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we must consider also the other forms of predication. |
two. it is an interesting and not unimportant question which is touched upon by martin, whether the atlantis of plato in any degree held out a guiding light to the early navigators. he is inclined to think that there is no real connexion between them. |
thus far, by fate's decrees and thy commands, thro' ambient seas and thro' devouring sands, our exil'd crew has sought th' ausonian ground; and now, at length, the flying coast is found. |
every other art can instruct or persuade about its own particular subject-matter; for instance, medicine about what is healthy and unhealthy, geometry about the properties of magnitudes, arithmetic about numbers, and the same is true of the other arts and |
history tells of the downfall of kings and their ministers. tyrants go in fear of their lives. --ch. six. ( d ) fame conferred on the unworthy is but disgrace. the splendour of noble birth is not a man's own, but his ancestors'.--ch. seven. |
seventeen. give euclid's definition of proportion. |
lying with his wife. accordingly intaphrenes did not think it fit that any one should announce his coming; but as he was one of the seven, he desired to enter. |
fought about the shadow of helen at troy in ignorance of the truth. |
it in their fabulous way upon animate necessity. |
two. nor is it sufficient to possess this virtue as if it were some kind of art, unless we put it in practice. an art, indeed, though not exercised, may still be retained in knowledge; but virtue consists wholly in its proper use and action. |
twenty one. if a, b, one hundred be three points in the circumference of a circle, and five hundred, e the middle points of the arcs ab, ac; then if the line de intersect the chords ab, ac in the points f, g, af is equal to ag. |
if the commensurate universal is unequivocal-then the universal will possess being not less but more than some of the particulars, inasmuch as it is universals which comprise the imperishable, particulars that tend to perish. |
that little i have done for it, is no more at my own disposal; it may know many things that are gone from me, and from me hold that which i have not retained; and which, as well as a stranger, i should borrow thence, should i stand in need. |
m. not to me only; but i apprehend, though i have often been surprised at it, that it appeared so to our ancestors many ages before socrates; from whom is derived all that philosophy which relates to life and morals. |
expansion of the same matter. there are two types in each case, both in the dense and in the rare; for both the heavy and the hard are thought to be dense, and contrariwise both the light and the soft are rare; and weight and hardness fail to coincide in |
two. he was a pupil of some of the magi and chaldans, whom xerxes had left with his father as teachers, when he had been hospitably received by him, as herodotus informs us; one hundred twenty seven and from these men he, while still a boy, learned the |
"by these footsteps a sagacious mind many easily find all other matters (are sufficient to enable one to learn the rest well.)" --lucretius, i. four hundred three. |
seven. if the opposite sides of a hexagon be equal and parallel, its diagonals are concurrent. |
this is the natural memory which is allied to sense, such as children appear to have and barbarians and animals. it is necessarily limited in range, and its limitation is its strength. |
socrates: you seem not to be aware that the whole of our discussion from the very beginning has been a search after knowledge, of which we are assumed not to know the nature. |
they say that to do injustice is, by nature, good; to suffer injustice, evil; but that the evil is greater than the good. |
and in general, all that which is termed the incontinence of pleasure and is deemed a reproach under the idea that the wicked voluntarily do wrong is not justly a matter for reproach. |
socrates: do you mean that i am not in earnest? |
(two). as to things good or bad in their consequences, and by the aptness that is in them to procure us good or evil in the future, we judge amiss several ways. |
for it must be noted, that men must either be caressed or else annihilated; they will revenge themselves for small injuries, but cannot do so for great ones; the injury therefore that we do to a man must be such that we need not fear his vengeance. |
now because ec is equal to ea (const.), and ef is equal to eb, the triangles cef, aeb have the sides ce, ef in one equal to the sides ae, eb in the other; and the angle cef equal to aeb xv. . therefore iv. |
the same pace of a horse seems to me one while hard, and another easy; and the same way one while shorter, and another longer; and the same form one while more, another less agreeable: i am one while for doing every thing, and another for doing nothing at |
stay at the office till night, and was the first that came to the council-house, and the last that left it. and if no public business engaged him, it was very hard to have access, or to speak with him, he being retired at home and locked up. |
in parts only, which is a species of motion imparted by physic. this should only be resorted to by men of sense in extreme cases; lesser diseases are not to be irritated by medicine. |
functions: thus seeing and feeling must be his first condition, which would be common to him and all other animals. |
now (a) the change or movement of each thing is only in the thing which changes or where the thing itself which moves or changes may chance to be. but time is present equally everywhere and with all things. |
if there be two lines (a, bc), one of which is divided into any number of parts (bd, de, ec), the rectangle contained by the two lines (a, bc), is equal to the sum of the rectangles contained by the undivided line (a) and the several parts of the divided |
if they fled from their native land. having resolved upon this, they parted into two bodies, and making their numbers equal they fought with one another: and when these had all been killed by one another's hands, then the people of the kimmerians buried |
these threw great stones at their assailants in defence of themselves their tents and their ships. |
to another, i replied, i might have a difficulty in explaining; but i am sure that you will admit a proposition which one am about to make. |
he imagines himself to have changed the relation of the human mind towards god and nature; they remain the same as before, though he has drawn the imaginary line by which they are divided at a different point. |
do you also show not your theorems to the uninstructed, but show the acts which come from their digestion. |
but, by reading between the lines, an attentive student can detect in it a great deal of the positive doctrine afterwards incorporated in the social contract . |
even if it is true as true can be that the whole is not moved (for what is fixed by itself and is in itself must be immovable), yet we must explain why it is not its nature to be moved. it is not enough just to make this statement and then decamp. |
this, however, does not touch our argument. the maximum may be determined either in the power or in its object. the application of this is plain. superior sight is sight of the smaller body, but superior speed is that of the greater body. |
these pleasant walks? here let us live, though in fallen state, content. |
cleinias: i suppose, megillus, that this companion virtue of which the stranger speaks, must be temperance? |
garlands on their heads, and a great company with them, hymning their praises and calling them by sweet names; insolence they term breeding, and anarchy liberty, and waste magnificence, and impudence courage. |
i am sorry for several gentlemen who, through the folly of their physicians, have in their youth and health wholly shut themselves up: it were better to endure a cough, than, by disuse, for ever to lose the commerce of common life in things of so great |
then we have a mc, and a mc, b nc, and b nc. therefore (ab) (mn)c, and (ab) (mn)c. hence ab is the same multiple of c that a b is of c. |
for she herself alone can affect and move herself, and according as the dogmata and opinions are, which she doth vouchsafe herself; so are those things which, as accessories, have any co-existence with her. |
one. the sum of the squares on the segments of a line of given length is a minimum when it is bisected. |
the foregoing is an easy proof of the converse of the theorem which is contained in euclid's celebrated fifth definition. |
also able to be ruled. consequently, the empire of the world has almost always remained in the hands of those nations who enjoy a milder climate. those who dwell near the frozen north have uncivilized tempers- |
likewise, also, it is really necessary whenever he (the questioner) first, by an induction made by means of the view laid down, arrives at a certain statement and then tries to demolish that statement: for when once this has been demolished, the view |
greater them the angle (five hundred) contained by the sides of the other. |
five. if two right-angled s abc, abd be on the same hypotenuse ab, and the vertices one hundred and five hundred be joined, the pair of angles subtended by any side of the quadrilateral thus formed are equal. |
twenty five. the line joining the middle points of the diagonals of a quadrilateral circumscribed to a circle- |
some affirm that sentence was passed in the presence of artaxerxes; that darius, after he had been convicted by clear evidence, falling prostrate before him, did humbly beg his pardon; that instead of giving it, he, rising up in rage and drawing his |
if then (one) the body, whose movement is circular, is fire or some other element, its natural motion must be the contrary of the circular motion. but a single thing has a single contrary; and upward and downward motion are the contraries of one another. |
for this the king of parthia afterwards put orobazus to death. some people commended sylla for his lofty carriage towards the barbarians; others again accused him of arrogance and unseasonable display. |
and yet we must not be entirely careless of our reputation, nor regard the good opinion of our fellow-citizens as a weapon which we can afford to despise in conducting the business of our life, however lowering it may be to tout for it by flattery and |
after taking sollium, a town belonging to corinth, and presenting the city and territory to the acarnanians of palaira, they stormed astacus, expelled its tyrant evarchus, and gained the place for their confederacy. |
for many days ensuing. afterwards, they burnt them down to the ground and demolished them, being incensed at those who kept the capitol, because they would not yield to summons; but, on the contrary, when assailed, had repelled them, with some loss, from |
archon." he was well liked by the common people, would salute every particular citizen by his own name, and always show himself a just judge in questions of business between private men; he said to simonides, the poet of ceos, who desired something of |
dem.-the ratio a : b a- b, and the ratio of ma : mb ma- mb; but since the value of a fraction is not altered by multiplying its numerator and denominator by the same number, |
she sees a full light, which illuminates certain places; but that light borders upon the most profound darkness. and between these she is so dazzled and confounded, that she scarcely can pronounce with certainty and assurance concerning any one object. |
after being chosen as the leaders of the ionians and of the other allies of athenian origin, to punish the mede, the athenians accused some of failure in military service, some of fighting against each other, and others, as the case might be, upon any |
and to enhance this flattery, by a common vote it was decreed to change the style of the city, and not to have the years named any longer from the annual archon; a priest of the two tutelary divinities, who was to be yearly chosen, was to have this honor, |
the infinite, then, exists in no other way, but in this way it does exist, potentially and by reduction. |
so much, then, for the discussion of the void, and of the sense in which it exists and the sense in which it does not exist. |
socrates: then as to the other topics--are they not thrown down anyhow? is there any principle in them? why should the next topic follow next in order, or any other topic? |
but perdiccas, believing he was able enough to attain his own further objects without assistance, and that the country he left behind him might stand in need of an active and faithful governor, when he came into cilicia, dismissed eumenes, under color of |
there will not be continuity between any motion and any other indiscriminately any more than there is between any two things chosen at random in any other sphere: there can be continuity only when the extremities of the two things are one. |
it mattered little whether the description in plato agreed with the locality assigned to it or not. it was a legend so adapted to the human mind that it made a habitation for itself in any country. |
it is strange, too, to ask about things staying still but not about their motion,-why, i mean, one thing, if nothing stops it, moves up, and another thing to the centre. again, their statements are not true. |
fifteen. through a given point draw a right line which will meet two non-coplanar lines. |
from whatever side we approach our principle, we reach the same conclusion, that the social compact sets up among the citizens an equality of such a kind, that they all bind themselves to observe the same conditions and should therefore all enjoy the same |
the athenians called the officers in command, and told them that they were going to make peace and that they would be included in the treaty. the generals assenting, the peace was concluded, and the athenian fleet afterwards sailed away from sicily. |
philolaus is known to us from the phaedo of plato as a pythagorean philosopher residing at thebes in the latter half of the fifth century b.one hundred., after the dispersion of the original pythagorean society. |
therefore if it is not right that that punishment should be inflicted on the criminal, it is also not right that he should be convicted, since that punishment must inevitably follow a conviction." |
but their progress is right to the end and object, which is in their way, as it were, and lieth just before them: that is, which is feasible and possible, whether it be that which at the first they proposed to themselves, or no. |
thus fenced, and, as they thought, their shame in part covered, but not at rest or ease of mind, they sat them down to weep; nor only tears rained at their eyes, but high winds worse within began to rise, high passions, anger, hate, mistrust, suspicion, |
most of the syracusan and thurian sailors were freemen, and these the freest crews in the armament were likewise the boldest in setting upon astyochus and demanding their pay. |
conception, drawn from the representations of apprehension, must harmonize. |
and although they are to a certain extent voluntary, (for they are diverted from their course by reproof or by admonition,) still they are liable to such emotions that even those acts of theirs which are intentional sometimes seem either unavoidable, or |
the above, then, may be taken as sufficient to establish that there are principles and what they are and how many there are. now let us make a fresh start and proceed. |
man, if his head had been covered with a thicker pulp of flesh, might have been a longer-lived animal than he is, but could not have had as quick perceptions. |
one must leave a little room for the infidelity or indiscretion of a servant; if you have left enough, in gross, to do your business, let the overplus of fortune's liberality run a little more freely at her mercy; 'tis the gleaner's portion. |
water and air are, and are generated 'from' each other, but not in the way in which bricks come 'from' a house and again a house 'from' bricks; and it is better to assume a smaller and finite number of principles, as empedocles does. |
could alone have created them. into the workings of this eternal mind or intelligence he does not enter further; nor would there have been any use in attempting to investigate the things which no eye has seen nor any human language can express. |
"thou hast divined me well," answered the voluntary beggar, with lightened heart. "i love honey, i also grind corn; for i have sought out what tasteth sweetly and maketh pure breath: |
nevertheless, tramps in want of a lodging keep coming with their mouths full of lies, and not a word of truth; every one who finds his way to ithaca goes to my mistress and tells her falsehoods, whereon she takes them in, makes much of them, and asks them |
also the matter of magnitude and quality-being separable from these matters by definition, but not separable in place unless qualities are, in their turn, separable. |
one part survives, the other does not: what is not an opposite survives (for 'man' survives), but 'not-musical' or 'unmusical' does not survive, nor does the compound of the two, namely 'unmusical man'. |
sixteen. the chians then with the remainder of their ships fled away to their own land; but those of the chians whose ships were disabled by the damage which they had received, being pursued fled for refuge to mycale; and their ships they ran ashore there |
i mean, e.g, if you take a clod, where will it be moved or where will it be at rest? for ex hypothesi the place of the body akin to it is infinite. will it occupy the whole place, then? and how? |
but the proved innocence of pallas did pallas did not please men so much, as his arrogance offended them. |
all thy request for man, accepted son, obtain; all thy request was my decree: but, longer in that paradise to dwell, the law i gave to nature him forbids: those pure immortal elements, that know, no gross, no unharmonious mixture foul, eject him, tainted |
hence the unavoidable dialectics of pure reason, considered in metaphysics, as a natural tendency, deserves to be explained not as an illusion merely, which is to be removed, but also, if possible, as a natural provision as regards its end, though this |
again, since ac is equal to ce, ac is equal to ce ; but ae is equal to ac ce i. xlvii. . therefore ae is equal to ac . in like manner ef is equal to gf or cd . therefore ae ef is equal to ac cd ; but ae ef is equal to af i. xlvii. . |
you have paid a great ransom, and have received the body of your son; were you still alive and a prisoner the sons whom you have left at home would have to give three times as much to free you; and so it would be if agamemnon and the other achaeans were |
greater ones, verily, have there been, and higher-born ones, than those whom the people call saviours, those rapturous blusterers! |
who will make her the most advantageous offer; still, as the stranger has come to your station i will find him a cloak and shirt of good wear, with a sword and sandals, and will send him wherever he wants to go. |
again, because the arcs ab, de are equal, adding the arc bcd to both, the arc abcd is equal to the arc bcde, and therefore three. xxvii. the angles aed, bae, which stand on them, are equal. |
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