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as downward movement is to a stone, will be merely accelerated by an external force, while an unnatural movement will be due to the force alone. in either case the air is as it were instrumental to the force. |
the desire to maintain them unaltered seems to be the origin of what at first sight is very surprising to us-the intolerant zeal of plato against innovators in religion or politics (laws); although with a happy inconsistency he is also willing that the |
time also is continuous. by continuous i mean that which is divisible into divisibles that are infinitely divisible: and if we take this as the definition of continuous, it follows necessarily that time is continuous. |
when he was sick, showed one of his friends that came to visit him, an amulet or charm that the women had hung about his neck; as much as to say, that he was very sick indeed when he would admit of such a foolery as that was. |
the act of him who nurses his wrath is more voluntary, and therefore more culpable. the degree of culpability depends on the presence or absence of intention, to which the degree of punishment should correspond. |
"and yet as sensible men, if we call in allies and court danger, it should be in order to enrich our different countries with new acquisitions, and not to ruin what they possess already; and we should understand that the intestine discords which are so |
affairs are generally good-for-nothing men, with whom it is discreditable to be compared, and miserable and dangerous to contend, especially when the multitude is in an excited state. |
there should be an interval which is other than the bodies which are moved. |
then ad : db :: the triangle ade : bde i. . and ae : ec :: the triangle ade : cde i. ; but ad : db :: ae : ec (hyp.). hence ade : bde :: ade : cde. therefore five. ix. |
sixty six. if a, b, one hundred, five hundred be four collinear points, find a point o in the same line with them such that oa.od ob.oc. |
from this it evidently follows that coming to a stand must occupy a period of time: for the motion of that which is in motion occupies a period of time, and that which is coming to a stand has been shown to be in motion: consequently coming to a stand |
from this side except on the supposition of a moral author of the world. |
xi. when four magnitudes are continual proportionals, the first is said to have to the fourth the triplicate ratio of that which it has to the second. |
to receive thy merited reward, the first assay of this right hand provoked, since first that tongue, inspired with contradiction, durst oppose a third part of the gods, in synod met their deities to assert; who, while they feel vigour divine within them, |
for i deem that the true votary of philosophy is likely to be misunderstood by other men; they do not perceive that he is always pursuing death and dying; and if this be so, and he has had the desire of death all his life long, why when his time comes |
for the planters are to blame rather than the plants, the educators and not the educated. still, we should endeavour to attain virtue and avoid vice; but this is part of another subject. |
causes should first be tried before a court of neighbours: if the decision is unsatisfactory, let them be referred to a higher court; or, if necessary, to a higher still, of which the decision shall be final. |
let a : b :: c : d, then b : a :: d : c. |
we must admit, however, that neither wild beasts nor any other creature except man is subject to anger: for, whilst anger is the foe of reason, it nevertheless does not arise in any place where reason cannot dwell. |
just as they say that the sea, which is of all things the most useful to men, is by blasts of winds falling upon it prevented from doing according to its own nature. |
one hundred ten epi touto , the reading of the aldine edition. the mss. have epi touto . stein suggests dia touto . |
and this, as i conceive, was the quality which, in addition to his natural gifts, pericles acquired from his intercourse with anaxagoras whom he happened to know. |
these are the elements of necessity which the creator received in the world of generation when he made the all-sufficient and perfect creature, using the secondary causes as his ministers, but himself fashioning the good in all things. |
all simple motion, then, must be motion either away from or towards or about the centre. this seems to be in exact accord with what we said above: as body found its completion in three dimensions, so its movement completes itself in three forms. |
so that, when the others commended philip for his able speaking, his beautiful person, nay, and also for his good companionship in drinking, demosthenes could not refrain from caviling at these praises; the first, he said, was a quality which might well |
on the one hand feeling has to be regarded as the dull and confused stirring of an almost infinite sympathy with the world-a pulse which has come from the far-distant movements of the universe, and bears with it, if but as a possibility, the wealth of an |
since 'nature' has two senses, the form and the matter, we must investigate its objects as we would the essence of snubness. that is, such things are neither independent of matter nor can be defined in terms of matter only. |
for, since it has left that from which it has changed and must be somewhere, it must be either in that to which it has changed or in something else. |
but in egypt the traditions of our own and other lands are by us registered for ever in our temples. the genealogies which you have recited to us out of your own annals, solon, are a mere children's story. |
(one) now it has three dimensions, length, breadth, depth, the dimensions by which all body also is bounded. but the place cannot be body; for if it were there would be two bodies in the same place. |
the number and order of them is, whereof it is made up. |
three. if the base of a triangle be given, and the sum of the sides, the rectangle contained by the perpendiculars from the extremities of the base on the external bisector of the vertical angle is given. |
and we, socrates, replied simmias, shall be charmed to listen to you. |
thereon the elders of the aetolians besought meleager; they sent the chiefest of their priests, and begged him to come out and help them, promising him a great reward. |
but first, a long succession must ensue; and his next son, for wealth and wisdom famed, the clouded ark of god, till then in tents wandering, shall in a glorious temple enshrine. |
the officers and generals at the customary rate; besides this i will honour those who show special merit. |
its womb some of its young covered with fur and others bare; and while one is just being shaped in the matrix, another is being conceived. |
the moment had gone by, the athenians being defeated and gone, and themselves not equal to the execution of brasidas's designs. |
i have contemplated the imprisonment of the offender, rather than the seizure of his goods,-though both will serve the same purpose,-because they who assert the purest right, and consequently are most dangerous to a corrupt state, commonly have not spent |
he was very intimate with clodius at the time of his tribuneship; he, who now enumerates the kindnesses which he did me. he was the firebrand to handle all conflagrations; and even in his house he attempted something. |
of the passions that stir the heart of man, there is one which makes the sexes necessary to each other, and is extremely ardent and impetuous; a terrible passion that braves danger, surmounts all obstacles, and in its transports seems calculated to bring |
sedition, when just ready to break out. for the most warlike and best-peopled countries of all italy formed a confederacy together against rome, and were within a little of subverting the empire; as they were indeed strong, not only in their weapons and |
acquired, and would not cease from his toils and transformations until he followed the revolution of the same and the like within him, and overcame by the help of reason the turbulent and irrational mob of later accretions, made up of fire and air and |
thus 'sitting' is an example of a separable attribute, while 'snubness' contains the definition of 'nose', to which we attribute snubness. |
which perhaps are not all the same as i comprehend them by my sense (for perception by sense is in many things very obscure and confused ) but those things at least, which i clearly and distinctly understand, that is to say, all those things which are |
there is no need to suppose that he drew from life; or that his knowledge of tyrants is derived from a personal acquaintance with dionysius. |
if the bile, which is only stale blood, or liquefied flesh, comes in little by little, it is congealed by the fibres and produces internal cold and shuddering. |
common view that the earth is in the middle. even as it is, there is nothing in the observations to suggest that we are removed from the centre by half the diameter of the earth. |
only by the arguments already set forth but also by a consideration of the views of those who differ from us in providing for its generation. |
mens ghosts, and fairies, and other matter of old wives tales. thirdly, by mixing with the scripture divers reliques of the religion, and much of the vain and erroneous philosophy of the greeks, especially of aristotle. |
all things pall after a while-sleep, love, sweet song, and stately dance-still these are things of which a man would surely have his fill rather than of battle, whereas it is of battle that the trojans are insatiate." |
and of others which are much more important. |
against their superior experience set your superior daring, and against the fear induced by defeat the fact of your having been then unprepared; remember, too, that you have always the advantage of superior numbers, and of engaging off your own coast, |
it is clear, then, from what has been said that time contains something indivisible, and this is what we call a present. |
the next day they took better order for their march, and the parthians, who thought they were marching rather to plunder than to fight, were much taken aback, when they came up and were received with a shower of missiles, to find the enemy not |
"thus did we converse, and anon proserpine sent up the ghosts of the wives and daughters of all the most famous men. they gathered in crowds about the blood, and i considered how i might question them severally. |
three. through one of two non-coplanar lines draw a plane parallel to the other. |
the phenomenon depends upon the fact that some things are such as to be (a) reciprocally susceptible and (b) readily adaptable in shape, i.e. easily divisible. |
any provision by way of exchange or merchandise, such are shepherds, husband-men, b robbers, fishermen, and hunters: some join different employments together, and thus live very agreeably; supplying those deficiencies which were wanting to make their |
the seat of the oracle of zeus, but he himself with the remainder of his army went on against the ethiopians. |
"the passage of the wheels in the narrow turning of the street"--juvenal, iii. two hundred thirty six. |
now we say that (a) the continuous is one or that (b) the indivisible is one, or (c) things are said to be 'one', when their essence is one and the same, as 'liquor' and 'drink'. |
but when the prince declares himself frankly in favour of one side, if the one to whom you adhere conquers, even if he is powerful and you remain at his discretion, he is under an obligation to you and friendship has been established, and men are never so |
this generation inclines a little to congratulate itself on being the last of an illustrious line; and in boston and london and paris and rome, thinking of its long descent, it speaks of its progress in art and science and literature with satisfaction. |
antony, as consul, was one of those who ran this course, and when he came into the forum, and the people made way for him, he went up and reached to caesar a diadem wreathed with laurel. |
in the expedition of the emperor charles five. |
bf is a right line; and, since it is coplanar with bd, be, which are each perpendicular to ab, it is eleven. iv. perpendicular to ab. therefore the angle abf is right; and the angle abc is right (hyp.). |
(thirty seven) cf. plat. "laws," viii. eight hundred thirty nine a; herbst, etc., cf. grotius, "de jure," ii. five, xii. four. |
our theory seems to confirm experience and to be confirmed by it. |
this, o citizens, that i cannot dispose of my own booty as i please!" but lysander, on the contrary, with the rest of the spoil, sent home for public use even the presents which were made him. |
for some things cause motion in only one way, while others can produce either of two contrary motions: thus fire causes heating but not cooling, whereas it would seem that knowledge may be directed to two contrary ends while remaining one and the same. |
your instant arms against the town prepare, the source of mischief, and the seat of war. |
() its reciprocal, to describe a circle about a triangle. |
corbulo too received an apology from mamercus, who was sulla's uncle and stepfather, and the most fluent speaker of that day. |
prop. thirty three.-problem. on a given right line (ab) to describe a segment of a circle which shall contain an angle equal to a given rectilineal angle (ten). |
having got the idea of succession and duration, by reflecting on the train of our own ideas, caused in us either by the natural appearances of those ideas coming constantly of themselves into our waking thoughts, or else caused by external objects |
why are the choicest portions served us and our cups kept brimming, and why do men look up to us as though we were gods? |
and the left right. if, when powerfully experiencing these and similar effects, the revolutions of the soul come in contact with some external thing, either of the class of the same or of the other, they speak of the same or of the other in a manner the |
they left the vanquished their gods as they left them their laws. a wreath to the jupiter of the capitol was often the only tribute they imposed. |
ab .bc .ca a b.b one hundred.one hundred a. |
thus the class that had the smallest number of members had the largest number of centuries, and the whole of the last class only counted as a single subdivision, although it alone included more than half the inhabitants of rome. |
all the time he kept on shouting at the top of his voice and exhorting the danaans. "my friends," he cried, "danaan heroes, servants of mars, be men my friends, and fight with might and with main. |
to return to his clemency: we have many striking examples in the time of his government, when, all things being reduced to his power, he had no more written against him which he had as sharply answered: yet he did not soon after forbear to use his |
first, therefore, observing that the argives, as well out of fear as hatred to the lacedaemonians, sought for protection against them, he gave them a secret assurance of alliance with athens. |
this antalcidas was a spartan, the son of one leon, who, acting for the king's interest, induced the lacedaemonians to covenant to let all the greek cities in asia and the islands adjacent to it become subject and tributary to him, peace being upon these |
and what he proposes by all these curious researches? he is immediately at a loss, and knows not what to answer. |
i mean the placing the figures firm upon their feet, making the hands grasp, and fastening the eyes on the spot where they should look. |
at the same moment he embraced the younger of his two grandsons with a flood of tears, and, noting the savage face of the other, said, "you will slay this boy, and will be yourself slain by another." |
thirty two. that we are to avoid pleasures, even at the expense of life. |
but much the safest plan is to speak of them as follows:-anything which we see to be continually changing, as, for example, fire, we must not call 'this' or 'that,' but rather say that it is 'of such a nature'; nor let us speak of water as 'this'; but |
penal are those, which declare, what penalty shall be inflicted on those that violate the law; and speak to the ministers and officers ordained for execution. |
thus it was one of the orders of the thirty tyrants, that the hustings in the assembly, which had faced towards the sea, should be turned round towards the land; implying their opinion that the empire by sea had been the origin of the democracy, and that |
twelve. how many circles can be described to touch three lines forming a triangle? |
which is now called the quirinal, and that he had commanded him to inform the people that they should build him a temple on that same hill, and offer him sacrifices under the name of quirinus. |
they were ancient customs, some of them older probably than the settlement in laconia, of which the origin is unknown; they occasionally received the sanction of the delphic oracle, but there was a still stronger obligation by which they were |
since according to common agreement there is nothing outside and separate in existence from sensible spatial magnitudes, the objects of thought are in the sensible forms, viz. both the abstract objects and all the states and affections of sensible things. |
hence it is that wisdom is the soundness of the mind, folly a sort of unsoundness, which is insanity, or a being out of one's mind: and these are much better expressed by the latin words than the greek, which you will find the case also in many other |
athenian: enough of this. and what, then, is to be regarded as the origin of government? will not a man be able to judge of it best from a point of view in which he may behold the progress of states and their transitions to good or evil? |
my meaning may be learned from homer; he, you know, feeds his heroes at their feasts, when they are campaigning, on soldiers' fare; they have no fish, although they are on the shores of the hellespont, and they are not allowed boiled meats but only roast, |
twenty seven this is the reading of the mss., but it is not consistent with the distance given in ch. one hundred one, nor with the actual facts: some editors therefore read "four" instead of "fourteen". |
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