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one hundred six. given the base of a triangle, the difference of the base angles, and the rectangle of the sides; construct the triangle. |
be indivisible. the question is begged because definable form is assumed as a premiss, and as a premiss which is to prove definable form. 'but not the same definable form', you may object. |
this, however, is impossible, since, if it were true, earth must, in its own world, move upwards, and fire to the centre; in the same way the earth of our world must move naturally away from the centre when it moves towards the centre of another universe. |
if it is divisible through and through, and if this division is possible, then it might be, at one and the same moment, divided through and through, even though the dividings had not been effected simultaneously: and the actual occurrence of this result |
lend me, for once, my friends, your valiant hands, to force from out their lines these dastard bands. less than a thousand ships will end this war, nor vulcan needs his fated arms prepare. let all the tuscans, all th' arcadians, join! |
we must begin our examination with movement; for doubtless, not only is it false that the essence of soul is correctly described by those who say that it is what moves (or is capable of moving) itself, but it is an impossibility that movement should be |
so' too, if water and earth are to result from fire and air respectively-both qualities must change. |
twelve. how many intersections can a line and a circle have? |
sixty one. if a traveller does not meet with one who is his better, or his equal, let him firmly keep to his solitary journey; there is no companionship with a fool. |
"still, in the name of the gods who once presided over our confederacy, and of our own good service in the hellenic cause, we adjure you to relent; to recall the decision which we fear that the thebans may have obtained from you; to ask back the gift that |
as she kept saying this to every thing which was given, at last euelthon sent out to her a present of a golden spindle and distaff, with wool also upon it: and when pheretime uttered again the same saying about this present, euelthon said that such things |
necessarily to all b. similarly also if the syllogism should be negative: for the proof will be the same. |
a better understanding about them: all these things, o my friend, have not yet been sufficiently declared to you by the legislator. |
thirty one. shame is pain accompanied by the idea of some action of our own, which we believe to be blamed by others. |
again, if any 'indivisible' is 'hard', there must also be one which is 'soft': but 'the soft' derives its very name from the fact that it suffers a certain action-for 'soft' is that which yields to pressure. |
three angles thereof are not greater then two right ones , tho upon the first consideration this came not into my thought. |
but this difficulty of obeying both god, and the civill soveraign on earth, to those that can distinguish between what is necessary, and what is not necessary for their reception into the kingdome of god, is of no moment. |
and in his letters, instead of the usual civil expressions, "greeting," "farewell," and so on, he substitutes, "may you act well," "may you live virtuously," and expressions of that sort. |
revolving,-in seven orbits seven stars. first, there was the moon in the orbit nearest the earth, and next the sun, in the second orbit above the earth; then came the morning star and the star sacred to hermes, moving in orbits which have an equal |
full procession to marcius with their pontifical array, and the dress and habit which they respectively used in their several functions, and should urge him, as before, to withdraw his forces, and then treat with his countrymen in favor of the volscians. |
will you believe that he passed the ten intervening days before his execution without the slightest despondency? it is marvellous how that man spoke and acted, and how peaceful he was. |
he who has been taught to play at the same games and with the same playthings will be content with the same laws. there is no greater evil in a state than the spirit of innovation. |
was done before the affair in question took place from which a hope arose of accomplishing it, and an opportunity was sought of doing it, what happened with respect to the affair itself, and what ensued afterwards. |
nineteen. what is euclid's limit of an angle? |
one hundred twenty four. from a point p in the plane of a given polygon perpendiculars are let fall on its sides; if the area of the polygon formed by joining the feet of the perpendiculars be given, the locus of p is a circle. |
prop. four.-problem. to inscribe a circle in a given triangle (abc). |
there comes into my mind an ancient doctrine which affirms that they go from hence into the other world, and returning hither, are born again from the dead. |
excellent institutions and arts; but of his school and system i shall, perhaps, find another opportunity to speak. |
of his luxuries and made no use of them, but laid himself down upon the grass also, without regard for his delicate and richly dyed clothing. |
a number of others came thrusting themselves on their company, to the number of six hundred, but the officers repelled them: "they had no notion of sharing their portion of the spoil," they said, "just as though the property lay already at their feet." |
prop. twenty five.-problem. an arc (abc) of a circle being given, it is required to describe the whole circle. |
being occasioned from the body, must needs be less natural to a spirit? |
the engagement of the rest was more of a voluntary nature. |
it realizes its activity and continues to rise higher. |
but white is not further subdivided by specific differences: hence any whitening is specifically one with any other whitening. |
therefore the circle described with o as centre, and oa as radius, will pass through the points b, one hundred, five hundred, e, and be described about the pentagon. |
hence he leads a divided existence; in which the better desires mostly prevail. |
if by this is meant, was he loyal to athenian institutions?-he can hardly be said to be the friend of democracy: but neither is he the friend of any other existing form of government; all of them he regarded as 'states of faction' (laws); none attained to |
thirty. if the sum of the perpendiculars let fall from a given point on the sides of a given rectilineal figure be given, the locus of the point is a right line. |
sake of the good, and not the good for the sake of them?-will you add a third vote to our two? |
also, those mathematicians who try to calculate the size of the earth's circumference arrive at the figure four hundred,zero stades. |
a short time will to all my madness prove, when stern reality presents itself. |
now the nile is our saviour from fire, and as there is little rain in egypt, we are not harmed by water; whereas in other countries, when a deluge comes, the inhabitants are swept by the rivers into the sea. |
all haste moved forwards with those that he had about him. his march was very difficult, through rugged places and in a great snow, but so swift that he left those that were to bring his provisions for the morning meal a great way behind. |
the cause, therefore, of the coming-to-be of the things which owe their existence to nature is that they are in such-and-such a determinate condition: and it is this which constitutes, the 'nature' of each thing-a 'nature' about which he says nothing. |
as for serum, that sort which is the watery part of blood is innocent, but that which is a secretion of black and acid bile is malignant when mingled by the power of heat with any salt substance, and is then called acid phlegm. |
do the rhetoricians appear to you always to aim at what is best, and do they seek to improve the citizens by their speeches, or are they too, like the rest of mankind, bent upon giving them pleasure, forgetting the public good in the thought of their own |
thirdly (c) in its most proper use, it is that which is, but is incapable of any destruction such that the thing which now is later ceases to be or might cease to be; or again, that which has not yet been destroyed, but in the future may cease to be. |
dem.-join be, four hundred. the triangles bde, ced are on the same base de, and between the same parallels bc, de. hence i. xxxvii. they are equal, and therefore five. vii. the triangle ade : bde :: ade : cde; |
when the light of the eye is surrounded by the light of day, then like falls upon like, and they unite and form one body which conveys to the soul the motions of visible objects. |
at the close of the year was consecrated an arch near the temple of saturn to commemorate the recovery of the standards lost with varus, under the leadership of germanicus and the auspices of tiberius; a temple of fors fortuna, by the tiber, in the |
nevertheless, how this can be so remains matter for inquiry; how it comes about, i mean, that the same motive force at one time causes a thing to be in motion, and at another does not do so: for the difficulty raised by our objector really amounts to |
you may make your mind easy about this contest, for no phaeacian can come near to such a throw as yours." |
a bond for ten millions of sesterces was entered into in the women's apartment, (where many things have been sold, and are still being sold,) by his ambassadors, well-meaning men, but timid and inexperienced in business, without my advice or that of the |
again, if void is a sort of place deprived of body, when there is a void where will a body placed in it move to? it certainly cannot move into the whole of the void. |
always coincident with itself. hence since the light is what is naturally carried up, and the heavy what is carried down, the boundary which contains in the direction of the middle of the universe, and the middle itself, are down, and that which contains |
mind, any more than the other is the full study of life. they both have narrowed their subject to suit the abstract scheme of the laboratory, where the victim of experiment is either altered by mutilation and artificial restrictions, or is dead. |
"and the point of the spear in its fury drove |
to accident are to be attached also all comparisons of things together, when expressed in language that is drawn in any kind of way from what happens (accidit) to be true of them; such as, for example, the question, 'is the honourable or the expedient |
the compound may he-actually other than the constituents from which it has resulted; nevertheless each of them may still he-potentially what it was before they were combined, and both of them may survive undestroyed. |
thirdly, if a thing is capable of any particular motion, it is also capable of the corresponding contrary motion or the corresponding coming to rest, and a thing that is capable of becoming is also capable of perishing: consequently, if there be becoming |
this discussion, however, involves the more general question whether the infinite can be present in mathematical objects and things which are intelligible and do not have extension, as well as among sensible objects. |
for nothing to the world below. this, however, is a later stage; at present we must treat more exactly the subject before us, which involves a preliminary enquiry into the generation of the body and its members, and as to how the soul was created-for what |
the fairies marry not; but there be amongst them incubi, that have copulation with flesh and bloud. the priests also marry not. |
"hoc est vivere bis, vita posse priore frui." |
ever be rightly constituted. but he should have seen that the masterful spirit of christianity is incompatible with his system, and that the priestly interest would always be stronger than that of the state. |
to tell the truth and to aim straight: that is the first persian virtue. am i understood?... |
duris, however, who even where he has no private feeling concerned, is not wont to keep his narrative within the limits of truth, is the more likely upon this occasion to have exaggerated the calamities which befell his country, to create odium against |
nineteen. suppose that at the palestra somebody hath all to-torn thee with his nails, and hath broken thy head. well, thou art wounded. yet thou dost not exclaim; thou art not offended with him. |
two hundred fifty one. it must be taken into the bargain, if various clouds and disturbances--in short, slight attacks of stupidity--pass over the spirit of a people that suffers and wants to suffer from national nervous fever and political ambition: for |
still, the head could not be left a bare globe of bone on account of the extremes of heat and cold, nor be allowed to become dull and senseless by an overgrowth of flesh. |
for prudence, is but experience; which equall time, equally bestowes on all men, in those things they equally apply themselves unto. |
we had scarce worn cloth a year, in compliance with the court, for the mourning of henry two., but that silks were already grown into such contempt with every one, that a man so clad was presently concluded a citizen: silks were divided betwixt the |
a light hath dawned upon me. not to the people is zarathustra to speak, but to companions! zarathustra shall not be the herd's herdsman and hound! |
two hundred four estellonto : many editors, following inferior mss., read eselthontes and make changes in the rest of the sentence. |
all that he did was done rationally in and by himself, and he moved in a circle turning within himself, which is the most intellectual of motions; but the other six motions were wanting to him; wherefore the universe had no feet or legs. |
most beloved qualities, idleness and freedom; by all these together i have conceived a mortal hatred to being obliged to any other, or by any other than myself. |
now, however, that you have convinced me by showing that you know all about our bed (which no human being has ever seen but you and i and a single maidservant, the daughter of actor, who was given me by my father on my marriage, and who keeps the doors of |
"when proserpine had dismissed the female ghosts in all directions, the ghost of agamemnon son of atreus came sadly up to me, surrounded by those who had perished with him in the house of aegisthus. |
consequently f (fire) as well as air will be able to be transformed into water: for it has qualities contrary to those of water, since fire was first taken to be black and then to be dry, while water was moist and then showed itself white. |
prop. twenty four.-theorem. in any parallelogram (ac), every two parallelograms (af, fc) which are about a diagonal are similar to the whole and to one another. |
socrates: and the reason for asking this second question would be, that there are other painters besides, who paint many other figures? |
for what cannot be can no more come-to-be than be, and movement is a coming to-be in one place from another. |
aware that he would now be obliged either to say what had been already said by the men whom he was slandering, or be proved a liar if he said the contrary, he told the athenians, whom he saw to be not altogether disinclined for a fresh expedition, that |
slew him. it is related that in this battle there were amazons fighting as auxiliaries with the barbarians, and that they came down from the mountains by the river thermodon. |
the cities were not of that very great extent, the people in general living in the country, and being employed in husbandry, which gave them, who took the lead in public affairs, an opportunity, if they had a turn for war, to make themselves tyrants; |
this, because he suppressed the tyrants, overthrew the barbarians, replenished the principal cities, that were desolate, with new inhabitants, and then restored the sicilian greeks to the privilege of living by their own laws." |
at the gate of the town the grave-diggers met him: they shone their torch on his face, and, recognising zarathustra, they sorely derided him. "zarathustra is carrying away the dead dog: a fine thing that zarathustra hath turned a grave-digger! |
light things and heavy things, which are moved either by that which brought the thing into existence as such and made it light and heavy, or by that which released what was hindering and preventing it); then all things that are in motion must be moved by |
forty five. if abc be an equilateral triangle, what is the locus of the point one thousand, if ma mb one thousand one hundred? |
but this may look like a fable. the city, however, being taken by storm, and the soldiers busied in pillaging and gathering an infinite quantity of riches and spoil, camillus, from the high tower, viewing what was done, at first wept for pity; and when |
consequently, also, it is unknowable, qua infinite; for the matter has no form. (hence it is plain that the infinite stands in the relation of part rather than of whole. |
the way of lycurgus seems the more natural with a view to the birth of children; the other, looking to a life to be spent together, is more moral. |
are best acquainted with their own wants, and ought therefore, when they demand nothing in derogation of the essentiall rights of soveraignty, to be diligently taken notice of. |
again, because ab is divided equally in o and unequally in e, the rectangle ae.eb, together with oe , is equal to ob -that is, to oc two. v. ; but oc is equal to oe ec i. xlvii. therefore |
we should not be able to derive from the justice of your cause such powerful arguments for the maintenance and reduction of your subjects, as we do from the reports of the success of your undertaking; and then i have to assure your majesty, that the |
of problems some are universal, others particular. universal problems are such as 'every pleasure is good' and 'no pleasure is good'; particular problems are such as 'some pleasure is good' and 'some pleasure is not good'. |
, and that the point of contact is equivalent to two common points, circles that touch cannot have any other point common. |
defenders. as to virtue, there is no particular b in which they all agree: for as all do not equally esteem all virtues, it reasonably follows that they will not cultivate the same. |
one. if ef, gh be parallels to the adjacent sides of a parallelogram abcd, the diagonals eh, gf of two of the four picts into which they divide it and one of the diagonals of abcd are concurrent. |
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