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about the hour of noontide, however, when the sun stood exactly over zarathustra's head, he passed an old, bent and gnarled tree, which was encircled round by the ardent love of a vine, and hidden from itself; from this there hung yellow grapes in |
thus, in the figure-one, two; seven, eight are called exterior angles; three, four; five, six, interior angles. |
or, how can the essences or forms of things be distinguished from the eternal ideas, or essence itself from the soul? or, how could there have been motion in the chaos when as yet time was not? |
in the funeral procession cypress coffins are borne in cars, one for each tribe; the bones of the deceased being placed in the coffin of their tribe. |
cannot 'have been combined' since they have no being at all. |
your sole prudence or good fortune, will easily conclude with me that we have not so vivid an example as yours of maternal affection in our times. |
borough of xypetion, being one of the presidents, and the rest of the presidents, his colleagues, put the following decree to the vote. and the decree was proposed by thrason, of anaca, the son of thrason. |
then the whole dz must be the motion of ag: for dz must constitute the motion of ag inasmuch as de and ez severally constitute the motions of each of its parts. |
this is equivalent to the statement, "if two right lines have two points common to both, they coincide in direction," that is, they form but one line, and this holds true even when one of the points is at infinity. |
colony, who is their legislator, finds them troublesome and rebellious. |
in the spirit of the statesman who said, 'let me make the ballads of a country, and i care not who make their laws,' plato would say, 'let the amusements of children be unchanged, and they will not want to change the laws. |
and thirdly, that they ought to ascertain the character of such ideas as are relative to one another, such as knowledge, or magnitude, or authority; considering that the things which come under our notice from partaking of their nature, have the same |
hosts, in arms oppos'd, with equal horror wounds: "o trojan race, your needless aid forbear, and know, my ships are my peculiar care. with greater ease the bold rutulian may, with hissing brands, attempt to burn the sea, than singe my sacred pines. |
pleas'd with the bribe, the god receiv'd his pray'r: for, while his shield protects a friend distress'd, the dart came driving on, and pierc'd his breast. |
instant and declared enmity of corinth. it were, rather, wise to try and counteract the unfavourable impression which your conduct to megara has created. |
democracy than an oligarchy; and afterwards in what manner any one ought to proceed who desires to establish either of these states, i mean every species of democracy, and also of oligarchy. |
enthymemes also have been described, and the sources from which they should be derived; there being both special and general lines of argument for enthymemes. |
with passions so little active, and so good a curb, men, being rather wild than wicked, and more intent to guard themselves against the mischief that might be done them, than to do mischief to others, were by no means subject to very perilous dissensions. |
internal heat followed the air to and fro. these, as we affirm, are the phenomena of respiration. |
socrates: then is not the syllable in the same case as the elements or letters, if it has no parts and is one form? |
heaven put it in her heart to do wrong, and she gave no thought to that sin, which has been the source of all our sorrows. |
our next task is to study coming-to-be and passing-away. we are to distinguish the causes, and to state the definitions, of these processes considered in general-as changes predicable uniformly of all the things that come-to-be and pass-away by nature. |
xxvi. a rectilineal figure bounded by more than three right lines is usually called a polygon. |
nor could they be extinguished by the fall of rain, or by river-water, or by any other moisture, till some countrymen, in despair of a remedy and in fury at the disaster, flung stones from a distance, and then, approaching nearer, as the flames began to |
so, too, young branches are eagerly eaten by the goat, but are bitter to mankind; and hemlock is nutritious for the quail, but deadly to man; and pigs eat their own dung, but a horse does not. |
cannot be free. the reason whereof is very manifest. |
the second place is that of matth. sixteen. "thou art peter, and upon this rocke i will build my church, and the gates of hell shall not prevail against it." |
object is necessarily subject to rules, because without such rules we never could attain to cognition of an object. |
or thus: ab ac cb, cb cb. hence ab.cb ac.cb cb . prop. iii. is the particular case of prop. i., when the undivided line is equal to a segment of the divided line. |
nor can number taken in abstraction be infinite, for number or that which has number is numerable. if then the numerable can be numbered, it would also be possible to go through the infinite. |
these things are useful in the management of one's affairs; to be skilful in the nature of cattle, which are most profitable, and where, and how; as for instance, what advantage will arise from keeping horses, or oxen, or sheep, or any other live stock; |
hence it is incumbent on the person who specializes in physics to discuss the infinite and to inquire whether there is such a thing or not, and, if there is, what it is. |
what herbart calculated were actions and reactions of idea-forces: what the modern experimental school proposes to measure are to a large extent the velocities of certain physiological processes, the numerical specification of certain facts. |
for whenever in any three numbers, whether cube or square, there is a mean, which is to the last term what the first term is to it; and again, when the mean is to the first term as the last term is to the mean-then the mean becoming first and last, and |
one hundred twelve. if a chord of a given circle subtend a right angle at a given point, the locus of the intersection of the tangents at its extremities is a circle. |
moreover, in such cases it is one member of the pair determinately, and not either the one or the other, which must be present. |
but what is moved is moved from something to something, and all magnitude is continuous. therefore the movement goes with the magnitude. |
dependence on the physical law that we should follow some impulse or inclination. |
unless any one who approves of punishment for the promulgation of opinions, flatters himself that he is a wiser and better man than marcus aurelius--more deeply versed in the wisdom of his time, more elevated in his intellect above it--more earnest in his |
of eternity; but, on the other side, not finding it necessary, but, on the contrary, apparently absurd, that body should be infinite, they forwardly conclude that they can have no idea of infinite space, because they can have no idea of infinite matter. |
the theory resembles that about the stone being worn away by the drop of water or split by plants growing out of it: if so much has been extruded or removed by the drop, it does not follow that half the amount has previously been extruded or removed in |
we were able to find out and furnish, are all supplied to you, and there is this especially besides, which is the chief thing of all, that is, we give you freely in addition our mothers and our sisters, in order that ye may perceive fully that ye are |
when, on the other hand, the content is freed from the mixedness and fortuitousness, attaching to it in the practical feeling and in impulse, and is set and grafted in the individual will, not in the form of impulse, but in its universality, so as to |
of making a discovery of this nature to seleucus. |
shall we say, then, that madness has its use? |
for such action and feeling as forms bad character, blinds the eye of the soul and corrupts the moral principle, and the place of practical wisdom is taken by that parody of itself which aristotle calls "cleverness"-the "wisdom" of the unscrupulous man of |
hence abc is equal to abf, which is impossible i., axiom ix. . therefore the lines bc, bd, be are coplanar. |
(similarly with the parts of wholes which are not continuous.) further, if each of the two parts is indivisibly one with the whole, the difficulty arises that they will be indivisibly one with each other also. |
for the ratios of smaller bodies may be repeated among greater bodies. |
a differentiating quality: and the other member of this contrariety, e.g. heat, will belong to some other 'element', e.g. to fire. but fire will certainly not be 'hot air'. for a change of that kind (a) is 'alteration', and (b) is not what is observed. |
but dicaearchus writes that there were two arcadians in the army of castor and pollux, the one called echedemus and the other marathus; from the first that which is now called academia was then named echedemia, and the village marathon had its name from |
when two effeminate fellows were getting out of his way, he said, "do not be afraid, a dog does not eat beetroot." being once asked about a debauched boy, as to what country he came from, he said, "he is a tegean." |
or thus: on ab describe the square abde, and cut off ah, eg, df each equal to cb. join cf, fg, gh, hc. now the four s ach, cbf, fdg, geh are evidently equal; therefore their sum is equal to four times the ach; but the ach is half the rectangle ac.ah (i. |
for when anything is displaced this will always happen, unless it comes round in a circle; but locomotion is not always circular, but sometimes in a straight line. |
whether to the objects that are presented to its senses or to its internal affections, as can take place in our own case apart from the guidance of the will. |
salmacida, spolia sine sudore et sanguine. |
i would have thy victory and freedom long for a child. living monuments shalt thou build to thy victory and emancipation. |
in order to get a yet firmer hold upon pompey, caesar having a daughter, julia, who had been before contracted to servilius caepio, now betrothed her to pompey, and told servilius he should have pompey's daughter, who was not unengaged either, but |
seventy. if a circle touch internally two sides, ca, cb, of a triangle and its circumscribed circle, the distance from one hundred to the point of contact on either side is a fourth proportional to the semiperimeter, and ca, cb. |
materials to create more worlds- into this wild abyss the wary fiend stood on the brink of hell and looked a while, pondering his voyage; for no narrow frith he had to cross. |
however, as in this philosophical and critical age such empiricism can scarcely be serious, and it is probably put forward only as an intellectual exercise and for the purpose of putting in a clearer light, by contrast, the necessity of rational a priori |
the tendency to argue from the higher to the lower, from man to the world, has led to many errors, but has also had an elevating influence on philosophy. |
by his mighty magic, and is first-rate at inventing or disposing of any sort of calumny on any grounds or none. all of them agree in asserting that a speech should end in a recapitulation, though they do not all agree to use the same word. |
if then, it is agreed that things are either the result of coincidence or for an end, and these cannot be the result of coincidence or spontaneity, it follows that they must be for an end; and that such things are all due to nature even the champions of |
twenty six. two parallel chords of a circle are twelve perches and sixteen perches respectively, and their distance asunder is two perches; find the length of the diameter. |
falsa, ad animi assensum, nihil interest: "amongst things that seem, whether true or false, it signifies nothing to the assent of the mind." |
they brought their enemies near their ruin, but never entirely conquered them. there was yet a greater conformity in the free good-will and lavish abundance of their entertainments and general hospitalities, and in the youthful laxity of their habits. |
heraclitus having written so many natural tracts concerning the last and general conflagration of the world, died afterwards all filled with water within, and all bedaubed with dirt and dung without. |
in the second book, when glaucon insists that justice and injustice shall be considered without regard to their consequences, adeimantus remarks that they are regarded by mankind in general only for the sake of their consequences; and in a similar vein of |
shown out of deut. thirteen. one. c. and in the new testament there was but one onely mark; and that was the preaching of this doctrine, that jesus is the christ, that is, the king of the jews, promised in the old testament. |
it argues more wisdom to contrive at first the fabric of the world with such perfect foresight that, of itself, and by its proper operation, it may serve all the purposes of providence, than if the great creator were obliged every moment to adjust its |
distribute it abroad. and here i cannot but smile to think how i have paid myself in showing the foppery of this kind of learning, who myself am so manifest an example; for, do i not the same thing throughout almost this whole composition? |
and if not of all, the exceptions will be contradictories of which admittedly only one is true; but if of all, again either the negation will be true wherever the assertion is, and the assertion true wherever the negation is, or the negation will be true |
for just as in geometry it is useful to be practised in the elements, and in arithmetic to have the multiplication table up to ten at one's fingers' ends-and indeed it makes a great difference in one's knowledge of the multiples of other numbers |
but neither does time exist without change; for when the state of our own minds does not change at all, or we have not noticed its changing, we do not realize that time has elapsed, any more than those who are fabled to sleep among the heroes in sardinia |
if it has been proved to be an object of knowledge without qualification, we must put as middle term 'that which is', but if we add the qualification 'that it is good', the middle term must be 'that which is something'. |
rest of the peloponnesians to help them, do nowadays threaten to make an incursion into attica single-handed; and the athenians, who formerly, if they had to deal with the boeotians (seven) only, made havoc of their territory, are now afraid the boeotians |
now judiciousness is neither entirely identical with knowledge or opinion (for then all would have been judicious), nor is it any one specific science, as medical science whose object matter is things wholesome; or geometry whose object matter is |
grote supposes, not that (greek) means 'revolving,' or that this is the sense in which aristotle understood the word, but that the rotation of the earth is necessarily implied in its adherence to the cosmical axis. |
were of empirical content. this kind of logic would also examine the origin of our cognitions of objects, so far as that origin cannot be ascribed to the objects themselves; while, on the contrary, general logic has nothing to do with the origin of our |
hostile shore more their own than that sea which had cost them so much labour to win; the syracusans, whether they were flying from the flying athenians, whom they well knew to be eager to escape in whatever way they could. |
he kept as a companion a boy whom he used to carry about with him, not only when he had troops under his charge, but even when the care of a province was committed to him. |
he, from his nostrils huge mouth, expires black clouds of smoke, amidst his father's fires, gath'ring, with each repeated blast, the night, to make uncertain aim, and erring sight. |
moreover, whatever possesses weight or lightness will have its place either at one of the extremes or in the middle region. but this is impossible while the world is conceived as infinite. |
for not the whole race only, but each individual-barring inevitable accidents-comes into the world having a fixed span, and the triangles in us are originally framed with power to last for a certain time, beyond which no man can prolong his life. |
worthy of our increased audience. what do you allude to? said laelius; or what was the discussion we broke in upon? scipio was asking me, replied philus, what i thought of the parhelion, or mock sun, whose recent apparition was so strongly attested. |
and will and intelligence are an important stage in that process. |
it was very pleasant, when i stayed late in town, to launch myself into the night, especially if it was dark and tempestuous, and set sail from some bright village parlor or lecture room, with a bag of rye or indian meal upon my shoulder, for my snug |
he hastened forward, with his arms like the wings of a bird. four. when the guest had retired, he would report to the prince, 'the visitor is not turning round any more.' chap. four. one. |
changes, and may be dissolved from time to time without the assistance of the courts. besides, he will remark that there is a much greater choice of friends than of wives--you may have more of them and they will be far more improving to your mind. |
on similar grounds, therefore, five hundred (dryness) will also belong to f. |
three. three equal lines could not be drawn from the same point to the same line. |
furthermore, in the case of becoming and perishing it would seem to be an utterly absurd thing if as soon as anything has become it must necessarily perish and cannot continue to exist for any time: and, if this is true of becoming and perishing, we have |
no man can quite exclude this element of necessity from his labor. no man can quite emancipate himself from his age and country, or produce a model in which the education, the religion, the politics, usages and arts of his times shall have no share. |
four. what is the difference between linear and superficial measurement? ans. linear measurement has but one dimension; superficial has two. |
it is not possible to be at once white and black, and therefore it must also be impossible for a thing to be affected at one and the same moment by the forms of both, assuming it to be the case that sensation and thinking are properly so described. |
at last, after five days, an end was put to the conflagration at the foot of the esquiline hill, by the destruction of all buildings on a vast space, so that the violence of the fire was met by clear ground and an open sky. |
for the schoolmen, though they acknowledge the existence of matter, and that the whole mundane fabric is framed out of it, are nevertheless of opinion that it cannot subsist without the divine conservation, which by them is expounded to be a continual |
it is they that have brought about this terrible war with the achaeans. tell me, then, who is yonder huge hero so great and goodly? i have seen men taller by a head, but none so comely and so royal. surely he must be a king." |
that is to say, justice is useful when money is useless? |
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