now therefore it seems good to me that we should cross over and go forward from the crossing as far as they go in their retreat, and endeavour to get the better of them by doing as follows:-the massagetai, as i am informed, are without experience of |
eight. how is the area of a parallelogram found? |
and so the apostles were the first christian bishops, instituted by christ himselfe: in which sense the apostleship of judas is called (acts one.twenty.) his bishoprick. |
and they tell another story of the same kind of a fellow in denmark, who being condemned to lose his head, and the like condition being proposed to him upon the scaffold, refused it, by reason the girl they offered him had hollow cheeks and too sharp a |
and it is right that you should recollect the eagerness which you had to see him, when you pressed us all to secure plato's visit to you, promising to provide for him, and to treat him hospitably in every respect, and to ensure his safety both while he |
eight. the rectangle of.op is equal to the square of the radius. |
for to be pleased in the fiction of that, which would please a man if it were reall, is a passion so adhaerent to the nature both of a man, and every other living creature, as to make it a sinne, were to make sinne of being a man. |
wisdom; all of them grotesque and absurd in their form--because they address themselves to "all," because they generalize where generalization is not authorized; all of them speaking unconditionally, and taking themselves unconditionally; all of them |
xxix. a quadrilateral whose four sides are equal is called a lozenge. |
viii. magnitudes that can be made to coincide are equal. |
therefore, in order to narrating with clearness, we must go back to those previous rules for explaining and illustrating facts, in which brevity is enjoined and taught. |
we must first distinguish the senses in which we use the words 'ungenerated' and 'generated', 'destructible' and 'indestructible'. |
there hostility so admirable as the christian. |
as, for example, where he says'-- in the essay on false shame. --that the inhabitants of asia came to be vassals to one only, for not having been able to pronounce one syllable, which is no. |
--who has not seen peevish gamesters chew and swallow the cards, and swallow the dice, in revenge for the loss of their money? |
before the appropriation of land, he who gathered as much of the wild fruit, killed, caught, or tamed, as many of the beasts, as he could; he that so imployed his pains about any of the spontaneous products of nature, as any way to alter them from the |
and does it become a philosopher to boast that he is not afraid of these things, and that he has discovered them to be false? |
alone among solids they leave the sphere undivided, as not possessing more than one surface: for the division into surfaces is not just dividing a whole by cutting it into its parts, but division of another fashion into parts different in form. |
he now had leave to bestow purple hats and cloaks, which among the macedonians is one of the greatest honors the king can give. |
then if bg is taken to be indivisible, two things without parts will have to be contiguous (which is impossible): if on the other hand it is taken to be divisible, there will be something prior to g to which the magnitude has changed, and something else |
and because the abstinence from a present pleasure that offers itself is a pain, nay, oftentimes a very great one, the desire being inflamed by a near and tempting object, it is no wonder that that operates after the same manner pain does, and lessens in |
lycurgus, the most perfect legislator that ever was, virtuous and invented this very unjust practice of making the helots, who were their slaves, drunk by force, to the end that the spartans, seeing them so lost and buried in wine, might abhor the excess |
cor. one.-the side of a regular hexagon inscribed in a circle is equal to the radius. |
who has imposed laws on the roman people? and who, with armed troops and guards, has excluded both the people and the magistrates from the forum? who has filled the senate with armed men? |
"tegmina queis capitum, raptus de subere cortex." |
business which was brought before him; but after this he passed the time in drinking and in jesting at his boon-companions, and was frivolous and playful. |
six. the transverse lines bk, cg are perpendicular to each other. |
there is great dispute even what the soul is, where it is, and whence it is derived: with some, the heart itself ( cor ) seems to be the soul, hence the expressions, excordes , vecordes , concordes; and that prudent nasica, who was twice consul, was |
pompey. the report of these actions at rome, quieted those who were there, and some who had fled thence returned. |
but no one imagines that any seed of immortality is to be discerned in our mortal frames. |
i perceive that phenomena succeed one another, that is to say, a state of things exists at one time, the opposite of which existed in a former state. in this case, then, i really connect together two perceptions in time. |
it is natural that this should happen; for the movement goes with the distance and the time with the movement, because they are quanta and continuous and divisible. |
another time, when the assembly had refused to hear him, and he was going home with his head muffled up, taking it very heavily, they relate that satyrus, the actor, followed him, and being his familiar acquaintance, entered into conversation with him. |
naked and tombless see, o passer-by, the thirty thousand men of thessaly, slain by the aetolians and the latin band, that came with titus from italia's land: alas for mighty macedon! that day, swift as a roe, king philip fled away. |
it is fire, or in both directions-whatever be the nature of the inserted body. |
one hundred seventeen for if, as we find it in the writings of metrodorus, not only expediency but happiness in life depends wholly upon a sound physical constitution and the reasonable expectation that it will always remain sound, then that |
dem.-let the sides bc, ce, which are opposite to the equal angles a and five hundred, be conceived to be placed so as to form one continuous line, the triangles being on the same side, and so that the equal angles bca, ced may not have a common vertex. |
such as have sensuality to encounter, freely make use of this argument, to shew that it is altogether "vicious and unreasonable; that when it is at the height, it masters us to that degree that a man's reason can have no access," and instance our own |
for they are men of the highest courage, of the most consummate wisdom, and they will act in perfect harmony with each other. but my exhortations to rapid and instant action are prompted by a desire not merely for victory, but for speedy victory. |
two spheres, of the planets and of the world beyond them, all together moving around the earth, which is their centre. |
there are some unhappy circumstances in which we can only keep our liberty at others' expense, and where the citizen can be perfectly free only when the slave is most a slave. such was the case with sparta. |
but inequality easily makes its way among cowardly and ambitious minds, which are ever ready to run the risks of fortune, and almost indifferent whether they command or obey, as it is favourable or adverse. |
the silent heart encourages her; o friend, never strike sail to a fear! come into port greatly, or sail with god the seas. not in vain you live, for every passing eye is cheered and refined by the vision. |
six. the three lines of intersection of three planes are either parallel or concurrent. |
but when the treaty was disavowed by the senate, and the general surrendered to the samnites, one of the senators asserted that the man who held the pig ought also to be given up." the charge is, "he ought to be given up." the denial is, "he ought not." |
called it "le contr un." he wrote in his youth,-- "not being as yet eighteen years old."--edition of one thousand five hundred eighty eight. |
at this time a sheep happened to yean a lamb, with the perfect shape and color of a tiara upon the head, and testicles on each side; which portent alexander regarded with such dislike, that he immediately caused his babylonian priests, whom he usually |
must extend to all alike. for all are equally undifferentiated in form, but any one is different numerically from any other. |
next we have to speak of the elections of the wardens of the agora and of the city. the wardens of the city shall be three in number, and they shall have the care of the streets, roads, buildings, and also of the water-supply. |
but the phrase, "not more one thing," c., has sometimes an affirmative sense, indicating the equality of certain things, as for instance, in this sentence, "a pirate is not worse than a liar." |
and, indeed, they were now grown far better soldiers than ever they had been, being so continually kept in training, by the frequency of the lacedaemonian expeditions against them. |
'twas for the chastisement of our pride, and for the instruction of our miserable condition and incapacity, that god wrought the perplexity and confusion of the tower of babel. |
by his success, but acting moderately and wisely under the circumstances, and acquiescing in the event. |
elections, as was enjoyed by the citizens of rome; a fourth related to the price of corn, which was to be sold at a lower rate than formerly to the poor; and a fifth regulated the courts of justice, greatly reducing the power of the senators. |
makes life intolerable to the sufferer. then let what we are saying concerning these cases be embodied in a law: if any one finds fault with the established laws respecting testaments, both as to other matters and especially in what relates to marriage, |
now all unmixed and primary bodies are produced by such causes as these. as to the subordinate species which are included in the greater kinds, they are to be attributed to the varieties in the structure of the two original triangles. |
may i have the pleasure, he said, of hearing your opinion? |
thirty one. "those desires which do not lead to pain, if they are not satisfied, are not necessary. it is easy to impose silence on them when they appear difficult to gratify, or likely to produce injury. |
on the same principle also, prudence is more desirable in old age; for no man chooses the young to guide him, because he does not expect them to be prudent. |
to this was added the yet more appalling horror of poppaea beholding the severed head which was conveyed to rome. |
man does hurt contrary to the law (unless by way of requital of hurt), voluntarily, i.e. knowing to whom he does it and wherewith, he acts unjustly. |
by this step it was revealed and published to the world how many infamous citizens we had in the republic? |
for, by thus doing, diogenes and heraclitus, and others like them, deservedly became divine, and were so recognized. |
dem.-draw the perpendicular ph; then, since of, ph are perpendiculars on ab, and op is bisected in i, it is easy to see that ih if. again, since op, og are bisected in i, f; if one pg-that is, if one two the radius. |
and this is the reason that children, the common people, women, and sick folks, are most apt to be led by the ears. |
for i have an idea of figure, size, and situation of solid parts in general, though i have none of the particular figure, size, or putting together of parts, whereby the qualities above mentioned are produced; which qualities i find in that particular |
(two.) from symbols, e.g., from the fact of having read or heard certain words we remember things and form certain ideas concerning them, similar to those through which we imagine things (two. xviii. note). |
secondly, it is impossible of right, that men should do so, because all men being born under government, they are to submit to that, and are not at liberty to begin a new one. |
the contradictions involved in the conception of time or motion, like the infinitesimal in space, were a source of perplexity to the mind of the greek, who was driven to find a point of view above or beyond them. |
if extended substance, they say, is infinite, let it be conceived to be divided into two parts; each part will then be either finite or infinite. if the former, then infinite substance is composed of two finite parts, which is absurd. |
there the veins all meet; it is their centre or house of guard whence they carry the orders of the thinking being to the extremities of his kingdom. |
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