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socrates: then now is the time, my dear theaetetus, for me to examine, and for you to exhibit; since although theodorus has praised many a citizen and stranger in my hearing, never did i hear him praise any one as he has been praising you. |
ahi : cef in the duplicate ratio of ah : ce; hence abh : cde ahi : cef five. xi. . similarly, ahi : cef aij : cfg. in these equal ratios, the triangles abh, ahi, aij are the antecedents, and the triangles cde, cef, cfg the consequents, and five. xii. |
there is always some madness in love. but there is always, also, some method in madness. |
i. solon the son of execestides, a native of salamis, was the first person who introduced among the athenians, an ordinance for the lowering nine of debts; for this was the name given to the release of the bodies and possessions of the debtors. |
clearly, therefore, the differentia does not partake of the genus, so that 'odd' too is no species but a differentia, seeing that it does not partake of the genus. |
the people had never before bestowed so many consulships on any one man, except on valerius corvinus only, and he, too, they say, was forty-five years between his first and last; but marius, from his first, ran through five more, with one current of good |
antony grew up a very beautiful youth, but, by the worst of misfortunes, he fell into the acquaintance and friendship of curio, a man abandoned to his pleasures; who, to make antony's dependence upon him a matter of greater necessity, plunged him into a |
neither can it bee said, that hee that does it, scandalizeth, or layeth any stumbling block before his brother; because how wise, or learned soever he be that worshippeth in that manner, another man cannot from thence argue, that he approveth it; but that |
ninety. hearing this, cyrus was above measure pleased, because he thought that croesus advised well; and he commended him much and enjoined the spearmen of his guard to perform that which croesus had advised: and after that he spoke to croesus thus: |
dem.-let ab, four hundred meet the plane ten at the points b, five hundred. join bd, and in the plane ten draw de at right angles to bd; take any point e in de. join be, ae, ad. then because ab is normal to ten, the angle abe is right. |
and as this circular movement required no feet, the universe was created without legs and without feet. |
member is moved to performe his duty) are the nerves, that do the same in the body naturall; the wealth and riches of all the particular members, are the strength; salus populi (the peoples safety) its businesse; counsellors, by whom all things needfull |
anxious above everything to avoid suspicion, and confident that he could quash the charge by means of money, he returned a second time to sparta. |
he on all occasions treated the commanders of the confederates haughtily and roughly; and the common soldiers he punished with stripes, or standing under the iron anchor for a whole day together; neither was it permitted for any to provide straw for |
in walls on both sides of the railroad cut nearest the pond; and, moreover, there are most stones where the shore is most abrupt; so that, unfortunately, it is no longer a mystery to me. one detect the paver. |
sixty five. if r, r denote the radii of the circles inscribed in the triangles into which a right-angled triangle is divided by the perpendicular from the right angle on the hypotenuse; then, if c be the hypotenuse, and s the semiperimeter, r r (s c)two. |
why, you know, i said, that the eyes, when a person directs them towards objects on which the light of day is no longer shining, but the moon and stars only, see dimly, and are nearly blind; they seem to have no clearness of vision in them? |
histories, concerning the religious rites of the greeks and romanes, i doubt not but he might find many more of these old empty bottles of gentilisme, which the doctors of the romane church, either by negligence, or ambition, have filled up again with the |
we have three things, the movent, the moved, and thirdly that in which the motion takes place, namely the time: and these are either all infinite or all finite or partly-that is to say two of them or one of them-finite and partly infinite. |
but this self-centred being is not merely a formal factor of sensation: the soul is virtually a reflected totality of sensations-it feels in itself the total substantiality which it virtually is-it is a soul which feels. |
a plausible profession this in words, but really unmeaning and delusive, and the greater the disguise of freedom which marked it, the more cruel the enslavement into which it was soon to plunge us. |
though you cannot apprehend what it is, yet you see what kind of thing it is, or if you do not quite see that, yet you certainly see how great it is. what, then? |
if time is infinite in respect of its extremities, length is also infinite in respect of its extremities: if time is infinite in respect of divisibility, length is also infinite in respect of divisibility: and if time is infinite in both respects, |
this is the account which the most of those that were present at the battle give of it, yet own that the disorder they were in, and the absence of any unity of action would not give them leave to be certain as to particulars. |
he felt a longing desire to see them and also an abhorrence of them; at first he turned away and shut his eyes, then, suddenly tearing them open, he said,-'take your fill, ye wretches, of the fair sight.' |
the question-to whom (to what authority and how organised) belongs the power to make a constitution? is the same as the question, who has to make the spirit of a nation? |
those which possess no such factor. assuming, then, that the contrariety, in respect to which they are transformed, is one, the elements' will inevitably be two: for it is 'matter' that is the 'mean' between the two contraries, and matter is imperceptible |
punishment he deserved. for, going to take catana, he lost syracuse; whereupon they report he said, he had lost a city and got a bauble. then, attempting messena, he had most of his men cut off, and, among the rest, dion's murderers. |
'all' is here used metaphorically for 'many,' all being a species of many. so in the verse,--'alone she hath no part...,' omicron iota eta , 'alone,' is metaphorical; for the best known may be called the only one. |
it is therefore better to suppose that in all instances of coming-to-be the matter is inseparable, being numerically identical and one with the 'containing' body, though isolable from it by definition. |
eighty one. these were the nations which served in the campaign by land and had been appointed to be among the foot-soldiers. |
socrates: and if the truth of all things always existed in the soul, then the soul is immortal. wherefore be of good cheer, and try to recollect what you do not know, or rather what you do not remember. |
be balanced by an equal transformation of air into water (for it is clear that the air produced from water is bulkier than the water): it is necessary therefore, if compression does not exist, either that the next portion will be pushed outwards and make |
with that we are not concerned here. but the notion of perfection in a practical sense is the fitness or sufficiency of a thing for all sorts of purposes. |
rudely), no interest at all, but is altogether indifferent: and whatsoever else thou hast heard and assented unto concerning either pain or pleasure? but the care of thine honour and reputation will perchance distract thee? |
in a democracy, the whole assembly cannot faile, unlesse the multitude that are to be governed faile. and therefore questions of the right of succession, have in that forme of government no place at all. |
note.--when, therefore, as we said in the note to three. |
true excellence being, as tu mu says: "to plan secretly, to move surreptitiously, to foil the enemy's intentions and balk his schemes, so that at last the day may be won without shedding a drop of blood." sun tzu reserves his approbation for things that |
and chosen them out, and that they were declared our comptrollers by express procuration: |
this proposition may be inferred as a cor. to the last, which is one of the fundamental propositions in mathematics. |
eleven. and ab(ac ad) ac.ad, or one ac- one ad- two ab-. |
charge the enemy on foot. at the sight of this, hannibal was heard to say, "this pleases me better than if they had been delivered to me bound hand and foot." |
stranger though he was, he knew no fear on finding himself single-handed among so many, but challenged them to contests of all kinds, and in each one of them was at once victorious, so mightily did minerva help him. |
choice-worthy is good, and the more so the greater good. |
assembly of men, which are to governe by his right, and in his name; as curators, and protectors of his person, and authority. |
repercussion; but specifically they are different. |
now if place is what primarily contains each body, it would be a limit, so that the place would be the form or shape of each body by which the magnitude or the matter of the magnitude is defined: for this is the limit of each body. |
hb :bf ::de :ef ; that is, ac :ce ::gc :cb. |
hence it is evident that the fine derives from the moist, while the coarse derives from the dry. again (b) the viscous' derives from the moist: for 'the viscous' (e.g. oil) is a 'moist' modified in a certain way. |
cor. two.-bc is a mean proportional between ab, bd; and ac between ab, ad. |
lastly, for the errors brought in from false, or uncertain history, what is all the legend of fictitious miracles, in the lives of the saints; and all the histories of apparitions, and ghosts, alledged by the doctors of the romane church, to make good |
when air seemed to go upwards and fire to pierce through air-when water and earth fell downward, they were seeking their native elements. |
first, they applied to external nature the relations of them which they found in their own minds; and where nature seemed to be at variance with number, as for example in the case of fractions, they protested against her (rep.; arist. metaph.). |
i am zarathustra the godless: where do i find mine equal? and all those are mine equals who give unto themselves their will, and divest themselves of all submission. |
really governs for others, and so justice, men say, is a good not to one's self so much as to others, as was mentioned before), therefore some compensation must be given him, as there actually is in the shape of honour and privilege; and wherever these |
still we must do all that we can to imitate the life which is said to have existed in the days of cronos, and, as far as the principle of immortality dwells in us, to that we must hearken, both in private and public life, and regulate our cities and |
before them in this latter capacity. even in the cases which he assigned to the archons' cognizance, he allowed an appeal to the courts. |
now the medium causes a difference because it impedes the moving thing, most of all if it is moving in the opposite direction, but in a secondary degree even if it is at rest; and especially a medium that is not easily divided, i.e. |
a real quantity, infinitely less than any finite quantity, containing quantities infinitely less than itself, and so on in infinitum ; this is an edifice so bold and prodigious, that it is too weighty for any pretended demonstration to support, because it |
him, saying that it was not permitted by religious rule for a stranger to sacrifice in that place. cleomenes however bade the helots take away the priest from the altar and scourge him, and he himself offered the sacrifice. |
we have now to consider the much discussed question of the rotation or immobility of the earth. |
and he gave dominion to the motion of the same and like, for that he left single and undivided; but the inner motion he divided in six places and made seven unequal circles having their intervals in ratios of two and three, three of each, and bade the |
the other is the variable or changing element, the residuum of disorder or chaos, which cannot be reduced to order, nor altogether banished, the source of evil, seen in the errors of man and also in the wanderings of the planets, a necessity which |
apprehend your being, it would be but like grasping water; for the more you clutch your hand to squeeze and hold what is in its own nature flowing, so much more you lose of what you would grasp and hold. |
eleven. extension and body not the same. |
reason). moreover, it is not meant by this that it is necessary to suppose the existence of god as a basis of all obligation in general (for this rests, as has been sufficiently proved, simply on the autonomy of reason itself). |
and i know another, who has unexpectedly advanced his fortunes by following a clear contrary advice. |
consequently, if the 'elements' are infinitely many, there will also belong to the single 'element' an infinite number of contrarieties. but if that be so, it will be impossible to define any 'element': impossible also for any to come-to-be. |
this is why death, too, is by a figure of speech called the end, because both are last things. |
thus do i ever advise them to have things done properly, according to my capacity; and lastly, demea, i command my cooks to look into every dish as if it were a mirror, and tell them what they should do." --terence, adelph., iii. three, seventy one. |
they then felt that they could endure it no longer, but that the time had come for them to throw themselves heart and soul upon the hostile power, and break it, if they could, by commencing the present war. |
for there are some who think it possible both for the ungenerated to be destroyed and for the generated to persist undestroyed. |
--ille etiam caecos instare tumultus saepe monet, fraudesque et operta tunescere bella. |
since the account of their year takes beginning from that day: the third day after its creation the ancient gods died, and the new ones were since born daily. |
seventy seven. in the same case the diameter of the circle circumscribed about the triangle abc ab.bc.ca divided by the area of abc. |
for to define the infinite you must use quantity in your formula, but not substance or quality. |
"my child," answered euryclea, "what are you talking about? you know very well that nothing can either bend or break me. |
these and like arguments failed to impress the emperor. he at once addressed himself to answer them, and thus harangued the assembled senate. |
appointed joshua for the generall of their army. for thus god saith expressely (numb. |
nature akin to that of man with other forms and perceptions, and thus created another kind of animal. |
to the gods who preside over birth. let him keep his hands, too, from the stranger; instead of taking upon himself to chastise him when he is insolent, he shall bring him before the wardens of the city, who shall examine into the case, and if they find |
finite magnitude during an infinite time. but the first movent causes a motion that is eternal and does cause it during an infinite time. it is clear, therefore, that the first movent is indivisible and is without parts and without magnitude. |
he had made himself so completely master of the views of these two princes, that he told de thou that the king of navarre would have been prepared to embrace catholicism, if he had not been afraid of being abandoned by his party, and that the duke of |
note.--yet dejection can be more easily corrected than pride; for the latter being a pleasurable emotion, and the former a painful emotion, the pleasurable is stronger than the painful (four. xviii.). |
of their production, by supposing external bodies in their likeness rather than otherwise; and so it might be at least probable there are such things as bodies that excite their ideas in our minds. |
i will now return to the phenomena of respiration. the fire, entering the belly, minces the food, and as it escapes, fills the veins by drawing after it the divided portions, and thus the streams of nutriment are diffused through the body. |
qualified by 'to become' as its property, and the subject qualified by the verb to be destroyed' will have as its property the predicate rendered with this qualification. |
then, since four hundred is cut at right angles by of, which passes through the centre, it is bisected in f iii. , and divided unequally in e. hence |
to the whole motion, there would be more than one being-in motion corresponding to the same motion), the argument being the same as that whereby we showed that the motion of a thing is divisible into the motions of the parts of the thing: for if we take |
determination not to be outweighed by any sensible conditions, nay, wholly independent of them. but how is the consciousness, of that moral law possible? |
fourteen. remember, that to change thy mind upon occasion, and to follow him that is able to rectify thee, is equally ingenuous, as to find out at the first, what is right and just, without help. |
and if this way shall have its issue according to your mind, then each one of you ought to remember me also concerning liberation, fifty one since i have done for the sake of the hellenes so hazardous a deed by reason of my zeal for you, desiring to show |
it is your dearest self, your virtue. the ring's thirst is in you: to reach itself again struggleth every ring, and turneth itself. |
and, dividing themselves into two companies, one part of them marched openly from sphettus, with their father, against the city, the other, hiding themselves in the village of gargettus, lay in ambush, with a design to set upon the enemy on both sides. |
five. that which causes philosophers to be regarded half-distrustfully and half-mockingly, is not the oft-repeated discovery how innocent they are--how often and easily they make mistakes and lose their way, in short, how childish and childlike they |
that being so, motion must also be continuous, because what is always is continuous, whereas what is merely in succession is not continuous. |
our faculties do not play us true, and both parties are relieved by solitude. |
city made a desert place; all that i saw, and part of which one was: not ev'n the hardest of our foes could hear, nor stern ulysses tell without a tear. |
and so while she was living as the wife of rufius crispinus, a roman knight, by whom she had a son, she was attracted by the youth and fashionable elegance of otho, and by the fact too that he was reputed to have nero's most ardent friendship. |
'the third day hence to fertile phthia shalt thou go.' (homer, il.) |
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