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now a motion that is always shifting its ground from moment to moment can be continuous: but a motion that is repeatedly localized within certain fixed limits cannot be so, since then the same thing would have to undergo simultaneously two opposite |
six. constantly repeated ideas can scarce be lost. |
no more its first vigour and firmness; 'twere better to begin gently and coldly, and to keep one's breath and vigorous efforts for the height and stress of the business. |
def. vi.-a line such as ef, which is perpendicular to a system of concurrent and coplanar lines, is said to be perpendicular to the plane of these lines, and is called a normal to it. |
ought we not to fear and reverence him more than all the rest of the world: and if we desert him shall we not destroy and injure that principle in us which may be assumed to be improved by justice and deteriorated by injustice;--there is such a principle? |
nero's reply was substantially this:- "my being able to meet your elaborate speech with an instant rejoinder is, i consider, primarily your gift, for you taught me how to express myself not only after reflection but at a moment's notice. |
in the first, and as general in the latter. he was, moreover, infinitely desirous to employ his authority with effect upon the war, which made him slight those home-honors and prerogatives. |
as long as the war between the lacedaemonians and athenians lasted, he could find occupation at home; but after the peace, he persuaded his own city that the thracians were injuring the hellenes, and having secured his object, set sail, empowered by the |
got out of the block, he cut away the flat of his own foot, forty five and after that, since he was guarded still by warders, he broke through the wall and so ran away to tegea, travelling during the nights and in the daytime entering a wood and resting |
these can take long views. also those who have parents living, or children, or wives; for these are our own, and the evils mentioned above may easily befall them. |
the following is the modern definition of curve-contact:- when two curves have two, three, four, c., consecutive points common, they have contact of the first, second, third, c., orders. |
especially when thou shalt call to mind this also, that whatsoever is once changed, shall never be again as long as the world endureth. and thou then, how long shalt thou endure? |
service. in short, if they had stuck to the siege, the capture of troy would have cost them less time and less trouble. |
thirdly (c) for destructive purposes, see if it fails to be a property of that of which it is as much a property: for then neither will it be a property of that of which it is as much a property as of the former, while if it be a property of the former, |
anger, as we have said, is eager to punish; and that such a desire should exist in man's peaceful breast is least of all according to his nature; for human life is founded on benefits and harmony, and is bound together into an alliance for the common help |
besides, a view which asserts atomic bodies must needs come into conflict with the mathematical sciences, in addition to invalidating many common opinions and apparent data of sense perception. |
ten. he used to say, too, that speech was the image of actions, and that the king was the mightiest man as to his power; but that laws were like cobwebs-for that if any trifling or powerless thing fell into them, they held it fast; but if a thing of any |
to the like end the gifts of speech and hearing were bestowed upon us; not for the sake of irrational pleasure, but in order that we might harmonize the courses of the soul by sympathy with the harmony of sound, and cure ourselves of our irregular and |
thing should be. but then especially, when thou dost find fault with either an unthankful, or a false man, must thou reflect upon thyself. |
and is it not true that on the whole "woman" has hitherto been most despised by woman herself, and not at all by us?--we men desire that woman should not continue to compromise herself by enlightening us; just as it was man's care and the consideration |
you know the first lines of the iliad, in which the poet says that chryses prayed agamemnon to release his daughter, and that agamemnon flew into a passion with him; whereupon chryses, failing of his object, invoked the anger of the god against the |
laertes had bought her with his own money when she was quite young; he gave the worth of twenty oxen for her, and shewed as much respect to her in his household as he did to his own wedded wife, but he did not take her to his bed for he feared his wife's |
also in my friends, i discover by their productions their inward inclinations; not by arranging this infinite variety of so diverse and unconnected actions into certain species and chapters, and distinctly distributing my parcels and divisions under known |
after this preface let our law run as follows, and may fortune favour us: no landowner among the magnetes, whose city the god is restoring and resettling--no one, that is, of the five thousand forty families, shall become a retail trader either |
are purged away. but the contemporary of plato and socrates was incapable of resisting the power of any analogy which occurred to him, and was drawn into any consequences which seemed to follow. |
'every science is good', 'no science is good'; the others i call contradictories. |
at length as the morning star was beginning to herald the light which saffron-mantled dawn was soon to suffuse over the sea, the flames fell and the fire began to die. |
he that will carefully peruse the history of mankind, and look abroad into the several tribes of men, and with indifferency survey their actions, will be able to satisfy himself, that there is scarce that principle of morality to be named, or, rule of |
four hundred ninety six. law (right) considered as the realisation of liberty in externals, breaks up into a multiplicity of relations to this external sphere and to other persons ( four hundred ninety one, four hundred ninety three seqq.). |
occupiers had imposed upon them the tribute of a talent to the olympian zeus. till the attic war this tribute was paid by the lepreans, who then took the war as an excuse for no longer doing so, and upon the eleans using force appealed to lacedaemon. |
offerings besides, and especially there were in it two pillars, forty seven the one of pure gold and the other of an emerald stone of such size as to shine by night: forty eight and having come to speech with the priests of the god, i asked them how long |
our next point is that that which is without parts cannot be in motion except accidentally: i.e. |
in like manner phocion's language, also, was full of instruction, abounding in happy maxims and wise thoughts, but admitted no embellishment to its austere and commanding brevity. |
and this prerogative that the poets make such a mighty matter of, our erect stature, looking towards heaven our original, |
dem.-from b draw bg perpendicular to the plane df eleven. xi. , and let it meet that plane in g. through g draw gh parallel to ed, and gk to ef. now, since gh is parallel to ed (const.), and ab to ed (hyp.), ab is parallel to gh eleven. ix. . |
the dolonkians then passed along the sacred road through the land of the phokians and of the boeotians, and as no man invited them, they turned aside and came to athens.. |
of the oriental, especially the mohammedan, modes of envisaging god, we may rather say that they represent the absolute as the utterly universal genus which dwells in the species or existences, but dwells so potently that these existences have no actual |
twenty two. this applies to the whole genus. but some persons err as to the character either of themselves, or of the judges, or of their adversaries and not only in actual fact, but often in word. |
prizes are assigned for single combat. five this is the manner of burial among the thracians. |
dionysius wondered much at his greatness of mind, and received his offer with satisfaction. |
fifteen-seventeen de qua quoniam in catone maiore satis multa diximus, illim one hundred fifty three assumes, quae ad hunc locum pertinebunt. |
cause means either what is particular or a genus, or an incidental attribute or a genus of that, and these either as a complex or each by itself; and all six either as actual or as potential. |
now the primary when that has reference to the end of the change is something really existent: for a change may really be completed, and there is such a thing as an end of change, which we have in fact shown to be indivisible because it is a limit. |
for he is hanging between matter and mind; he is under the dominion at the same time both of sense and of abstractions; his impressions are taken almost at random from the outside of nature; he sees the light, but not the objects which are revealed by the |
animal to every swan and to some white thing, and white to every swan, then if we take as premisses that a belongs to all b, and b to all one hundred, a will belong to all one hundred truly: for every swan is an animal. |
nothing that is by chance can be indestructible or ungenerated, since the products of chance and fortune are opposed to what is, or comes to be, always or usually, while anything which exists for a time infinite either absolutely or in one direction, is |
he was at enmity with caesar, but yet no one feared to be his friend, no one shrank from him as though he were blasted by lightning: although he fell from so high a place, yet some one was found to catch him in his lap. |
about the greatest action which the athenians ever did, and which ought to have been the most famous, but, through the lapse of time and the destruction of the actors, it has not come down to us. |
day on which he is determining a suit. regarding then the judges also as magistrates, let us say who are fit to be judges, and of what they are to be judges, and how many of them are to judge in each suit. |
three hundred seventy two. without knowledge there is no meditation, without meditation there is no knowledge: he who has knowledge and meditation is near unto nirvana. |
and he may do so as often as he pleases. |
fire, if set at the centre, should stay there, like earth, since it will be indifferently related to every point on the extremity. nevertheless it will move, as in fact it always does move when nothing stops it, away from the centre to the extremity. |
when one hundred fifty six you are not given a sufficiently distinguished place at table you have begun to be angry with your fellow-guests, with your host, and with him who is preferred above you. idiot! |
both teaching and being taught (the same thing), or both restoring to and being restored to the same health. |
fourteen. let me repeat then, "the clear indication of virtue, to which a mind of like character is naturally attracted, is the beginning of friendship." when that is the case the rise of affection is a necessity. |
but crude and unmeaning as this philosophy is, it exercised a great influence on his successors, not unlike that which locke exercised upon berkeley and berkeley upon hume himself. all three were both sceptical and ideal in almost equal degrees. |
i mean, for instance, that you are now in the heavens because you are in the air and it is in the heavens; and you are in the air because you are on the earth; and similarly on the earth because you are in this place which contains no more than you. |
furnish even to the dry places plenty of good water. |
people can have disappeared in so short a time. what? are those enormous profits to be endured which the household of marcus antonius has swallowed up? |
and if in consequence of this we must say that two things are of equal velocity if they accomplish locomotion over an equal distance in an equal time, we have to admit the equality of a straight line and a circumference. what, then, is the reason of this? |
and it is right to call anything that which nature intends it to be, and which belongs to it, rather than that which it is by constraint and contrary to nature. the evidence of the senses further corroborates this. |
nisus observ'd the discipline, and said: "our eager thirst of blood may both betray; and see the scatter'd streaks of dawning day, foe to nocturnal thefts. no more, my friend; here let our glutted execution end. |
his own sons by cleopatra were to have the style of kings of kings; to alexander he gave armenia and media, with parthia, so soon as it should be overcome; to ptolemy, phoenicia, syria, and cilicia. |
but it may also be shown universally, not only by such reasoning as we advanced in our discussion of principles (though in that passage we have already determined universally the sense in which the existence of an infinite is to be asserted or denied), |
on the other hand by putting to death three men they would not very greatly have damaged the enemy; but when these returned back to hellas, he thought it likely that the hellenes, hearing of his power, would deliver up their freedom to him themselves, |
again, since the angles acb, dfe are xx. the halves of the equal angles aob, dhe, they are equal i. axiom vii. . therefore (def. x.) the segments acb, dfe are similar, and their chords ab, de have been proved equal; therefore xxiv. the segments are equal. |
should rouse you from your grief with more authority if i had first shaken it off myself. i feared, too, lest fortune, though overcome by me, might nevertheless overcome some one of my family. |
again, as the arc of a circle when contracted into a smaller space does not acquire a new part which is convex, but what was there has been contracted; and as any part of fire that one takes will be hot; so, too, it is all a question of contraction and |
on shore one hundred ninety four at casthanaia: and the violence of the storm could not be resisted. |
but it is evidently an inverted order; for vi. viii. are definitions of proportion, and v. is only a test of proportion, and is not a definition but a theorem, and one which, instead of being taken for granted, requires proof. |
--and men there are who will condemn others to death for crimes that they themselves do not repute so much as faults. |
and burnt before his face. however, afterwards in a battle near valentia, he gave great defeat to herennius and perpenna, two commanders among the refugees who had fled to sertorius, and now lieutenants under him, in which he slew above ten thousand men. |
cassius was of an ancient and honourable, though plebeian house, at rome. though he was brought up by his father under a severe training, he won esteem more frequently by his good-nature than by his diligence. |
have to deny that the number of elements is infinite. |
i shall make whatever befals me become a good thing, but i prefer that what befals me should be comfortable and pleasant and unlikely to cause me annoyance: for you need not suppose that any virtue exists without labour, but some virtues need spurs, while |
in fact their explanation of the observations is not consistent with the observations. and the reason is that their ultimate principles are wrongly assumed: they had certain predetermined views, and were resolved to bring everything into line with them. |
to a given, right line (ab) to apply a parallelogram which shall be equal to a given triangle (one hundred), and have one of its angles equal to a given angle (five hundred). |
of the squares of the distances of the orthocentre from the vertices. |
men. to the other months they gave denominations according to their order; so the fifth was called quintilis, sextilis the sixth, and the rest, september, october, november, and december. |
putting in motion a force of marines, he broke up the seditious combination in its very first beginnings. |
when they stretch out their hands towards us." |
every term which possesses a variety of meaning includes those various meanings either owing to a mere coincidence of language, or owing to a real order of derivation in the different things to which it is applied: but, though this may be taken to hold of |
and how can the cause give it that reallity , unless it self have it? |
stilpo having escaped from the burning of his town, where he lost wife, children, and goods, demetrius poliorcetes seeing him, in so great a ruin of his country, appear with an undisturbed countenance, asked him if he had received no loss? |
for an animal is an object of perception or of sight in a particular respect only; for it is in respect of its body that it is perceived and seen, not in respect of its soul, so that-'object of sight' and 'object of perception' could not be the genus of |
then said i: 'verily, thy pleas are plausible--yea, steeped in the honeyed sweetness of music and rhetoric. but their charm lasts only while they are sounding in the ear; the sense of his misfortunes lies deeper in the heart of the wretched. |
dem.-let a be the centre of one of the circles. join ap, and produce it to meet the second circle again in e. i say the centre of the second circle is in the line pe. if not, let it be elsewhere, as at b. |
he can, upon the supposition that that revolution has proceeded after the same manner whilst he was asleep or thought not, as it used to do at other times, he can, i say, imagine and make allowance for the length of duration whilst he slept. |
have something which they hide--namely, intellect. |
if then we are to look to the end and then pronounce the man blessed, not as being so but as having been so at some previous time, surely it is absurd that when he is happy the truth is not to be asserted of him, because we are unwilling to pronounce the |
nineteen. what say you to this? if these are deities, which we worship and regard as such, why are not serapis and isis two hundred fifty five placed in the same rank? and if they are admitted, what reason have we to reject the gods of the barbarians? |
(one) it is not absurd that the actualization of one thing should be in another. teaching is the activity of a person who can teach, yet the operation is performed on some patient-it is not cut adrift from a subject, but is of a on b. |
or thus: produce ba to five hundred, and make ad bc. on db describe the square dbef. cut off bg, ei, fl each equal to bc. through a and i draw lines parallel to df, and through g and fifty, lines parallel to ab. |
nineteen the proof of this rests on the represented unity of intuition, by means of which an object is given, and which always includes in itself a synthesis of the manifold to be intuited, and also the relation of this latter to unity of apperception. |
we need not a whale, elephant, or a crocodile, nor any such-like animals, of which one alone is sufficient to dispatch a great number of men, to do our business; lice are sufficient to vacate sylla's dictatorship; and the heart and life of a great and |
now to investigate whether being is one and motionless is not a contribution to the science of nature. |
and i, having burnt all his books, and torn up all his papers, came to athens and applied myself to the study of philosophy:- |
pansa summoned the senate to receive the report of the ambassador, when cicero made a severe speech, proposing very vigorous measures against antonius, which, however, galenus and his party were still numerous enough to mitigate very greatly; and even |
for to imagine that the archetype was created would be blasphemy, seeing that the world is the noblest of creations, and god is the best of causes. |
"if tangents be drawn to a circle, at the angular points of an inscribed polygon of any number of sides, they will form a regular polygon of the same number of sides circumscribed to the circle." |
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