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the two cases, as we said, are not parallel; for, in the construction of the figure, when the various steps are completed the required figure forthwith results; but in these other demonstrations what results is not that which was required. |
when anyone tells me, that he saw a dead man restored to life, i immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened. |
dem.-let the supplemental chords corresponding to one, two, c., be denoted by r , r , c.; then three. xxxv. ex. two , we have |
because ad is parallel to ec, ba : ae :: bd : six hundred ii. ; but bd : six hundred :: ba : ac (hyp.). therefore five. xi. ba : ae :: ba : ac, and hence five. ix. ae is equal to ac; therefore the angle aec is equal to ace; but aec is equal to bad i. |
the crop of english hay is carefully weighed, the moisture calculated, the silicates and the potash; but in all dells and pond holes in the woods and pastures and swamps grows a rich and various crop only unreaped by man. |
for they mean by 'the rich' the few who have the most valuable possessions, although the owner of them may quite well be a rogue. and if this is true, i can never assent to the doctrine that the rich man will be happy--he must be good as well as rich. |
hegesistratos an eleian and the most famous of the telliadai, whom before these events the spartans had taken and bound, in order to put him to death, because they had suffered much mischief from him. |
again, (all the monists make use of 'alteration': but) without an agent and a patient there cannot be 'altering' any more than there can be 'dissociating' and 'associating'. |
and so people do not assign movement to non-existent things, though they do assign some other predicates. e.g. |
but being once convinced that we know nothing farther of causation of any kind than merely the constant conjunction of objects, and the consequent inference of the mind from one to another, and finding that these two circumstances are universally allowed |
in the republic he represents man as freely choosing his own lot in a state prior to birth-a conception which, if taken literally, would still leave him subject to the dominion of necessity in his after life; in the statesman he supposes the human race to |
were marching below in the direction of the plain.. |
just such another gulf i suppose that egypt was, and that the one ran in towards ethiopia from the northern sea, and the other, the arabian, of which i am about to speak, seventeen tended from the south towards syria, the gulfs boring in so as almost to |
and if a thing is in motion over the whole kbg and its motion is the three five hundred, e, and z, and if it is not in motion at all over the partless section a but has completed its motion over it, then the motion will consist not of motions but of |
but "criminal fraud," as aquilius says, consists in false pretence. criminal fraud in the light of moral rectitude. |
remote from such a fault, and if his disgraceful or infamous course of life cannot possibly be mitigated by any speech,--then it will be proper to say that the inquiry does not concern his life and habits, but is about that crime for which he is now |
contests. eighty two of these men the greater number never returned back, but were slain by the athenians in egina; and the commander himself, eurybates, fighting in single combat eighty three killed in this manner three men and was himself slain by the |
socrates: then, if he is not coming, you and the two others must supply his place. |
publius sextius, having amongst others retained cicero as his advocate in a certain cause, was yet desirous to say all for himself, and would not allow anybody to speak for him; when he was about to receive his acquittal from the judges, and the ballots |
what initiates it must be single, unmoved, ungenerated, and incapable of 'alteration'; and if the circular movements are more than one, their initiating causes must all of them, in spite of their plurality, be in some way subordinated to a single |
the knowledge of arithmetic which is thus acquired is a great help, either to the general or to the manager of a household; wherever measure is employed, men are more wide-awake in their dealings, and they get rid of their ridiculous ignorance. |
fourteen. in a given circle inscribe a triangle whose three sides shall pass through three given points. |
all these are to be reckoned among the second and co-operative causes which god, carrying into execution the idea of the best as far as possible, uses as his ministers. |
this generation is very sure to plant corn and beans each new year precisely as the indians did centuries ago and taught the first settlers to do, as if there were a fate in it. |
"the man that wandreth out of the way of understanding, shall remain in the congregation of the giants," and job twenty six.five. "behold the giants groan under water, and they that dwell with them." here the place of the damned, is under the water. |
since co is the square on four hundred, and ck the square on cb, and cb is the half of four hundred, co is equal to four times ck iv., cor. one . again, since cg, gi are the sides of equal squares, they are equal i. xlvi., cor. one . |
that everywhere space (which in its entirety is itself no longer the boundary of another space) has three dimensions, and that space cannot in any way have more, is based on the proposition that not more than three lines can intersect at right angles in |
and what municipal town is there which he does not despise who looks with such contempt on aricia; a town most ancient as to its antiquity; if we regard its rights, united with us by treaty; if we regard its vicinity, almost close to us; if we regard the |
we then feel a new sentiment or impression, to wit, a customary connexion in the thought or imagination between one object and its usual attendant; and this sentiment is the original of that idea which we seek for. |
duty of the geometer to refute the squaring of the circle by means of segments, but it is not his duty to refute antiphon's proof. |
i had withdrawn so far within the great ocean of solitude, into which the rivers of society empty, that for the most part, so far as my needs were concerned, only the finest sediment was deposited around me. |
this view has a dialectical difficulty. perhaps it is necessary that the actuality of the agent and that of the patient should not be the same. |
they are found principally in the first half of the dialogue. |
(one) of the intersection of its perpendiculars; |
principles, and the nature of the substratum. whether the form or the substratum is the essential nature of a physical object is not yet clear. but that the principles are three, and in what sense, and the way in which each is a principle, is clear. |
what, then, is the 'first mover' of the 'elements'? what causes their motion? presumably not love and strife: on the contrary, these are causes of a particular motion, if at least we assume that 'first mover' to be an originative source'. |
again, the tripod fell 'of itself', because, though when it fell it stood on its feet so as to serve for a seat, it did not fall for the sake of that. |
it is not every chance direction which is 'up', but where fire and what is light are carried; similarly, too, 'down' is not any chance direction but where what has weight and what is made of earth are carried-the implication being that these places do not |
but hobbes, spinoza, and leibniz, were most attentively heard in the passages where they favoured or combatted the dominant social and theological prepossessions. |
now of the two triangles, the isosceles has one form only; the scalene or unequal-sided has an infinite number. |
too much attention to the arrangement of words, that without it there can be no energy and no force. |
prop. twenty three.-problem. at a given point (a) in a given right line (ab) to make an angle equal to a given rectilineal angle (def). |
even so, this cannot be true of all such principles, since there must clearly be something that causes things that move themselves at one time to be and at another not to be. |
but, because you do not conceive that nature is able to produce such effects without some rational aid, you are forced, like the tragic poets, when you cannot wind up your argument in any other way, to have recourse to a deity, whose assistance you would |
but there are many others who would agree that it is wrong to give the earth the central position, looking for confirmation rather to theory than to the facts of observation. |
again, if the possession of angles makes a body produce heat and combustion, every element produces heat, though one may do so more than another. |
(some, for instance, postulate fire and earth: some add air, making three: and some, like empedocles, reckon water as well, thus postulating four.) |
they, however, had no idea of any form of being other than the substance of things perceived; and when they saw, what no one previously had seen, that there could be no knowledge or wisdom without some such unchanging entities, they naturally transferred |
in all the governments that there are, the public person consumes without producing. whence then does it get what it consumes? from the labour of its members. the necessities of the public are supplied out of the superfluities of individuals. |
do not you think, therefore, that there is any benefit, or that there is any advantage which can be procured by injustice, precious enough to counterbalance the constant pressure of remorse, and the haunting consciousness that retribution awaits the |
and may not know what they do and say in time of war, when they are fighting or holding parley with their enemies. |
if then when this is not white b must be great, it results that if b is not great, it is great, just as if it were proved through three terms. |
again, it belongeth to the nature of a miracle, that it be wrought for the procuring of credit to gods messengers, ministers, and prophets, that thereby men may know, they are called, sent, and employed by god, and thereby be the better inclined to obey |
wendland, paul, philo und die cynisch-stoische diatribe . berlin, one thousand eight hundred ninety five. |
i desire therefore that i and everybody else should always connect necessarily the same perceptions under the same circumstances. |
by this, i conceive, he meant to convey the maximum and the minimum complement: at any rate, he does not specify the amount of any others in his catalogue of the ships. |
to inquire after the beginning of a man's ideas is the same as to inquire after the beginning of his soul. for, by this account, soul and its ideas, as body and its extension, will begin to exist both at the same time. |
measure of all other motions. again, rotatory motion is also the only motion that admits of being regular. |
wherefore the younger philip did not jest, but said very true, when he called the city of corinth "the fetters of greece." |
you may take it that neither does the object in question exhibit it; e.g. if some form of knowledge be good in a greater degree than pleasure, while no form of knowledge is good, then you may take it that pleasure is not good either. |
made to find a way in and out through the pores of the body, and the rays of fire which are bound fast within followed the passage of the air either way, never at any time ceasing so long as the mortal being holds together. |
hence one of the two lives is naturally and necessarily more pleasant and the other more painful, and he who would live pleasantly cannot possibly choose to live intemperately. |
we do not ascribe to chance or mere coincidence the frequency of rain in winter, but frequent rain in summer we do; nor heat in the dog-days, but only if we have it in winter. |
vague and insignificant forms of speech, and abuse of language, have so long passed for mysteries of science; and hard and misapplied words, with little or no meaning, have, by prescription, such a right to be mistaken for deep learning and height of |
quite another judgment therefore is required before perception can become experience. |
cassander, king of macedon, dying, and his eldest son, philip, who succeeded him, not long surviving his father, the two younger brothers fell at variance concerning the succession. |
and has not this been our own case in the matter of equals and of absolute equality? |
must itself be spherical, then on these grounds also it is clear that the heavens are spherical. |
and so, when the conspirators were assured by his own repeated language that the commander of the praetorian guard had come over to their side, they once more eagerly discussed the time and place of the fatal deed. |
you will accept it then, if you please, as having been yours before i owed it to you, and will confer on me the favour of loving it, whether for its own sake or for mine; and i will keep my debt to one thousand. |
the water, indeed, of the river oxus, is said to be the smoothest to the feeling of all waters, and to leave a gloss on the skins of those who bathe themselves in it. |
for in the times before the great flood athens was the greatest and best of cities and did the noblest deeds and had the best constitution of any under the face of heaven.' solon marvelled, and desired to be informed of the particulars. |
so as when speaking of a house we do not call its arrival at perfection an alteration (for it would be absurd to suppose that the coping or the tiling is an alteration or that in receiving its coping or its tiling a house is altered and not perfected), |
seven. what false assumption is made in the demonstration? |
twenty eight.twelve.) were a vision of his sleep; therefore onely fancy, and a dream; yet being supernaturall, and signs of gods speciall presence, those apparitions are not improperly called angels. |
and v., we see that if two triangles possess either condition, they also possess the other. triangles are unique in this respect. in all other rectilineal figures one of the conditions may exist without the other. |
amongst the scythians, where their diviners failed in the promised effect, they were laid, bound hand and foot, upon carts loaded with firs and bavins, and drawn by oxen, on which they were burned to death.-- herodotus, iv. sixty nine. |
but the extremity of the whole, which we call 'above', is in position above and in nature primary. and since the universe has an extremity and a centre, it must clearly have an up and down. common usage is thus correct, though inadequate. |
them in detail, and thus striking a panic into the whole army. for a long while the athenians persevered in this fashion, but after advancing for four or five furlongs halted to rest in the plain, the syracusans also withdrawing to their own camp. |
should give his denial to the magistrates in writing, and not swear; for it is a dreadful thing to know, when many lawsuits are going on in a state, that almost half the people who meet one another quite unconcernedly at the public meals and in other |
thirty nine. given the middle points of the sides of a convex polygon of an odd number of sides, construct the polygon. |
one must, however, maintain this verdict of historical justice in a determined manner, and defend it against present prejudices and appearances: the european noblesse--of sentiment, taste, and manners, taking the word in every high sense--is the work and |
virtutibus et vitus, by w bridgman, one thousand eight hundred four politica, from the french of regius, one thousand five hundred ninety eight, by w ellis, one thousand seven hundred seventy six, one thousand seven hundred seventy eight, one thousand |
those things, then, which do not signify substance, are not said to 'come-to-be' without qualification, but only to 'come-to-be-so-and-so'. |
now virtue is concerned with feelings and actions, in which the excess is wrong and the defect is blamed but the mean is praised and goes right; and both these circumstances belong to virtue. |
albeit in all other matters rank and birth make great distinctions between men, yet virtue is open to all; she despises no one provided he thinks himself three hundred seventy six worthy to possess her. |
this is really to attack what in plutarch is most excellent and most to be commended; for in his parallels (which is the most admirable part of all his works, and with which, in my opinion, he is himself the most pleased) the fidelity and sincerity of his |
reason, do what they can, to make men think, that sanctity and naturall reason, cannot stand together. |
height. by this fluctuation the pond asserts its title to a shore, and thus the shore is shorn , and the trees cannot hold it by right of possession. these are the lips of the lake on which no beard grows. it licks its chaps from time to time. |
for as on the one hand nothing which is not an animal can have this sense, so on the other it is the only one which is indispensably necessary to what is an animal. this explains, further, the following difference between the other senses and touch. |
for every judge of right, and wrong, is not judge of what is commodious, or incommodious to the common-wealth. |
good order, he was resolved to place one over him to be his keeper, who should be accountable for his good behavior. |
it is evident, then, that that which has become must previously have been in process of becoming, and that which is in process of becoming must previously have become: for all magnitudes and all periods of time are infinitely divisible. |
since then, that in which primarily a thing is coming to a stand must be a period of time and not something indivisible, and since all time is infinitely divisible, there cannot be anything in which primarily it is coming to a stand. |
ninety six. sigeion then in this matter had come under the rule of the athenians. |
moreover, no weight can consist of parts not possessing weight. for how, except by the merest fiction, can they specify the number and character of the parts which will produce weight? |
they might also count upon surprising many in the fields outside, incredulous of their coming; and at the moment that the enemy was carrying in his property the army would not want for booty if it sat down in force before the city. |
for, if it be not expressly agreed upon before to the contrary, 'tis a combined party of all four, and if your second be killed, you have two to deal withal, with good reason; and to say that it is foul play, it is so indeed, as it is, well armed, to |
further, we say that all excellences depend upon particular relations. |
found clodius hidden in the chamber of the maid with whom he had come in. this matter being much talked about, caesar put away his wife, pompeia, and clodius was prosecuted for profaning the holy rites. |
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