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three. if db, de, ef be consecutive sides of a regular decagon inscribed in a circle, prove bf bd radius of circle. |
they apply equally well to that which exists and to that which does not. |
are we to say then that all their movements, even those which are mutually contrary, are due to constraint? no, for a body which has no natural movement at all cannot be moved by constraint. |
some parts while insusceptible in others. |
this proposition might have been appended as a cor. to the preceding, since the triangles are the halves of equiangular parallelograms, or it may be proved by joining ae, and showing that it is parallel to bd. |
when conferred without regard to right and wrong, or to the good or evil consequences which may follow. |
confident that the former will survive the dangers, they are by no means so sure that the latter will not be prematurely exhausted, especially if the war last longer than they expect, which it very likely will. |
towards the use of pleasure as we do towards that of pain! |
one. if in a fixed triangle we draw a variable parallel to the base, the locus of the points of intersection of the diagonals of the trapezium thus cut off from the triangle is the median that bisects the base. |
geryones, says the tale, dwelt away from the region of the pontus, living in the island called by the hellenes erytheia, near gadeira which is outside the pillars of heracles by the ocean.-as to the ocean, they say indeed that it flows round the whole |
again, since df is equal to db, df is equal to db : to each add ad , and we get ad df equal to ad db ; but ad df is equal to af ; therefore af is equal to ad db ; and we have proved af equal to ac cd . therefore ad db is equal to ac cd . |
nam quanto pluris ei regi putas, qui exercitu populi romani populum ipsum romanum oppressisset civitatemque non modo liberam, sed etiam gentibus imperantem servire sibi coegisset? |
the motion of things that are moved by something else must proceed in one of four ways: for there are four kinds of locomotion caused by something other than that which is in motion, viz. pulling, pushing, carrying, and twirling. |
if we admit that pleasures differ in kind, the opposition between these two modes of speaking is rather verbal than real; and in the greater part of the writings of plato they alternate with each other. |
and if we take the case of quantitative change, we shall get a like result, for here too the change is in something continuous. it is evident, then, that only in qualitative motion can there be anything essentially indivisible. |
intellectual life in the individual, enabling the subject to be a concrete immediacy, an "ideality" of soul-enabling the matter of consciousness, religious, moral, c., to be his as this self, this soul, and no other, and be neither a mere latent |
that is an offensive one, which offends the inclinations of those who hear it; as if any one were to praise the judiciary law of caepio before the roman knights, who are themselves desirous of acting as judges. |
thus, then, nature makes matters equal and establishes a certain order, giving to the single motion many bodies and to the single body many motions. |
and go to meet those ships which were sailing round. |
the good is the beautiful, and the beautiful is the symmetrical, and there is no greater or fairer symmetry than that of body and soul, as the contrary is the greatest of deformities. |
ismene. so say the envoys who returned to thebes. |
these, then, are the books which theophrastus composed. |
closely related to them shall have the privileges of the kings and give two votes besides their own, making three in all. four thousand two hundred one. |
the case of the rural tribes and their members there was no question of curi as the tribes had then become a purely civil institution, and, a new system of levying troops having been introduced, the military divisions of romulus were superfluous. |
"one must not forget that the production of images is simultaneous with the thought; for from the surface of the bodies images of this kind are continually flowing off in an insensible manner indeed, because they are immediately replaced. |
-ab-.oc-- -bc-.oa- ca-cob--. a b oc b one hundred oa ca ob |
the passionate earnestness of parmenides contrasts with the vacuity of the thought which he is revolving in his mind. |
the syracusans, and had only become a maritime power when obliged by the mede. |
and this unity of feeling we admitted to be the greatest good, as was implied in our own comparison of a well-ordered state to the relation of the body and the members, when affected by pleasure or pain? |
there were one thousand of them slain; there died, also, of the thebans three hundred, who were killed with their enemies, while chasing them into craggy and difficult places. |
that athens was about to send to sicily. alcibiades also urgently advised the fortification of decelea, and a vigorous prosecution of the war. |
eighteen. when the general is weak and without authority; when his orders are not clear and distinct; |
he was the greatest possible enemy to the sophists, as timon tells us. but philo, on the contrary, was very fond of arguing; on which account timon speaks of him thus:- |
thus far, socrates, i have shown you clearly enough, if i am not mistaken, that your countrymen are right in admitting the tinker and the cobbler to advise about politics, and also that they deem virtue to be capable of being taught and acquired. |
"but we shall say in answer to this argument also that while there is some justification for their thinking that the changing, when it is changing, does not exist, yet it is after all disputable; for that which is losing a quality has something of that |
thirty nine. if a man's thoughts are not dissipated, if his mind is not perplexed, if he has ceased to think of good or evil, then there is no fear for him while he is watchful. |
now if a law to this effect could only be made perpetual, and gain an authority such as already prevents intercourse of parents and children--such a law, extending to other sensual desires, and conquering them, would be the source of ten thousand |
is it not then better to perish a thousand times than to be unable to live in one's own city without a guard of armed men? |
further, the worse deed is that which involves the doer in special shame; that whereby a man wrongs his benefactors-for he does more than one wrong, by not merely doing them harm but failing to do them good; that which breaks the unwritten laws of |
for the egyptians say that vulcan was the son of nilus, and that he was the author of philosophy, in which those who were especially eminent were called his priests and prophets. |
then ad ac cd ac in like manner, db cb ; therefore ad db ac cb ac . but since the angle adb is right, ad db ab ; |
there are many senses in which motion is said to be 'one': for we use the term 'one' in many senses. |
ornament of all succeeding poesy. and yet there is no good judgment that will condemn this in the ancients, and that does not incomparably more admire the equal polish, and that perpetual sweetness and flourishing beauty of catullus's epigrams, than all |
beyond this front, is there to be a fair court, but three sides of it, of a far lower building than the front. and in all the four corners of that court, fair staircases, cast into turrets, on the outside, and not within the row of buildings themselves. |
"there are writings of the stoics which we find lying upon silken cushions."--horace, epod., viii. fifteen. |
(yet their essence is not the same, just as changing from health is different from changing to disease.) nor are motion respectively from a contrary and from the opposite contrary contrary motions, for a motion from a contrary is at the same time a motion |
twenty seven. what proposition is xix. a special case of? |
sertorius, meantime, showed the loftiness of his temper in calling together all the roman senators who had fled from rome, and had come and resided with him, and giving them the name of a senate; and out of these he chose praetors and quaestors, and |
the same then will be true of the body continuous with it: for that which is continuous with the spherical is spherical. the same again holds of the bodies between these and the centre. |
our senses enable us to perceive very few of the attributes of the heavenly bodies. but let not that deter us. the reason must be sought in the following facts. everything which has a function exists for its function. |
(six) as the affairs of greece centre 'in' the king, and generally events centre 'in' their primary motive agent. |
and ulysses answered, "it would be a long story madam, were i to relate in full the tale of my misfortunes, for the hand of heaven has been laid heavy upon me; but as regards your question, there is an island far away in the sea which is called 'the |
so that proposition xxvii. is the converse of xxvi., and xxix. of xxviii. |
he cannot leave his old enemies, the sophists, in possession of the field; and therefore he proposes that youth shall learn by heart, instead of the compositions of poets or prose writers, his own inspired work on laws. |
there are some who think that the existence of rarity and density shows that there is a void. if rarity and density do not exist, they say, neither can things contract and be compressed. |
other benches had been already placed. meanwhile callias and alcibiades got prodicus out of bed and brought in him and his companions. |
but whereas thou dost profess thyself desirous of hearing, with what ardour wouldst thou not burn didst thou but perceive whither it is my task to lead thee!' |
forty six. people have long since observed, that in all substances the proper subject, that which remains after all the accidents (as predicates) are abstracted, consequently that which forms the substance of things remains unknown, and various complaints |
animals unseen by reason of their smallness and without form; these again are separated and matured within; they are then finally brought out into the light, and thus the generation of animals is completed. |
threatenings of pain and misfortune. nevertheless, this is actually the case, and if human nature were not so constituted, no mode of presenting the law by roundabout ways and indirect recommendations would ever produce morality of character. |
again, whatsoever necessarily follows from the idea which is adequate in god, not by virtue of his possessing in himself the mind of one man only, but by virtue of his containing, together with the mind of that one man, the minds of other things also, of |
four that is, to triumph over. "two spears were set upright ... |
being', it is necessary that the contradictories of both terms should be predicable of one and the same thing, and thus that, intermediate between what always is and what always is not, there should be that to which being and not-being are both possible; |
caius's oratory was impetuous and passionate, making everything tell to the utmost, whereas tiberius was gentle, rather, and persuasive, awakening emotions of pity. his diction was pure, and carefully correct, while that of caius was vehement and rich. |
when the reader is brought by this curious phenomenon to fall back upon the proof of the presumption upon which it rests, he will feel himself obliged to investigate the ultimate foundation of all the cognition of pure reason with me more thoroughly. |
the same kind of argument holds good against parmenides also, besides any that may apply specially to his view: the answer to him being that 'this is not true' and 'that does not follow'. |
this, therefore, is cause in the sense of material origin for the things which are such as to come-to-be; while cause, in the sense of their 'end', is their 'figure' or 'form'-and that is the formula expressing the essential nature of each of them. |
here also (as before) what he says is not the idea of the sun, and yet is described, is that very thing which i call the idea . |
believe me, my brethren! it was the body which despaired of the earth-it heard the bowels of existence speaking unto it. |
with respect to sickness, i shall not repeat the vain and false declamations which most healthy people pronounce against medicine; but i shall ask if any solid observations have been made from which it may be justly concluded that, in the countries where |
for when he had an opportunity of taking him, he purposely let it slip, and struck up a peace with him, leaving sparta to bewail an unworthy slavery; whether it were that he feared, if the war should be protracted, rome would send a new general who might |
conceding to this view of the subject the utmost that can be claimed for it by those most easily satisfied with the amount of understanding of truth which ought to accompany the belief of it; even so, the argument for free discussion is no way weakened. |
and he who would attain all virtue should be trained amid pleasures as well as pains. hence there should be convivial intercourse among the citizens, and a man's temperance should be tested in his cups, as we test his courage amid dangers. |
taste and relish of the sweets of liberty. for this custom, too, is ascribed to numa, whose wish was, they conceive, to give a place in the enjoyment of the yearly fruits of the soil to those who had helped to produce them. |
something over and above the body displaced. but there is no such extension. one of the bodies which change places and are naturally capable of being in contact with the container falls in whichever it may chance to be. |
nicias was a younger man, yet was in some reputation even whilst pericles lived; so much so as to have been his colleague in the office of general, and to have held command by himself more than once. |
cor. two.-the parallelograms inscribed in a triangle, and having one angle common with it, are proportional to the rectangles contained by the segments of the sides of the triangle, made by the opposite corners of the parallelograms. |
and if so, we shall be right in saying that the soul is prior and superior to the body, and the body by nature subject and inferior to the soul? 'quite right.' |
let kings but lead the dance and begin to leave off this expense, and in a month the business will be done throughout the kingdom, without edict or ordinance; we shall all follow. |
partition firm and sure, the waters underneath from those above dividing: for as earth, so he the world built on circumfluous waters calm, in wide crystalline ocean, and the loud misrule of chaos far removed; lest fierce extremes contiguous might |
i love to let them step deeper into the mire; and so deep, that, if it be possible, they may at last discern their error. |
and therefore teribazus was to the young prince flame added upon flame, ever urging him, and saying, that in vain those wear their hats upright who consult not the real success of their affairs, and that he was ill befriended of reason if he imagined, |
if we had to define a threshold, we should say 'wood or stone in such and such a position', and a house we should define as 'bricks and timbers in such and such a position',(or a purpose may exist as well in some cases), and if we had to define ice we |
theodamas compared archidamus to an euxenus who could not do geometry-a proportional simile, implying that euxenus is an archidamus who can do geometry. |
even in the former class, however, there seems to be something similar, for a cold thing in a sense causes heating by turning away and retiring, just as one possessed of knowledge voluntarily makes an error when he uses his knowledge in the reverse way. |
for different men are formed by nature for different things. do you think that if you do these things, you can eat in the same manner, drink in the same manner, and in the same manner loathe certain things? |
again, because the angle bca is equal to bef, the line ca i. xxviii. is parallel to ef. in like manner, bf is parallel to four hundred; therefore the figure acdf is a parallelogram; hence ac is equal to df, and four hundred is equal to af. |
there is here, o brutus, an important topic, which does not escape your notice, and which requires another large volume. |
indeed motion cannot be attributed to god; not because he is an immaterial, but because he is an infinite spirit. |
jove sent me; it was no doing of mine; who could possibly want to come all this way over the sea where there are no cities full of people to offer me sacrifices or choice hecatombs? |
pyrrhus in the air of his face had something more of the terrors, than of the augustness of kingly power; he had not a regular set of upper teeth, but in the place of them one continued bone, with small lines marked on it, resembling the divisions of a |
the external elements by their attraction are always diminishing the substance of the body: the particles of blood, too, formed out of the newly digested food, are attracted towards kindred elements within the body and so fill up the void. |
and once, when there was a sedition in the city, he took part neither with the citizens, nor with the inhabitants of the plain, nor with the men of the sea-coast. |
sureties that he would marry her, before he took her away; and if they did not agree well together, the law was laid down that he should pay back the money. it was allowed also for any one who wished it to come from another village and buy. |
one hundred eight. three analogies.--those men who frame general rules from the phenomena and afterwards derive the phenomena from those rules, seem to consider signs rather than causes. |
disposition leads him to do so; he will do it alike to those whom he does know and those whom he does not, and those with whom he is intimate and those with whom he is not; only in each case as propriety requires, because it is not fitting to care alike |
dem.-join co, and let fall perpendiculars from o on the five sides of the pentagon. now the triangles abo, cbo have the side ab equal to bc (hyp.), and bo common, and the angle abo equal to cbo (const.). hence the angle bao is equal to bco i. iv. |
this is true of fire, air, and water, which, being composed of similar triangles, are interchangeable; earth, however, which has triangles peculiar to itself, is capable of dissolution, but not of change. |
and still more strongly, under a figurative expression, |
for if we take a determinate part of a finite magnitude and add another part determined by the same ratio (not taking in the same amount of the original whole), and so on, we shall not traverse the given magnitude. |
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