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fifteen. other conditions being equal, if one force is hurled against another ten times its size, the result will be the flight of the former. |
but if one were to make the conversion, then he would be doing what we have described and effecting a reciprocal proof with three propositions. |
but, if homer never did any public service, was he privately a guide or teacher of any? |
so it follows necessarily from what has been said above that there are only three kinds of change, that from subject to subject, that from subject to non-subject, and that from non-subject to subject: for the fourth conceivable kind, that from non-subject |
on the other hand, we have the less reason to suppose this discovery the effect of any accidental fire, as mines are only formed in barren places, bare of trees and plants; so that it looks as if nature had taken pains to keep the fatal secret from us. |
for the things which come-to-be by natural process all exhibit, in their coming-to-be, a uniformity either absolute or highly regular: while any exceptions any results which are in accordance neither with the invariable nor with the general rule are |
those, on the other hand, who do not make their coming-to-be reciprocal-who refuse to suppose that any one of the 'elements' comes-to-be out of any other taken singly, except in the sense in which bricks come-to-be out of a wall-are faced with a paradox. |
meanwhile they begged the boeotians to place panactum in her hands in order that she might, if possible, obtain pylos in exchange for it, and so be more in a position to resume hostilities with athens. |
five. the two terms of a ratio are called the antecedent and the consequent. these correspond to the numerator and the denominator of a fraction. |
if any one doubts the happiness of diogenes, he would doubt whether the position of the immortal gods was one of sufficient happiness. |
the breach of this law, is called ingratitude; and hath the same relation to grace, that injustice hath to obligation by covenant. |
in earnest, considering what is come to our knowledge from the course of this terrestrial polity, i have often wondered to see in so vast a distance of places and times such a concurrence of so great a number of popular and wild opinions, and of savage |
yet plato also speaks of an 'annus magnus' or cyclical year, in which periods wonderful for their complexity are found to coincide in a perfect number, i.e. a number which equals the sum of its factors, as six one two three. |
soc. and, on the other, he who has the knowledge of what is right is more righteous than he who lacks that knowledge? |
this proposition, together with iv. and viii., includes all the cases of the congruence of two triangles. part one. may be proved immediately by superposition. |
but such a shadowy enquiry is not worth pursuing further. |
aristides, making this proposal and bringing back the ambassadors into the assembly, charged them to tell the lacedaemonians that all the treasure on the earth or under it, was of less value with the people of athens, than the liberty of greece. |
as when for example, i imagine a triangle, tho perhaps such a figure exists no where out of my thoughts, nor ever will exist, yet the nature thereof is determinate, and its essence or form is immutable and eternal, which is neither made by me nor depends |
have runners you must have light arms--no one can carry a heavy weight when running, and bows and arrows are convenient because they are light. |
in all seriousness, the innocence of thinkers has something touching and respect-inspiring in it, which even nowadays permits them to wait upon consciousness with the request that it will give them honest answers: for example, whether it be "real" or not, |
rattling sky. wrath, terror, treason, tumult, and despair (dire faces, and deform'd) surround the car; friends of the god, and followers of the war. |
more than of courage. the motives of so powerful a persuasion may be diverse, for our fancy does what it will, both with itself and us. the execution that was done near orleans-- the murder of the duke of guise by poltrot. |
to the tribe of levi were assigned certain cities for their habitation, with the suburbs for their cattell: but for their portion, they were to have the tenth of the fruits of the land of their brethren. |
not at all, my good sir, i said; i am trying to understand them; and i wish that you would be a little clearer. |
time is made to consist of moments or a length of points. |
forty three. and truly these signs are so regularly disposed that a divine wisdom evidently appears in them: |
in the same way that which is to receive perpetually and through its whole extent the resemblances of all eternal beings ought to be devoid of any particular form. |
and of this kind the effect is very much diversified, being sometimes greater or less; so that which is the most efficacious is often called the only cause, though it is in reality but the main one. |
like gorgias, he is overthrown because he compromises; he is unwilling to say that to do is fairer or more honourable than to suffer injustice. |
by his present circumstances, and hearing further that all the enterprises and actions of his life were answerable to what he saw of him, but chiefly, as it seemed, a divine influence aiding and directing the first steps that were to lead to great |
expanded, elfish,-capped and based by heaven, earth and sea. |
i have thus shown the various classes of bodies as they are diversified by their forms and combinations and changes into one another, and now i must endeavour to set forth their affections and the causes of them. |
one the having virtue; another, virtue itself; a third, useful food and exercise; and fourthly, we call skill in flute playing and acting, good. |
the one, they reasoned, must have already existed in the other; for since everything that comes into being must arise either from what is or from what is not, and it is impossible for it to arise from what is not (on this point all the physicists agree), |
this little dialogue is a perfect piece of dialectic, in which granting the 'common principle,' there is no escaping from the conclusion. it is anticipated at the beginning by the dream of socrates and the parody of homer. |
pergamus is not famed for arms alone, but often hears its praise resound for its fine horses, at the holy pisa. yet, if a mortal may declare, its fate as hidden in the breast of jove, it will be famous for its woes. |
and it is equally impossible (iii) that more than one of these additional properties should belong to the single 'indivisible'. |
minister to its appetites. the stomach, however, merely ridiculed the silliness of the members, who appeared not to be aware that the stomach certainly does receive the general nourishment, but only to return it again, and redistribute it amongst the |
than the unlike. this he finished off, making the surface smooth all round for many reasons; in the first place, because the living being had no need of eyes when there was nothing remaining outside him to be seen; nor of ears when there was nothing to be |
but it was shown earlier' that they mean different things.-therefore, if it is true to say of anything that it is a man, it must be a two-footed animal (for this was what 'man' meant); and if this is necessary, it is impossible that the same thing should |
dem.-in the triangle cae, bd is parallel to ce; therefore ab : bc :: ad : de ii. ; but ab is equal to ten, and bc, ad each equal to y . therefore ten : y :: y : de. hence de is a third proportional to ten and y . |
then thus the mighty ruler of the main: "what may not venus hope from neptune's reign? my kingdom claims your birth; my late defence of your indanger'd fleet may claim your confidence. |
lay scattered along the intrenchments or wandered from tent to tent, wakeful rather than watchful. a ghastly dream appalled the general. |
'he who neglects education walks lame to the end of his life, and returns imperfect and good for nothing to the world below.' |
the poet of the future may return to his greater calling of the prophet or teacher; indeed, we hardly know what may not be effected for the human race by a better use of the poetical and imaginative faculty. |
but, rome, 'tis thine alone, with awful sway, to rule mankind, and make the world obey, disposing peace and war by thy own majestic way; to tame the proud, the fetter'd slave to free: these are imperial arts, and worthy thee." |
the stern dignity of antiquity showed itself in grave reserve; the stern dignity of the present day shows itself in quarrelsome perverseness. |
for this reason one says, abstain from food; another says, give food; another says, bleed; and another says, use cupping. what is the reason? is it any other than that a man cannot properly adapt the preconceptions of health to particulars? |
christian mans own brest, between the christian, and the man. |
again (three) according to the theory all such things are already present in one another and do not come into being but are constituents which are separated out, and a thing receives its designation from its chief constituent. |
my townsmen have all heard the tradition, the oldest people tell me that they heard it in their youth, that anciently the indians were holding a pow-wow upon a hill here, which rose as high into the heavens as the pond now sinks deep into the earth, and |
against their wills." in real truth, however, agesilaus was not their master in this, but those that prudently and opportunely, as men do young dogs, set them on their enemies, and brought them safely off after they had tasted the sweets of victory and |
what would socrates think of our newspapers, of our theology? |
yet without this crude use of analogy the ancient physical philosopher would have stood still; he could not have made even 'one guess among many' without comparison. |
nor is this view again without its difficulties: for, after a man has lived in blessedness to old age and died accordingly, many changes may befall him in right of his descendants; some of them may be good and obtain positions in life accordant to their |
smells are not divided into kinds; all of them are transitional, and arise out of the decomposition of one element into another, for the simple air or water is without smell. |
ten atque ea sic definiunt, ut, rectum quod sit, id officium perfectum esse definiant; medium autem officium id esse dicunt, quod cur factum sit, ratio probabilis reddi possit. |
approaches is callias. we shall explain in another place that there is an upward limit also to the process of predicating: for the present we must assume this. |
but what owe i to his commands above, who hates me, and hath hither thrust me down into this gloom of tartarus profound, to sit in hateful office here confined, inhabitant of heaven and heavenly born- here in perpetual agony and pain, with terrors and |
twenty eight this rises in the market-place itself of kelainai and runs into the maiander: and here also is hanging up in the city the skin of marsyas the silenos, which is said by the phrygians to have been flayed off and hung up by apollo. |
it was a subject especially congenial to the ponderous industry of certain french and swedish writers, who delighted in heaping up learning of all sorts but were incapable of using it. |
a continued body under one immutable superficies, existing in a determined time and place; it is evident, that, considered in any instant of its existence, it is in that instant the same with itself. |
"the other part o' th' soul diffus'd all o'er the body, does obey the reason's lore." |
earth, owing to the survival of the dry of the fire and the cold of the water. so, too, in the same way, fire and water will result from air plus earth. |
the original impression to other parts, it has no effect of motion on the whole animal, and therefore produces no effect on the patient. |
that appears to me to be most true, he said. |
this, coming down from the mountain aforesaid, ravaged the fields of the mysians, and although the mysians went out against it often, yet they could do it no hurt, but rather received hurt themselves from it; so at length messengers came from the mysians |
they still call the tarpeian rock, from which they used to cast down malefactors. |
sector boc one two rectangle contained by the arc bc, and the radius of the circle abc xx. ex. fourteen and sector epf one two rectangle contained by the arc ef and the radius of the circle edf; and since the circles are equal, their radii are equal. |
again (b) we may assume weights which are commensurate; for it makes no difference whether we begin with the weight or with the mass. |
to all these points may be added another, which at once depends on and strengthens them. hot countries need inhabitants less than cold countries, and can support more of them. there is thus a double surplus, which is all to the advantage of despotism. |
"go to the house, and kill the best pig that you can find for dinner. meanwhile i want to see whether my father will know me, or fail to recognise me after so long an absence." |
it was now the time of the celebration of the isthmian games; and the seats around the racecourse were crowded with an unusual multitude of spectators; greece, after long wars, having regained not only peace, but hopes of liberty, and being able once more |
or thus, directly: construct the triangle acg, whose three sides ag, gc, ca shall be respectively equal to the three sides de, ef, fd of the triangle def xxii. . join bg. then because bc is greater than ef, bc is greater than cg. hence xviii. |
we never can so thoroughly defeat the vast diversity and malignity of misfortune with which we are threatened as not to feel the weight of many gusts if we offer a large spread of canvas to the wind: we must draw our affairs into a small compass, to make |
therefore the sum of abc, cda is two right angles. |
went away. and when hierocles, the governor of the pirus, attacked him in the temple of amphiaraus, and said a great deal about the taking of eretria, he made no other reply beyond asking him what antigonus's object was in treating him as he did. |
consequently a free will must find its principle of determination in the law, and yet independently of the matter of the law. but, besides the matter of the law, nothing is contained in it except the legislative form. |
he is poor and they are rich; his profession that he teaches nothing is opposed to their readiness to teach all things; his talking in the marketplace to their private instructions; his tarry-at-home life to their wandering from city to city. |
the answer they got from corinth was that, if they would withdraw their fleet and the barbarians from epidamnus, negotiation might be possible; but, while the town was still being besieged, going before arbitrators was out of the question. |
and as in their judgment either of the two,-the world as much as god-has the same solid substantiality as the other, they infer that in the philosophic idea god is composed of god and the world. |
the largest of these walls is in size about equal to the circuit of the wall round athens; and of the first circle the battlements are white, of the second black, of the third crimson, of the fourth blue, of the fifth red: thus are the battlements of all |
why do you alone attack those men whom we are all bound almost to worship? |
but i will not stay my anger, nor permit any god to help the danaans till i have accomplished the desire of the son of peleus, according to the promise i made by bowing my head on the day when thetis touched my knees and besought me to give him honour." |
dem.-the triangles daf, eaf have the side ad equal to ae (const.) and af common; therefore the two sides da, af are respectively equal to ea, af, and the base df is equal to the base ef, because they are the sides of an equilateral triangle (def. xxi.). |
this passion was so sovereign in him over all the rest, and with so absolute authority possessed his soul, that it guided him at pleasure. |
in general, both the argument about increase of size and that about water poured on to the ashes get in their own way. |
such is the athens for which these men, in the assertion of their resolve not to lose her, nobly fought and died; and well may every one of their survivors be ready to suffer in her cause. |
every division should have a patron god or hero; to these a portion of the domain should be appropriated, and at their temples the inhabitants of the districts should meet together from time to time, for the sake of mutual help and friendship. |
finally, therefore, the categories are only capable of empirical use, inasmuch as they serve merely to subject phenomena to the universal rules of synthesis, by means of an a priori necessary unity (on account of the necessary union of all consciousness |
intelligible to particular individuals. moreover, to the same people different things are more intelligible at different times; first of all the objects of sense; then, as they become more sharpwitted, the converse; so that those who hold that a |
but yet this account is not fully satisfactory ; for error is not only a meer negation , but 'tis a privation , or a want of a certain knowledge , which ought (as it were) to be in me. |
quarters, and raising the battle-cry aloud. |
we are to content ourselves with the light it pleases the sun to communicate to us, by virtue of his rays; and who will lift up his eyes to take in a greater, let him not think it strange, if for the reward of his presumption, he there lose his sight. |
be caused by the form of the earth's surface, which is therefore spherical. again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size. |
the real creation began, not with matter, but with ideas. |
hence growth must not be regarded as a process from a matter without magnitude to an actuality of magnitude: for this would be a body's coming-to-be rather than its growth. |
but those which perfume the air most delightfully, not passed by as the rest, but being trodden upon and crushed, are three; that is, burnet, wildthyme, and watermints. |
thus, how much soever men are in earnest and constant in pursuit of happiness, yet they may have a clear view of good, great and confessed good, without being concerned for it, or moved by it, if they think they can make up their happiness without it. |
(three), the free and easy ways of men and animals, which are characteristic of liberty, as foreign mercenaries and universal mistrust are of the tyrant; |
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