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but water, when divided by fire or by air, on re-forming, may become one part fire and two parts air; and a single volume of air divided becomes two of fire. |
which describes him as the good citizen who passes through life undefiled and is obedient to the words of the legislator, both when he is giving laws and when he assigns praise and blame. |
to remove the war and the danger so far from the frontier of the athenians, that even success would profit the enemy but little, should they be conquerors, whereas, if they were defeated, sparta itself was hardly safe. |
theaetetus: i see no reason why we should be ashamed of our demonstration, socrates. |
it is normal to their plane, that is, it is normal to ten. |
but if the reason of differences of weight is not this, but rather the heaviness of earth and the lightness of fire, then some of the planes will be light and others heavy (which involves a similar distinction in the lines and the points); the earthplane, |
he is the 'guardian of his orphans,' although this is a responsibility which he wishes to throw upon callias, the friend and patron of all sophists, declaring that he himself had early 'run away' from philosophy, and was absorbed in mathematics. |
drives round the air at the other, and that which is driven round falls into the fire and becomes warm, and that which goes forth is cooled. |
dem.-describe a circle about the triangle. let fall the perpendicular cf. produce cf to meet the circle in g. make fo fg. join ag, ao. produce ao to meet bc in five hundred. |
this series, of which the intervals are afterwards filled up, probably represents (one) the diatonic scale according to the pythagoreans and plato; (two) the order and distances of the heavenly bodies; and (three) may possibly contain an allusion to the |
sixty five. and the lacedemonians would never have captured the sons of peisistratos at all; for they on their side had no design to make a long blockade, and the others were well provided with food and drink; so that they would have gone away back to |
jerome, who holdeth the rest, namely, the wisdome of solomon, ecclesiasticus, judith, tobias, the first and second of maccabees, (though he had seen the first in hebrew) and the third and fourth of esdras, for apocrypha. |
twenty eight. what is the condition that must be fulfilled that four points may be concyclic? |
this aptness of language is one thing that makes people believe in the truth of your story: their minds draw the false conclusion that you are to be trusted from the fact that others behave as you do when things are as you describe them; and therefore |
but the leading men of the state failed to convict him on all the charges. when they pressed the case, he appealed to the emperor. |
cato got together little less than seven thousand talents of silver; but apprehensive of what might happen in so long a voyage by sea, he provided a great many coffers, that held two talents and five hundred drachmas apiece; to each of these he fastened a |
for gods: so let no one be surprised at her committing any act of cruelty three hundred seventy five or injustice; for how could she show any humanity or moderation in her dealings with private families, when her pitiless fury has so often hung the very |
difference of the base angles be equal to a right angle; (two) in geometrical progression if one base angle be right; (three) in harmonical progression if the sum of the base angles be equal to a right angle. |
; hence the sum of the three angles acb, bac, abc is two right angles. |
further, those who divide bodies into planes and generate them out of planes seem to bear witness to the truth of this. |
"ad primum lapidem vectari quum placet, hora sumitur ex libro; si prurit frictus ocelli angulus, inspecta genesi, collyria quaerit;" |
dem.-because ae is equal to eb (const.), the triangle aec is equal to the triangle ebc xxxviii. , therefore the triangle abc is double of the triangle ebc; but the parallelogram eg is also double of the triangle ebc xli. |
to the accomplishment of which, it will not be necessary for me to prove them all false (for that perhaps i shall never atcheive) but because my reason perswades me, that i must withdraw my assent no less from those opinions which seem not so very certain |
onset; so that their fording was likely to be tumultuous and without order, a mere general struggle which should be the foremost. |
therefore in the case we are now considering there is nothing to prevent the motion being continuous and free from all intermission: for rotatory motion is motion of a thing from its place to its place, whereas rectilinear motion is motion from its place |
one another. now to the other gods the egyptians do not think it right to sacrifice swine; but to the moon and to dionysos alone at the same time and on the same full-moon they sacrifice swine, and then eat their flesh: and as to the reason why, when they |
speeches of theirs which are exceedingly praised, are so generally because they are concisely expressed. and it is now near four hundred years since this doctrine has been established among the greeks; we have only lately recognised it. |
horses, beasts of burden, baggage, were thrown overboard, in order to lighten the hulls which leaked copiously through their sides, while the waves too dashed over them. |
i. we all, o pansa, ought both to feel and to show the greatest gratitude to you, who--though we did not expect that you would hold any senate to day,--the moment that you received the letters of marcus brutus, that most excellent citizen, did not |
prop. eleven.-problem. to inscribe a regular pentagon in a given circle (abcde). |
this objection consists of two parts, which we shall examine separately; first , that, if human actions can be traced up, by a necessary chain, to the deity, they can never be criminal; on account of the infinite perfection of that being from whom they |
and, further, the weight of unequal masses will be the same, since the infinite and the finite cannot be equal. it does not matter whether the weights are commensurable or not. if (a) they are incommensurable the same reasoning holds. |
great political problems which he discusses in the republic and the laws. there are no speculations on physics in the other dialogues of plato, and he himself regards the consideration of them as a rational pastime only. |
for how should you divide it? or how can the infinite have the one part up and the other down, or an extremity and a centre? |
if freedom can with any propriety of speech be applied to power, it may be attributed to the power that is in a man to produce, or forbear producing, motion in parts of his body, by choice or preference; which is that which denominates him free, and is |
that scourge of all dishonesty, the law against fraud, proposed by our friend aquillius; that sort of fraud, he says, by which one thing is pretended and another done. can we, then, think that this plentiful fountain of evil sprung from the immortal gods? |
cause is to be found elsewhere. the void, they say, which is imprisoned in bodies, lightens them and sometimes makes the larger body the lighter. the reason is that there is more void. |
the latter. and agreeably to those conditions of the simple and local value of figures, were contrived methods of finding, from the given figures or marks of the parts, what figures and how placed are proper to denote the whole, or vice versa. |
the distinction here turns upon the difference of the categories. for some things signify a this somewhat, others a such, and others a so-much. |
let us start as follows. all things which admit of 'combination' must be capable of reciprocal contact: and the same is true of any two things, of which one 'acts' and the other 'suffers action' in the proper sense of the terms. |
see), the act of thinking cannot be the best of things. therefore it must be of itself that the divine thought thinks (since it is the most excellent of things), and its thinking is a thinking on thinking. |
our new question too-viz. 'what is the cause of the unbroken continuity of coming-to-be?'-is sufficiently perplexing, if in fact what passes-away vanishes into 'what is not' and 'what is not' is nothing (since 'what is not' is neither a thing, nor |
moreover, if the soldiers themselves are to cultivate that common land which is appropriated for their support, there will be no distinction between the soldier and the husbandman, which the legislator intended there should be; and if there should be any |
three. if acd, bcd be adjacent angles, any parallel to ab will meet the bisectors of these angles in points equally distant from where it meets four hundred. |
the saying-"practice does everything," is his. he it was, also, who proposed to cut through the isthmus. |
the most pertinent question with which to begin will be this: in what sense is it asserted that all things are one? for 'is' is used in many senses. do they mean that all things 'are' substance or quantities or qualities? |
for in proportion as the force applied by the heavy thing towards disruption and division exceeds that which resides in the continuum, the quicker will it force its way down; only if the force of the heavy thing is the weaker, will it ride upon the |
i will tell you:-in the first place, i will deprive men of the foreknowledge of death, which they possess at present: this power which they have prometheus has already received my orders to take from them: in the second place, they shall be entirely |
there is nothing to prevent the first place from being 'in' something else-not indeed in that as 'in' place, but as health is 'in' the hot as a positive determination of it or as the hot is 'in' body as an affection. so we escape the infinite regress. |
the largest (or fixed stars) is spangled, and the seventh (or sun) is brightest; the eighth (or moon) coloured by the reflected light of the seventh; the second and fifth (saturn and mercury) are in colour like one another, and yellower than the |
the end of government being the good of the community, whatsoever alterations are made in it, tending to that end, cannot be an encroachment upon any body, since no body in government can have a right tending to any other end: and those only are |
it can only be, then, that it occupies less time, and thus we get the necessary consequence that the quicker will pass over an equal magnitude (as well as a greater) in less time than the slower. |
these boastful humours may counterfeit some content, for what will not fancy do? but as to wisdom, there is no touch of it. will they not seek the quadrature of the circle, even when on their wives? |
questioner be willing to take the safe and indefinite expression, 'such,' we should be satisfied. |
two. if the line which bisects the vertical angle of a triangle also bisects the base, the triangle is isosceles. |
a single defeat at sea is in all likelihood their ruin: should they hold out, in that case there will be the more time for us to exercise ourselves in naval matters; and as soon as we have arrived at an equality in science, we need scarcely ask whether we |
a motion from health and a motion to health (where the opposition, it would seem, is of the same kind as that between coming to be and ceasing to be); or motions respectively from contraries, e.g. |
the white phlegm, though dangerous when detained within by reason of the air-bubbles, yet if it can communicate with the outside air, is less severe, and only discolours the body, generating leprous eruptions and similar diseases. |
this feeling (which we call the moral feeling) is therefore produced simply by reason. it does not serve for the estimation of actions nor for the foundation of the objective moral law itself, but merely as a motive to make this of itself a maxim. |
-there boometh the clock-bell, there thrilleth still the heart, there burroweth still the wood-worm, the heart-worm. ah! ah! the world is deep! |
suspicion, in consequence of a dream which antigonus had. |
liberal man, he gives and forbears to receive, only he does neither in right manner or well. |
and it is clear that all the syllogisms are imperfect, and are completed by means of the figures mentioned. |
let e represent half the motive power a and z half the weight b: then the ratio between the motive power and the weight in the one case is similar and proportionate to the ratio in the other, so that each force will cause the same distance to be traversed |
relation to possible experience, and therefore cannot be proved except by means of a deduction of the possibility of experience, it is no wonder that while it has served as the foundation of all experience (for we feel the need of it in empirical |
tacitus. the ambassadors of samos, prepared with a long and elegant oration, came to cleomenes, king of sparta, to incite him to a war against the tyrant polycrates; who, after he had heard their harangue with great gravity and patience, gave them this |
now clear i understand what oft my steadiest thoughts have searched in vain; why our great expectation should be called the seed of woman: virgin mother, hail, high in the love of heaven; yet from my loins thou shalt proceed, and from thy womb the son of |
the general who loses a battle makes but few calculations beforehand. thus do many calculations lead to victory, and few calculations to defeat: how much more no calculation at all! |
"i hope, eumaeus," said he, "that jove will be as well disposed towards you as i am, for the respect you are showing to an outcast like myself." |
to explain, however, in what way the tribunes did sometimes represent it, it is enough to conceive how the government represents the sovereign. |
thirteen. the smallest median of a triangle corresponds to the greatest side. |
his love is constrained, his hatred is artificial, and rather un tour de force, a slight ostentation and exaggeration. he is only genuine so far as he can be objective; only in his serene totality is he still "nature" and "natural." |
irregular. so quickness and slowness are not species of motion nor do they constitute specific differences of motion, because this distinction occurs in connexion with all the distinct species of motion. |
my stomach-is surely an eagle's stomach? for it preferreth lamb's flesh. certainly it is a bird's stomach. |
perhaps there is not any one thing that deserves more to be looked after. |
whenever bodies are moving with their proper motion, the larger moves quicker. |
now rotatory motion can be eternal: but no other motion, whether locomotion or motion of any other kind, can be so, since in all of them rest must occur and with the occurrence of rest the motion has perished. |
i have taken notice (for, so many families, so many differing forms) that the ladies who have been strictest with their maids have had no better luck than those who allowed them a greater liberty. |
vi.) and doing such things as necessarily follow from its given nature (see the def. of appetite, three. ix. note). but the essence of reason is nought else but our mind, in so far as it clearly and distinctly understands (see the definition in two. xl. |
after the death of chalcideus and the battle at miletus, alcibiades began to be suspected by the peloponnesians; and astyochus received from lacedaemon an order from them to put him to death, he being the personal enemy of agis, and in other respects |
sect. fifty. but since gold and silver, being little useful to the life of man in proportion to food, raiment, and carriage, has its value only from the consent of men, whereof labour yet makes, in great part, the measure, it is plain, that men have |
i would recommend you, therefore, as i said before, not to encourage yourself in this polemical and controversial temper, but to find out, in a friendly and congenial spirit, what we really mean when we say that all things are in motion, and that to every |
the freedom of the will to refuse the evil and to choose the good is distinctly asserted. 'virtue is free, and as a man honours or dishonours her he will have more or less of her.' |
that there is no infinite body may be shown, as we have shown it, by a detailed consideration of the various cases. |
but he who seeks after knowledge and exercises the divine part of himself in godly and immortal thoughts, attains to truth and immortality, as far as is possible to man, and also to happiness, while he is training up within him the divine principle and |
if to beg his mercy, he will despise you; if to declare your commands he will not listen to them; and last of all, however severe the message may be which we give the ambassadors, the very name of ambassadors will extinguish this ardour of the roman |
river rhone in his armor, with his breastplate and shield, bearing himself up against the violence of the current; so strong and so well inured to hardship was his body. |
upon hearing the shouts, greater numbers still joining in the fight, it was not a little difficult for marius to contain his soldiers, who were afraid of losing the camp-servants; and the more warlike part of the enemies, who had overthrown manlius and |
and juno said, "sleep, why do you take such notions as those into your head? do you think jove will be as anxious to help the trojans, as he was about his own son? |
the citizens have a friendly feeling towards the athenians, believing themselves to be related to them. |
for we too hastily said that plato in the timaeus regarded all 'vices and crimes as involuntary.' |
mundus domus est maxima rerum, quam quinque altiton fragmine zon cingunt, per quam limbus pictus bis sex signis stellimicantibus, altus in obliquo there, lun bigas acceptat. |
but the spirit of persecution in plato, unlike that of modern religious bodies, arises out of the desire to enforce a true and simple form of religion, and is directed against the superstitions which tend to degrade mankind. |
two. if bd : six hundred :: ba : ac, the angle bac is bisected. |
hence the triangles agree in every respect; therefore bc is equal to ef, the angle b is equal to the angle e, the angle one hundred to the angle f, and the triangle bac to the triangle edf. |
so now all who escaped death in battle or by shipwreck had got safely home except ulysses, and he, though he was longing to return to his wife and country, was detained by the goddess calypso, who had got him into a large cave and wanted to marry him. |
that is called hard to which our flesh yields, and soft which yields to our flesh; and things are also termed hard and soft relatively to one another. |
another of his sayings was, "even the gods cannot strive against necessity." another was, "power shows the man." being once asked what was best, he replied, "to do what one is doing at the moment well." |
varius, a most impious wretch, was tortured and put to death. |
after these things, licinius stolo raised a great sedition in the city, and brought the people to dissension with the senate, contending, that of two consuls one should be chosen out of the commons, and not both out of the patricians. |
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