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then the wise and good will not desire to gain more than his like, but more than his unlike and opposite? |
the same but distinct: and within the sphere of place we have the above-mentioned distinctions. |
for (i) if magnitudes are not divisible through and through-if, on the contrary, there are indivisible solids or planes-then indeed no body would be susceptible through and through :but neither would any be continuous. |
square on the line joining the points of bisection. |
icosahedron,-according to their degrees of lightness or heaviness or power, or want of power, of penetration. the single particles of any of the elements are not seen by reason of their smallness; they only become visible when collected. |
their respective sizes. thus the weightless body will move the same distance as the heavy in the same time. but this is impossible. |
one, that the things or objects themselves reach not unto the soul, but stand without still and quiet, and that it is from the opinion only which is within, that all the tumult and all the trouble doth proceed. |
then thus the prince: "let no disputes arise: where fortune plac'd it, i award the prize. but fortune's errors give me leave to mend, at least to pity my deserving friend." |
and the pilot-that is to say, the true pilot-is he a captain of sailors or a mere sailor? |
that fancy was singular in a man who thought the whole world his city; it is true that he disdained travel, and had hardly ever set his foot out of the attic territories. |
sol.-inscribe a regular pentagon abcde in the circle xi. , and also an equilateral triangle agh ii. . join cg. cg is a side of the required polygon. |
in the same manner it can be proved that all the angles are equal; therefore the figure abcde is equiangular. hence it is a regular pentagon. |
twenty seven. with the same hypothesis, find the sides of the same regular figures. |
eight. if three magnitudes be continual proportionals, the first is to the third as the square of the difference between the first and second is to the square of the difference between the second and third. |
in "the authoress of the odyssey", i wrote: |
business done as follows:-they had, he said, great quantities of gold, both coined and uncoined, and also of silver and of drinking-cups; and these he advised they should send about to the hellenes without stint, more especially to those of the hellenes |
at present, because we are speaking of civil causes, we add the consideration of advantage to friendship, so that it appears a thing to be sought for the sake of the advantage also: wishing to prevent those men from blaming us who think that we are |
as once i stood to hail the rising day, roscius appearing on the left i spied: forgive me, gods, if i presume to say the mortal's beauty with th' immortal vied. |
art thou not the light of my fire? hast thou not the sister-soul of mine insight? |
when the constitution is disordered by excess of fire, continuous heat and fever are the result; when excess of air is the cause, then the fever is quotidian; when of water, which is a more sluggish element than either fire or air, then the fever is a |
xx. a triangle is a figure formed by three right lines joined end to end. the three lines are called its sides. |
first or second class, if he does not vote shall be punished;--he who is of the second class shall pay a fine of triple the amount which was exacted at first, and he who is of the first class quadruple. |
if he further persist, and appeal a second time, the case shall be heard before the select judges; and he shall pay, if defeated, the penalty and half as much again. |
now since wherever there is a movent, its motion always acts upon something, is always in something, and always extends to something (by 'is always in something' i mean that it occupies a time: and by 'extends to something' i mean that it involves the |
seventy five. absurdity of contending for the existence of matter as the occasion of ideas.--it is a very extraordinary instance of the force of prejudice, and much to be lamented, that the mind of man retains so great a fondness, against all the evidence |
where (in every difficult question) a man is rather astonied, and dazled with the variety of discourse upon it, than informed of the course he ought to take. |
with an abstract and physics with a more concrete object. there are many attributes necessarily present in physical bodies which are necessarily excluded by indivisibility; all attributes, in fact, which are divisible. |
it can be proved by this proposition that two lines which meet at infinity are parallel. |
but the use of such an argument is in all cases ridiculous if you are attacking others for what you do or would do yourself, or are urging others to do what you neither do nor would do yourself. |
a motion from health to disease and a motion from disease to health: for motions must be contrary to one another in one or more of these ways, as there is no other way in which they can be opposed. |
mothaces, followed with a few soldiers; and whilst euryclidas was delivering his message to the ephors, they ran upon them with their drawn swords, and slew them. |
persons amongst them to collect together some of the common people and their friends, and then revolt and set up for themselves, and come to blows with each other. |
there, and following the breath, fills up the vacant space; and this goes on like the rotation of a wheel, because there can be no such thing as a vacuum. |
the athenians laid waste their land, and as the inhabitants did not submit, sailed back to rhegium. thus the winter ended, and with it ended the fifth year of this war, of which thucydides was the historian. |
prop. seventeen.-problem. from a given point (p) without a given circle (bcd) to draw a tangent to the circle. |
this i am sure, i am under the greatest obligations to seek all occasions to acknowledge a long train of favours i have received from your lordship; favours, though great and important in themselves, yet made much more so by the forwardness, concern, and |
having considered objects of sense, we now pass on to sensation. |
in the case of an accidental attribute the universal proposition is easier to overthrow than to establish; for to establish it, one has to show that it belongs in every case, whereas to overthrow it, it is enough to show that it does not belong in one |
gifted with an active and inquiring spirit, and, above all, possessing a sound and healthy tone of mind, mademoiselle de gournay had been carried from her childhood with that tide which set in with sixteenth century towards controversy, learning, and |
prop. three.-problem. from the greater (ab) of two given right lines to cut off a part equal to (one hundred) the less. |
indeed, while he was still under age and wearing the praetexta, he had the courage to plead the cause of accused persons in court, and to make use of his influence so powerfully that it is well known that in some causes his exertions gained a verdict. |
for in a state in which one man is invested with a perpetual domination, especially of the monarchical character, although there be a senate in it, as there was in rome under the kings, and in sparta, by the laws of lycurgus, or even where the people |
ask my foot if their lauding and luring strains please it! verily, to such measure and ticktack, it liketh neither to dance nor to stand still. |
and we were to reply, that there is a clay of potters, there is a clay of oven-makers, there is a clay of brick-makers; would not the answer be ridiculous? |
also different? we have explained, then, what is meant by saying that motion is one generically or one specifically. |
but if we say that there is first a state of rest for an infinite time, and then motion is started at some moment, and that the fact that it is this rather than a previous moment is of no importance, and involves no order, then we can no longer say that |
not only must we show consideration for those whom we have conquered by force of arms but we must also ensure protection to those who lay down their arms and throw themselves upon the mercy of our generals, even though the battering-ram has hammered at |
but statira both in other matters openly opposed her, and was angry with her for thus, against all law and humanity, sacrificing to the memory of cyrus the king's faithful friends and eunuchs. |
and now, again, as they were going off, arrows and darts of a longer range indicted a great slaughter among them, and their ships were driven one against another; while they themselves were not able to retaliate in any way. |
each one of us shall pay you a fine worth twenty oxen, and we will keep on giving you gold and bronze till your heart is softened. until we have done this no one can complain of your being enraged against us." |
let us take that which is most necessary and profitable for human society; it will be marriage; and yet the council of the saints find the contrary much better, excluding from it the most venerable vocation of man: as we design those horses for stallions |
there is no difficulty, one said, in seeing how war will be carried on by them. |
the same night, a terrific storm came on, which flooded their former place of encampment to the depth of over twelve feet. the recalcitrant officers were amazed at the sight, and owned that they had been in the wrong. |
them: for which reason, says plato, -- in critias. |
now revolution about the centre is circular motion, while the upward and downward movements are in a straight line, 'upward' meaning motion away from the centre, and 'downward' motion towards it. |
let us here return to our coaches. instead of these, and of all other sorts of carriages, they caused themselves to be carried upon men's shoulders. |
dem.-suppose for simplicity that the solid angle a is contained by five plane angles bac, cad, dae, eaf, fab; and let the planes of these angles be cut by another plane in the lines bc, four hundred, de, ef, fb; then we have eleven. xx. , |
scientific question, and it is the interrogative form of the premisses from which the 'appropriate' conclusion of each science is developed. |
the bones and hair are of the latter kind, sight and hearing of the former. ordinary affections are neither pleasant nor painful. the impressions of sight afford an example of these, and are neither violent nor sudden. |
when he heard this mars smote his two sturdy thighs with the flat of his hands, and said in anger, "do not blame me, you gods that dwell in heaven, if i go to the ships of the achaeans and avenge the death of my son, even though it end in my being struck |
but king neptune had kept no blind look-out; he had been looking admiringly on the battle from his seat on the topmost crests of wooded samothrace, whence he could see all ida, with the city of priam and the ships of the achaeans. |
and now you would have the argument show that this community is consistent with the rest of our polity, and also that nothing can be better-would you not? |
this point may also be proved in another way-by taking a finite magnitude in which there resides a force the same in kind as that which resides in the infinite magnitude, so that this force will be a measure of the finite force residing in the infinite |
all the bystanders expressed their indignation at so brutal an answer, but philip bade them be silent, and let this thersites depart safe and sound. |
when zarathustra so spake, his disciple resented it, but was silent. and zarathustra also was silent; and his eye directed itself inwardly, as if it gazed into the far distance. at last he sighed and drew breath.- |
socrates: will you ask me, what sort of an art is cookery? |
because men had abstract ideas in a previous state, they must have always had them, and their souls therefore must have always existed. for they must always have been either men or not men. the fallacy of the latter words is transparent. |
character, cannot exist. now if these conceptions are to become subjectively practical, we must not rest satisfied with admiring the objective law of morality, and esteeming it highly in reference to humanity, but we must consider the conception of it in |
and if any unpleasantness has arisen between you, you ought to behave with humanity, and restore the man unhurt; for by so doing you will act justly, and do us a favour." |
and then reproaches pittacus for having said, 'hard is it to be good.' how is this to be reconciled? |
to succeed in a plot was to have a shrewd head, to divine a plot a still shrewder; but to try to provide against having to do either was to break up your party and to be afraid of your adversaries. |
and this at least is obvious: in case of foreign war a man will need allies, but all the more if in the ranks opposed to him should stand the flower of the enemy. |
that which, like a field, was to receive the divine seed, he made round every way, and called that portion of the marrow, brain, intending that, when an animal was perfected, the vessel containing this substance should be the head; but that which was |
ten. in any triangle, three times the sum of the squares on the sides is equal to four times the sum of the squares on the medians. |
for in general those things that do not admit of division are called one in so far as they do not admit of it; e.g. |
the theories that 'there is something common to all the "elements"', and that they are reciprocally transformed', are so related that those who accept either are bound to accept the other as well. |
nor can they be innumerable, because, if so, being will not be knowable: and in any one genus there is only one contrariety, and substance is one genus: also a finite number is sufficient, and a finite number, such as the principles of empedocles, is |
eudoxus and archytas had been the first originators of this far-famed and highly prized art of mechanics, which they employed as an elegant illustration of geometrical truths, and as a means of sustaining experimentally, to the satisfaction of the senses, |
but it has the merit, like that of duty to god, of reminding us that the ordinary latitude occupied by morality is not all that comes under the larger scope of ethics. the "ethics of individual life" is a subject which mr. |
t'ang, being in possession of the kingdom, selected from among all the people, and employed i yin, and all who were devoid of virtue disappeared.' chap. twenty three. tsze-kung asked about friendship. |
five. a, b, one hundred, five hundred are four collinear points, and ef is a common tangent to the circles described upon ab, four hundred as diameters: prove that the triangles aeb, cfd are equiangular. |
after alexander's death, when the quarrel broke out between the troops of the phalanx and the officers, his companions, eumenes, though in his judgment he inclined to the latter, yet in his professions stood neuter, as if he thought it unbecoming him, who |
i, being of a soft and heavy complexion, have no great experience of these vehement agitations, the most of which surprise the soul on a sudden, without giving it leisure to recollect itself. |
leave it undissolved; but the particles of fire, entering into the interstices of the water, do to the water what water does to earth and fire to air (the text seems to be corrupt.), and are the sole causes of the compound body of earth and water |
hence whatever the contrasted 'poles' of the changes may be whether fire and earth, or some other couple-the one of them will be 'a being' and the other 'a not-being'. |
two. in what case would the construction fail, if the equilateral triangle were described on the other side of de? |
to be such as actually have objects; because practical reason indispensably requires their existence for the possibility of its object, the summum bonum, which practically is absolutely necessary, and this justifies theoretical reason in assuming them. |
and, on the other hand, when men of better principles observe the enemies of religion lay so great a stress on unthinking matter, and all of them use so much industry and artifice to reduce everything to it, methinks they should rejoice to see them |
approved, he was justly called, later on, to account for the blood of citizens spilt in violation of the laws. such a reproach could never have been levelled at a dictator. |
cor. one.-if two equal lines pd, pf be drawn from a point p to the circumference of a circle, the diameter through p bisects the angle dpf formed by these lines. |
but (ii) those who postulate two from the start-as parmenides postulated fire and earth-make the intermediates (e.g. air and water) blends of these. the same course is followed (iii) by those who advocate three. |
nor, indeed, is it possible for one to be trustworthy and firm who is unsympathetic by nature and unmoved by what affects ourselves. |
therefore we must not hold that there was a moment when a came to be at b and that at the same moment five hundred was in motion from the extremity of z: for the fact of a's having come to be at b will involve the fact of its also ceasing to be there, and |
(a) we need only appeal to the distinction between the statements 'x will be' and 'x is about to which depends upon this fact. |
this incensed marcellus to revenge; and he therefore moved nearer hannibal. betwixt the two camps was a little hill, a tolerably secure post, covered with wood; it had steep descents on either side, and there were springs of water seen trickling down. |
an intermediate may be a starting-point of change, since for the purposes of the change it serves as contrary to either of two contraries: for the intermediate is in a sense the extremes. |
two. if ab.f four hundred.e, to prove ab : four hundred :: e : f. |
but seeing it is not likely our saviour would countenance a heathen rite, it is most likely it proceeded from the legall ceremony of washing after leprosie. |
they also recalled the seven chian vessels, forming part of their squadron blockading the fleet in spiraeum, and giving the slaves on board their liberty, put the freemen in confinement, and speedily manned and sent out ten fresh ships to blockade the |
it would be absurd if this were not the case: for a thing may remain still merely under violence: thus we shall have a thing being in a non-permanent state of rest without having become so. |
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