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and the boundless extent of plains, the hidden veins of gold and silver, and the infinite quarries of marble. |
cor. seven.-if one angle of a triangle be equal to the sum of the other two, it is a right angle. |
with them on various occasions. my excuse for relating these events, and for venturing on this digression, is that this passage of history has been omitted by all my predecessors, who have confined themselves either to hellenic history before the median |
or how can the answer be known to be satisfactory, if the objectors have no opportunity of showing that it is unsatisfactory? |
data. for (one) everything is capable of acting or being acted upon, of being or not being, either for an infinite, or for a definitely limited space of time; and the infinite time is only a possible alternative because it is after a fashion defined, as a |
if we were to say that the loves and pleasures of this third part were concerned with gain, we should then be able to fall back on a single notion; and might truly and intelligibly describe this part of the soul as loving gain or money. |
misfortune: he who has long prospered will have his share some day; those who seem to have been spared them have only had them put off. why does god afflict the best of men with ill-health, or sorrow, or other troubles? |
was absurd to imagine any divinities or powers delighted in slaughter and sacrifices of men; or, if there were an, such, they were to be neglected, as weak and unable to assist; such unreasonable and cruel desires could only proceed from, and live in weak |
then since p is the centre of ten, the three lines pa, pb, pc are equal to one another. |
endeavored to keep the city to a strict and temperate regimen. |
this concludes my account of place-both of its existence and of its nature. |
it was an high speech of seneca (after the manner of the stoics), that the good things, which belong to prosperity, are to be wished; but the good things, that belong to adversity, are to be admired. bona rerum secundarum optabilia; adversarum mirabilia. |
they profess not always to deliver their opinions barefaced and apparent to us; they have one while disguised them in the fabulous shadows of poetry, and at another in some other vizor; for our imperfection carries this also along with it, that crude meat |
belonging to thy body or life:) is without the jurisdiction of thine own will, and whatsoever in the ordinary course of human chances and accidents doth happen unto thee; so that thy mind (keeping herself loose and free from all outward coincidental |
one hundred twenty one. construct a polygon of an odd number of sides, being given that the sides taken in order are divided in given ratios by fixed points. |
the two states, ch'u and wu, had been constantly at war for over half a century, thirty one whereas the first war between wu and yueh was waged only in five hundred ten, thirty two and even then was no more than a short interlude sandwiched in the midst |
all animals smell in the same way, but man smells only when he inhales; if he exhales or holds his breath, he ceases to smell, no difference being made whether the odorous object is distant or near, or even placed inside the nose and actually on the wall |
from whence we may understand that they who gave these names to things were of the same opinion with socrates, that all silly people were unsound, which the stoics have carefully preserved as being derived from him; for whatever mind is distempered (and, |
and then assumes-he has not inferred-that man is animal. next, when presented with an exhaustive division of animal into terrestrial and aquatic, he assumes that man is terrestrial. |
money is not required to buy one necessary of the soul. |
again, the triangles bof, bog have the angle f equal to g, each being right; and obf equal to obg, because ob bisects the angle abc (const.), and ob common; hence i. xxvi. of is equal to og. |
as yet fully know whether there be any god , or not , 'tis but a slight and (as i may say) metaphysical reason of doubt, which depends only on that opinion of which i am not yet perswaded. |
what i mean is this: if the portions in this world behave similarly both to one another and to those in another world, then the portion which is taken hence will not behave differently either from the portions in another world or from those in the same |
now if it exists for infinite time let this capacity be actualized; and it will be in actuality at once existent and non-existent. |
but for the jewes to have such opinion, is somewhat strange. |
the reason is that the latter is assured to us by experiment, and is not contrasted with the certainty of ideal or mathematical knowledge. |
as regards the right and justice of their aims at empire, demetrius need not be blamed for seeking to rule a people that had always had a king to rule them. |
"no," replied jupiter, "with living"--"pilchards," said numa, interrupting him. these answers he had learnt from egeria. jupiter returned again to heaven, pacified and ilcos, or propitious. |
again, if it is the number of planes in a body that makes one heavier than another, as the timaeus explains, clearly the line and the point will have weight. for the three cases are, as we said before, analogous. |
ten. the rectangle contained by the side of an escribed square standing on the base of a triangle, and the difference between the base and altitude, is equal to twice the area of the triangle. |
(further, how can there be any 'before' and 'after' without the existence of time? or how can there be any time without the existence of motion? |
what he says, therefore, is no explanation of 'nature'. moreover, it is this which is both 'the excellence' of each thing and its 'good': whereas he assigns the whole credit to the 'mingling'. |
hindered it from predominating and advancing; and they so disturbed the nature of the other or diverse, that the three double intervals (i.e. between one, two, four, eight), and the three triple intervals (i.e. |
with this the son of peleus dashed his gold-bestudded sceptre on the ground and took his seat, while the son of atreus was beginning fiercely from his place upon the other side. |
the body, then, is turned into spheres or pyramids. let us grant that these figures may reasonably be supposed to cut and break up bodies as fire does; still it remains quite inexplicable that a pyramid must needs produce pyramids or a sphere spheres. |
(two) further, why, after always existing, was the thing destroyed, why, after an infinity of not being, was it generated, at one moment rather than another? |
but what about that which 'is' not except with a qualification? is it one of the two contrary poles of the chang-e.g. earth (i.e. the heavy) a 'not-being', but fire (i.e. the light) a 'being'? |
forty five. having heard this, forthwith they accompanied the men to the guard-posts, and when they had arrived there, alexander thus spoke to them: "athenians, i lay up these words of mine as a trust to you, charging you to keep them secret and tell them |
the danger, however, is not so great when the foundation remains, for then there is a possibility of recovery. |
on this menelaus was grieved, and made menacingly towards helenus, brandishing his spear; but helenus drew his bow, and the two attacked one another at one and the same moment, the one with his spear, and the other with his bow and arrow. |
born in the same month and year. nor does he explain how the lots could be so manipulated by the legislature as to bring together the fairest and best. |
grandeur that can have no place in the grandeur of epaminondas' courage. |
the same phenomenon occurs in other instances too. |
the veins about the nose are too narrow to admit earth and water, and too wide to detain fire and air; and for this reason no one ever perceives the smell of any of them; but smells always proceed from bodies that are damp, or putrefying, or liquefying, |
none answer'd this; but after silence spake a vessel of a more ungainly make: "they sneer at me for leaning all awry; what? did the hand then of the potter shake?" |
but this question depends on another set of arguments, and the truth will be made clear later. is possible for a thing to cause motion, though it is itself incapable of being moved. |
what a boldness and vehement confidence was it in him that he would not give over his attempt, but resolved upon two so great difficulties--which nevertheless he overcame; and, after having won that great battle against those without, soon reduced those |
one. what is the datum in this proposition? |
'at some time' means a time determined in relation to the first of the two types of 'now', e.g. 'at some time' troy was taken, and 'at some time' there will be a flood; for it must be determined with reference to the 'now'. |
sect. one hundred twenty seven. thus mankind, notwithstanding all the privileges of the state of nature, being but in an ill condition, while they remain in it, are quickly driven into society. |
one. the projection of any line on a plane is a right line. |
the timaeus of plato, like the protagoras and several portions of the phaedrus and republic, was translated by cicero into latin. about a fourth, comprehending with lacunae the first portion of the dialogue, is preserved in several mss. |
had the curiosity, or the method to find out. |
reasonings in the world could never lead us one step towards the knowledge of it. |
will it be said that each kind of thing has elements or principles of its own, and that the soul is formed out of the whole of these? in that case, the soul must be a quantum and a quale and a substance. |
subjected. the peoples right is equally invaded, and their liberty lost, whether they are made slaves to any of their own, or a foreign nation; and in this lies the injury, and against this only have they the right of defence. |
let a : b :: c : d; then if a be greater than c, b is greater than d; if equal, equal; if less, less. |
besides, those who have first heard the pleas of our adversaries will be more likely to credit the assertions which we are going to make. we shall be less open to the charge of procuring judgement by default. |
this long story of so light an accident would appear vain enough, were it not for the knowledge i have gained by it for my own use; for i do really find, that to get acquainted with death, needs no more but nearly to approach it. |
yes, my good sir, and there will be no better in which to look for a government. |
four hundred fourteen. the self-identity of the mind, thus first made explicit as the ego, is only its abstract formal identity. |
whewell and others with wasting their fine intelligences in wrong methods of enquiry; and their progress in moral and political philosophy has been sometimes contrasted with their supposed failure in physical investigations. |
one hundred nineteen. if three of the six points in which a circle meets the sides of any triangle be such, that the lines joining them to the opposite vertices are concurrent, the same property is true of the three remaining points. |
and their public virtues were the more agreeable to the people, because even in private matters they were ready to serve every citizen, by their exertions, their counsels, and their liberality. |
barbaric pride, luxury, and insolence of those who lavished their wealth in these vain and undesirable displays. |
sense, reason, all summed up in man. with what delight could i have walked thee round, if i could joy in aught, sweet interchange of hill, and valley, rivers, woods, and plains, now land, now sea and shores with forest crowned, rocks, dens, and caves! |
now there was a certain rich and honourable man among the trojans, priest of vulcan, and his name was dares. he had two sons, phegeus and idaeus, both of them skilled in all the arts of war. |
then they rallied and again faced the achaeans, but the argives stood compact and firm, and were not driven back. |
make use of the most lascivious means to that end then in use, as to have all the hairs of his body twitched off, and to wipe all over with perfumes with the extremest nicety. |
clear smooth lake, that to me seemed another sky. |
therefore fdc is greater than bcd: much more is bdc greater than bcd; but if bc were equal to bd, the angle bdc would be equal to bcd v. ; therefore bc cannot be equal to bd. |
thirty three. if a figure of any even number of sides be inscribed in a circle, prove that the sum of one set of alternate angles is equal to the sum of the remaining angles. |
after the fight, being filled with blood and dead bodies, upon this occasion, as we guess, might change its old name for that which it now bears. |
for it is possible that a should follow no b and all one hundred, though b does not belong to some one hundred, e.g. animal follows no science but every man, though science does not follow every man. |
'environing' exists-in isolation. it is, therefore, equally and indifferently any one of the 'elements', or else it is nothing. |
thirteen. if a triangle of given form move so that its three sides pass through three fixed points, the locus of any point in its plane is a circle. |
proof.--whatsoever takes place in the object of any idea, its idea is in god (by prop. iii. |
therefore if this differs in no respect from its place, why need we assume a place for bodies over and above the volume of each, if their volume be conceived of as free from attributes? |
there are these difficulties, then, in the way of the assumption that that which 'is not' can be in motion: and it may be further objected that, whereas everything which is in motion is in space, that which 'is not' is not in space: for then it would be |
three hundred sixty two you ought not, therefore, to allow any moment to be unoccupied by literary pursuits: at such times let literature repay to you the debt which your long and faithful love has laid upon it, let it claim you for its high priest and |
and afterwards the causes of things which are moved by others, and which work by chance and without order. of the second or concurrent causes of sight i have already spoken, and i will now speak of the higher purpose of god in giving us eyes. |
tragedian. but we shall continue to prohibit all poetry which goes beyond hymns to the gods and praises of famous men. not pleasure and pain, but law and reason shall rule in our state. |
so we have now to consider how motion is differentiated: and this discussion serves to show that the genus is not a unity but contains a plurality latent in it and distinct from it, and that in the case of equivocal terms sometimes the different senses in |
now, however, though i do not choose to praise any one when present, yet i must confess that i think you have delivered your thoughts clearly on an obscure and very intricate subject; that you are not only copious in your sentiments, but more elegant in |
my reason is much more free in prosperity, and much more distracted, and put to't to digest pains than pleasures: i see best in a clear sky; health admonishes me more cheerfully, and to better purpose, than sickness. |
there is no reason to suppose that any of the dialogues of plato were written before the death of socrates; the meno, which appears to be one of the earliest of them, is proved to have been of a later date by the allusion of anytus. |
but juno, when she saw him, knew that he and the old merman's daughter, silver-footed thetis, had been hatching mischief, so she at once began to upbraid him. "trickster," she cried, "which of the gods have you been taking into your counsels now? |
what kind of fearful things then do constitute the object-matter of the brave man? first of all, must they not be the greatest, since no man is more apt to withstand what is dreadful. |
is such that it is essentially capable of not-being. |
father, are you thus driving your mules and horses in the dead of night when other men are asleep? are you not afraid of the fierce achaeans who are hard by you, so cruel and relentless? |
when the prophet shall have spoken in the name of the lord, that which shall not come to passe, that's the word which the lord hath not spoken, but the prophet has spoken it out of the pride of his own heart, fear him not." |
on the monday morning he had become so ill that he quite despaired of himself; and he said to me very pitifully: "brother, do not you feel pain for all the pain i am suffering? |
hence it has become clear to me that the hellenes learnt the names of these gods later than those of the other gods, and trace their descent as if their birth occurred at the time when they first learnt their names. |
life, to confess to me the whole truth of the design." |
that the first deacons were chosen, not by the apostles, but by a congregation of the disciples; that is, of christian men of all sorts, is manifest out of acts six. |
prop. twenty one.-theorem. the angles (acb, adb) in the same segment of a circle are equal. |
none the less, if the two motions are commensurable, we are confronted with the consequence stated above, viz. that there may be a straight line equal to a circle. |
here is timaeus, of locris in italy, a city which has admirable laws, and who is himself in wealth and rank the equal of any of his fellow-citizens; he has held the most important and honourable offices in his own state, and, as i believe, has scaled the |
it is evident, therefore, if we consider them in general, that every one is by nature such as to come-to-be out of every one: and when we come to consider them severally, it is not difficult to see the manner in which their transformation is effected. |
the building of the temple of the capitoline jupiter had been vowed by tarquin, the son of demaratus, when warring with the sabines; tarquinius superbus, his son or grandson, built, but could not dedicate it, because he lost his kindom before it was quite |
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