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by a motion that is numerically one i mean a motion that proceeds from something numerically one and the same to something numerically one and the same in a period of time numerically one and the same: for a motion may be the same generically, |
the outer and the inner sphere cross one another and meet again at a point opposite to that of their first contact; the first moving in a circle from left to right along the side of a parallelogram which is supposed to be inscribed in it, the second also |
nineteenth year of the war-arrival of demosthenes-defeat of the athenians at epipolae-folly and obstinancy of nicias |
all things go the wrong way and cease to give nourishment to the body, no longer preserving their natural courses, but at war with themselves and destructive to the constitution of the body. |
"in the third watch of the night when the stars had shifted their places, jove raised a great gale of wind that flew a hurricane so that land and sea were covered with thick clouds, and night sprang forth out of the heavens. |
objects of mathematics they exist or not, and if they exist, how they exist. |
but, nothing is determined of the manner or action, and it may as truly (for aught we know) be termed "impulse," or "protrusion," as "attraction." |
the higher of the two, which is the seat of courage and anger, lies nearer to the head, between the midriff and the neck, and assists reason in restraining the desires. |
this-why is it that some things are not always at rest, and the rest always in motion? |
that the world is neither eternal nor infinite; i answer, that to my present purpose it is not needful, in this place, to make use of arguments to evince the world to be finite both in duration and extension. |
audire utile est, idem three hundred ten mihi dicere necesse est." |
desiring your majesty a happiness more tangible and less hazardous, and that you may be beloved rather than feared by your people, and believing that your welfare and theirs are of necessity knit together, i rejoice to think that the progress which you |
but should one follow them further-and ever further and further on, thinkest thou, dwarf, that these roads would be eternally antithetical?"- |
but before they could well come to blows with the first ranks, the barbarians shrunk back, and were hotly pursued by alexander, who drove those that fled before him into the middle of the battle, where darius himself was in person, whom he saw from a |
but as soon as it drew towards day, xenophon despatched the youngest of his men to the sick folk behind, with orders to make them get up and force them to proceed. |
sixty nine kuperou : it is not clear what plant is meant. |
but perhaps even this is impossible, that it should move at all; the same reason which showed that in the void all things are incapable of moving shows that the void cannot move, viz. the fact that the speeds are incomparable. |
dion had a friend called callippus, an athenian, who, plato says, first made acquaintance and afterwards obtained familiarity with him, not from any connection with his philosophic studies, but on occasion afforded by the celebration of the mysteries, and |
: :: a : c therefore - a c . in like manner, - b c ; therefore ----- a b ---two-- c; but a b c i. xlvii. . therefore ; that is, the sum of the figures on the sides is equal to the figure on the hypotenuse. |
the humour of tiberius is ridiculous, but yet common, who was more solicitous to extend his renown to posterity than to render himself acceptable to men of his own time. |
consider, then; is it better to go and meet the foe with arms advanced, or with arms reversed to watch him as he assails us on our rear? |
occurrence of coming to-be, because it is such as to change from contrary to contrary and because, in substances, the coming-to-be of one thing is always a passing-away of another, and the passing-away of one thing is always another's coming-to-be. |
had i taken the usual course, i should never have been able to bring my colleague round. what says the military classic-'swoop down on the market-place and drive the men off to fight.' this passage does not occur in the present text of sun tzu. |
there is a great heap of dead men's bones lying all around, with the flesh still rotting off them. |
either living i will uphold the loyalty of the legions, or pierced to the heart i will hasten on your repentance." |
command of their forces and the enjoyment of their entire confidence, was in a very different position from alcibiades, whom the lacedaemonians did not so much wish to adopt into their service, as to use, and then abandon. |
very end of the island, towards pylos, which was precipitous on the sea-side and very difficult to attack from the land, and where there was also a sort of old fort of stones rudely put together, which they thought might be useful to them, in case they |
dem.-since a : b :: b : c, we have a- b b- c. in like manner, b c a b. hence, multiplying a- c a c. therefore, if a be greater than c, a is greater than c; if equal, equal; if less, less. |
which is an opinion so false, that i am vexed it could ever enter into the understanding of a man that was honoured with the name of philosopher. |
however it happened, none of his physicians would venture to give him any remedies, they thought his case so desperate, and were so afraid of the suspicions and ill-will of the macedonians if they should fail in the cure; till philip, the acarnanian, |
divides each pair of opposite sides into inversely proportional segments; is divided by each pair of opposite lines into segments which, measured from the centre, are proportional to the sides; is divided by both pairs of opposite sides into segments |
we see nothing like this in the case of inanimate things, which are always set in motion by something else from without: the animal, on the other hand, we say, moves itself: therefore, if an animal is ever in a state of absolute rest, we have a motionless |
a few days afterwards the emperor proposed to the senate to confer the priesthood on vitellius, veranius and servaeus. to fulcinius he promised his support in seeking promotion, but warned him not to ruin his eloquence by rancour. |
and being asked by some one in what respect his son would be better if he received a careful education, he replied, "if he gets no other good, at all events, when he is at the theatre, he will not be one stone sitting upon another." |
yet this causes surprise, and it is thought impossible that something should come to be in the way described from what is not. |
superior to all such accidents as happen to all men indifferently, whether they be good or bad; continence they consider a disposition which never abandons right reason, or a habit which never yields to pleasure; endurance they call a knowledge or habit |
"videas desertaque regna pastorum, et longe saltus lateque vacantes." |
hence a b is the same multiple of c that a b is of c. |
a quick and earnest way of speaking, as mine is, is apt to run into hyperbole. there is nothing to which men commonly are more inclined than to make way for their own opinions; where the ordinary means fail us, we add command, force, fire, and sword. |
twenty four cogitata a b h a b p, edd.; cogitatu c, cogitato alii, madvig (ad de fin. p. six hundred ninety six). |
whilst he was consulting to seize upon some post in sicyonia, from whence he might make war upon the tyrant, there came to argos a certain sicyonian, newly escaped out of prison, brother to xenocles, one of the exiles, who being by him presented to aratus |
for that which is in succession is in succession to a particular thing, and is something posterior: for one is not 'in succession' to two, nor is the first day of the month to be second: in each case the latter is 'in succession' to the former. |
some, however, say that hoplites does not run by haliartus, but is a watercourse near coronea, falling into the river philarus, not far from the town in former times called hoplias, and now isomantus. |
as further evidence in favour of this they quote the case of elephants, a species occurring in each of these extreme regions, suggesting that the common characteristic of these extremes is explained by their continuity. |
the even carriage between two factions, proceedeth not always of moderation, but of a trueness to a man's self, with end to make use of both. |
two. if two triangles have two sides of one respectively equal to two sides of the other, and the contained angles supplemental, their areas are equal. |
this, then, is a catalogue of all the originally pure conceptions of the synthesis which the understanding contains a priori, and these conceptions alone entitle it to be called a pure understanding; inasmuch as only by them it can render the manifold of |
is actually of a certain size, and motion is thought to be a sort of actuality, but incomplete, the reason for this view being that the potential whose actuality it is is incomplete. this is why it is hard to grasp what motion is. |
for if evils have no admission into us but by the judgment we ourselves make of them, it should seem that it is, then, in our own power to despise them or to turn them to good. |
further, see if he has rendered a single common definition of terms that are used ambiguously. |
consciousness. for, as it is evident in the instance i gave but now, if the consciousness went along with the little finger when it was cut off, that would be the same self which was concerned for the whole body yesterday, as making part of itself, whose |
nay, sir, stand in fight with me yourself, that you may learn what manner of jove-begotten man am i that have come hither. jove first begot minos, chief ruler in crete, and minos in his turn begot a son, noble deucalion. |
of the particles coming from other bodies which fall upon the sight, some are smaller and some are larger, and some are equal to the parts of the sight itself. those which are equal are imperceptible, and we call them transparent. |
that is why, even if there were to be water which had not a container, the parts of it, on the one hand, will be moved (for one part is contained in another), while, on the other hand, the whole will be moved in one sense, but not in another. |
therefore ab is greater than four hundred. |
before the people, to whom they had a communication to make, until compelled to do so by the entreaties of the mantineans and eleans, who were still at argos. |
one hundred fifteen. state and prove the corresponding theorems for the centres of the escribed circles. |
but the limit as fixed by the nature of the drama itself is this: the greater the length, the more beautiful will the piece be by reason of its size, provided that the whole be perspicuous. |
now, it is evident that if ma- nb is greater than unity, mc- nd is greater than unity; but if ma- nb is greater than unity, ma is greater than nb; and if mc- nd is greater than unity, mc is greater than nd. |
wish of every man being that he could speak himself, the next to rival those who can speak by seeming to be quite up with their ideas by applauding every hit almost before it is made, and by being as quick in catching an argument as you are slow in |
acquire a robust and almost unalterable constitution. |
but if there were a man who had sufficient force, he would shake off and break through, and escape from all this; he would trample under foot all our formulas and spells and charms, and all our laws which are against nature: the slave would rise in |
dem.-because a is the centre of the circle bcd, ac is equal to ab (def. xxxii.). again, because b is the centre of the circle ace, bc is equal to ba. hence we have proved. |
such is the artificial contrivance of this mighty machine of nature that, whilst its motions and various phenomena strike on our senses, the hand which actuates the whole is itself unperceivable to men of flesh and blood. |
i shall make account of none but such men as these, their testimony and experience. let us examine how far they have proceeded, and where they stopped. the errors and defects that we shall find amongst these men the world may boldly avow as their own. |
profound, sleep comes over us scarce disturbed by dreams; but where the greater motions still remain, of whatever nature and in whatever locality, they engender corresponding visions in dreams, which are remembered by us when we are awake and in the |
for he, although he is eminent above all men in every description of oratory, still he does not always satisfy my ears; so greedy and capacious are they, and so unceasingly desiring something vast and infinite. |
common treasure onely; which fayling he hath no remedy, nor complaint, but against himselfe, that being privy to the acts of the assembly, and their means to pay, and not being enforced, did neverthelesse through his own folly lend his mony. |
indeed, the point we have raised constitutes a problem even for those who generate the 'elements' out of one another. in what manner does anything other than, and beside, the 'elements' come-to-be out of them? let me illustrate my meaning. |
if then in the case of the earth, supposed to be infinite, it is at rest, not because it is infinite, but because it has weight and what is heavy rests at the centre and the earth is at the centre, similarly the infinite also would rest in itself, not |
the boundaries of macedonia are well defined; the condition of the proconsul is well known; the amount of his army, if he has any at all, is fixed. but what had antonius to do at all with illyricum and with the legions of vatinius? |
suppose 'aquilinity' to be curvature in the nose or flesh, and flesh to be the matter of aquilinity. suppose further, that all flesh came together into a single whole of flesh endowed with this aquiline quality. |
as for example, there was a time, when in england a man might enter in to his own land, (and dispossesse such as wrongfully possessed it) by force. |
eleven cities were rivals for the honour, of which they were all equally ambitious, though they differed widely in resources. |
so that the enemy could hear them; and those in their immediate proximity actually took to their heels, left their quarters, and decamped, as was plain enough next morning, when not a beast was to be seen, nor sign of camp or wreath of smoke anywhere in |
now the moment in which it has changed cannot be the same as that in which it is at a (since in that case it would be in a and b at once): for we have shown above that that that which has changed, when it has changed, is not in that from which it has |
they differ. tell me, then, whether you agree with and assent to my first principle, that neither injury nor retaliation nor warding off evil by evil is ever right. and shall that be the premiss of our argument? or do you decline and dissent from this? |
that there are any favourers of atheism or the manichean heresy to be found. |
nor will this be very difficult to you, if you call to mind the actions and lives of the men i have named. |
i however am bound to report that which is reported, though i am not bound altogether to believe it; and let this saying be considered to hold good as regards every narrative in the history: for i must add that this also is reported, namely that the |
adore them if they do not absolutely hate it. |
dem.-one. produce bd (post. ii.) to meet ac in e. then, in the triangle bae, the sum of the sides ba, ae is greater than the side be xx. : to each add ec, and we have the sum of ba, ac greater than the sum of be, ec. |
as for vicissitudes of fortune, and other disappointments connected with worldly circumstances, these are principally the effect either of gross imprudence, of ill-regulated desires, or of bad or imperfect social institutions. |
one hundred seventy four. now the carians were reduced to subjection by harpagos without any brilliant deed displayed either by the carians themselves or by those of the hellenes who dwell in this land. |
chap. eleven. the master said to tsze-hsia, 'do you be a scholar after the style of the superior man, and not after that of the mean man.' chap. twelve. tsze-yu being governor of wu-ch'ang, the master said to him, 'have you got good men there?' |
for instance, is it necessary that solstices shall come-to-be, i.e. impossible that they should fail to be able to occur? |
prop. thirteen.-problem. to inscribe a circle in a regular pentagon (abcde). |
for clearly, if the soul be fire, only such modifications will happen to it as characterize fire qua fire: while if it be compounded out of the elements', only the corporeal modifications will occur in it. |
beginning at the head and extending through the whole of the trunk. |
he was at first alarmed under the impression that treachery was intended, but when they pledged their honour that they had come to restore to him his dominion, his spirit revived, and he asked what the sudden change meant. |
and cluvius rufus says, imperial letters, such as are sent with couriers, went into spain with the name of nero affixed adoptively to that of otho; but as soon as he perceived this gave offense to the chief and most distinguished citizens, it was omitted. |
that the sooner she could try her fortune again the better. |
particular personality, a sensibility common to its members, and a force and will of its own making for its preservation. |
for even if it were latin to use such words, i should not like to say specierum and speciebus . and we have often occasion to use these cases. |
thinner, and rarefies more readily, and in a higher degree, than the blood which proceeds immediately from the hollow vein? |
plainly tells us that all our ideas or notions contain in them some truth; for otherwise it could not be that god, who is wholly perfect and veracious, should have placed them in us. |
words give rise to dispute if they are ambiguous or inconsistent. |
moreover (b) their procedure is virtually the same as if one were to treat the saw (and the various instruments of carpentry) as 'the cause' of the things that come-to-be: for the wood must be divided if a man saws, must become smooth if he planes, and so |
now ab cannot be without parts: for there cannot be motion in that which is without parts, because the moving thing would necessarily have been already moved for part of the time of its movement: and that which is coming to a stand has been shown to be in |
'tis now many years since that my thoughts have had no other aim and level than myself, and that i have only pried into and studied myself: or, if i study any other thing, 'tis to apply it to or rather in myself. |
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