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it remains to dispose of the arguments which are supposed to support the view that the infinite exists not only potentially but as a separate thing. some have no cogency; others can be met by fresh objections that are valid. |
in the fifth year of the reign of tatius, some of his friends and kinsmen, meeting ambassadors coming from laurentum to rome, attempted on the road to take away their money by force, and, upon their resistance, killed them. |
six. if from the vertex one hundred of an isosceles triangle a line four hundred be drawn to any point in the base produced, prove that cd cb ad.db. |
the responsibility, however, for this rests with the answerer, because while refusing to grant other points, he does grant points of that kind. |
the heaviest thing will be that which sinks to the bottom of all things that move downward, and the lightest that which rises to the surface of everything that moves upward. |
a sublime one saw i to-day, a solemn one, a penitent of the spirit: oh, how my soul laughed at his ugliness! |
"again, by virtue of what, and when, will mathematical magnitudes be one? |
v. a surface is that which has length and breadth. |
ratios of number; (seven) that mathematical laws pervaded the world; and even qualitative differences were supposed to have their origin in number and figure; (eight) the annihilation of matter was denied by several of them, and the seeming disappearance |
how little nice he was in his diet, may be seen in the following instance. when at the table of valerius leo, who entertained him at supper at milan, a dish of asparagus was put before him, on which his host instead of oil had poured sweet ointment. |
hence these difficulties may be dismissed: but the problem immediately connected with them-whether combination is something relative to perception' must be set out and discussed. |
if then its movement has no maximum, it can have no irregularity, since irregularity is produced by retardation and acceleration. |
the lords of parlament in england were judges, and most difficult causes have been heard and determined by them; yet few of them were much versed in the study of the lawes, and fewer had made profession of them: and though they consulted with lawyers, |
wholly particular and his own. they brought him a child to which he was god-father, which, having taken into his arms, "good god," said he, "what a fine child! how beautiful to look upon! what a pretty face it has!" |
the first will be of gentleness of temper: two the second will be that which explains the nature and disposition of clemency; for since there are certain vices which have the semblance of virtue, they cannot be separated unless you stamp upon them the |
if the chord be produced both ways, the whole line is called a secant, and each of the parts into which a secant divides the circumference is called an arc-the greater the major conjugate arc, and the lesser the minor conjugate arc.-newcomb. |
and phavorinus, in his universal history, says that democritus said of anaxagoras, that his opinions about the sun and moon were not his own, but were old theories, and that he had stolen them. |
prop. eleven.-theorem. if one circle (cpd) touch another circle (apb) internally at any point p, the line joining the centres must pass through that point. |
nine. thrasybulus also wrote him a letter in the following terms:- |
"if the way of his life is thoroughly considered and traced out." --cicero, paradox, v. one. |
in eight hundred years; for with these forces, only slow and trifling acquisitions are made, but sudden and miraculous losses. |
another cause, when a man of noble birth was on his trial, we lifted up his little son, and filled the forum with wailing and lamentations;) but we must also endeavour to cause the judge to be angry, to appease him to make him feel ill-will, and favour, |
the opinions of these philosophers are not only destructive of superstition, which arises from a vain fear of the gods, but of religion also, which consists in a pious adoration of them. |
continue to perish, as empedocles says his 'man-faced ox-progeny' did. |
this message being brought him just as he was giving the signal to those about him for the onset, he bade them tell parmenio that he must have surely lost the use of his reason, and had forgotten, in his alarm, that soldiers, if victorious, become masters |
def.-the supplement of an arc is the difference between it and a semicircle. |
in the same time. but if e move z a distance g in a time five hundred, it does not necessarily follow that e can move twice z half the distance g in the same time. |
again, see whether the species and the genus fail to be used in relation to an equal number of things: for the general view is that the uses of both are alike and equal in number, as is the case with 'present' and 'grant'. |
thus wu tzu says: 'with a superior force, make for easy ground; with an inferior one, make for difficult ground.'" |
the saying of old antigonus was better, who, when he was to fight at andros, and one told him, "the enemy's ships are more than ours;" replied, "for how many then wilt thou reckon me?" |
indivisibles, and that of the slower into the two indivisibles ez, zh. then the time may also be divided into three indivisibles, for an equal magnitude will be passed over in an equal time. suppose then that it is thus divided into kl, lm, mn. |
the state. but when caesar had made an apology for himself, and satisfied the senate, his admirers were very much animated, and advised him not to depart from his own thoughts for anyone, since with the people's good favor he would erelong get the better |
seven. if a, b, c denote the sides of a triangle abc, and five hundred, five hundred the points where the internal and external bisectors of a meet bc; prove |
dragg'd him o'er the plain. swoln were his feet, as when the thongs were thrust thro' the bor'd holes; his body black with dust; unlike that hector who return'd from toils of war, triumphant, in aeacian spoils, or him who made the fainting greeks retire, |
solitary, indolent, and perpetually accompanied by danger, the savage cannot but be fond of sleep; his sleep too must be light, like that of the animals, which think but little and may be said to slumber all the time they do not think. |
-already glowest thou and dreamest, already drinkest thou thirstily at all deep echoing wells of consolation, already reposeth thy melancholy in the bliss of future songs!- |
contrariness. moreover, each several motion takes its name rather from the goal than from the starting-point of change, e.g. motion to health we call convalescence, motion to disease sickening. |
there can therefore be no contradiction between the laws of god, and the laws of a christian common-wealth. |
in the second speech socrates is exhibited as beating the rhetoricians at their own weapons; he 'an unpractised man and they masters of the art.' |
we also feel calm if we think that the offender will not see that he is punished on our account and because of the way he has treated us. for anger has to do with individuals. this is plain from the definition. hence the poet has well written: |
(six) again, just as every body is in place, so, too, every place has a body in it. what then shall we say about growing things? it follows from these premisses that their place must grow with them, if their place is neither less nor greater than they are. |
of that, he replied, there can be no doubt; such excessive care of the body, when carried beyond the rules of gymnastic, is most inimical to the practice of virtue. |
dem.-since o is the centre of the two circles, we have oa equal to op, and oc equal to ob. hence the two triangles aoc, pob have the sides oa, oc in one respectively equal to the sides op, ob in the other, and the contained angle common to both. hence i. |
if they hear any groaning or uproar as of men fighting about the house, they are not to come out, but are to keep quiet and stay where they are at their work." |
these exquisite subtleties are only fit for sermons; they are discourses that will send us all saddled into the other world. |
in like manner, the angle cea is equal to deb. |
bodies, we say, which have no natural movement, have no constrained movement; and where there is no natural and no constrained movement there will be no movement at all. |
and not to give expression to aught that might tend to the hurt of any one. |
it thus falls into confusion and contradictions, from which it conjectures the presence of latent errors, which, however, it is unable to discover, because the principles it employs, transcending the limits of experience, cannot be tested by that |
it must also be painful for the soul to be inextricably bound up with the body; nay more, if, as is frequently said and widely accepted, it is better for mind not to be embodied, the union must be for it undesirable. |
at the same time it is plain that a question of the form 'what is it?' is not a dialectical question, for a dialectical questioner must by the form of his question give his opponent the chance of announcing one of two alternatives, whichever he wishes. |
going. such, then, is the free-running kind of style; the compact is that which is in periods. by a period i mean a portion of speech that has in itself a beginning and an end, being at the same time not too big to be taken in at a glance. |
towards the middle of the sung period, by which time all the chief commentaries on sun tzu were in existence, a certain chi t'ien-pao published a work in fifteen chuan entitled "sun tzu with the collected commentaries of ten writers." |
(one) what the followers of empedocles do, though without observing it themselves, is to reduce the generation of elements out of one another to an illusion. |
to be inconsistent with one another. and, last of all, it will be a good thing, if the cause shall afford any opportunity for so doing, to take care that on our principles both the laws may seem to be upheld, but that on the principle contended for by our |
let this conclude what we have to say in support of our contention that there never was a time when there was not motion, and never will be a time when there will not be motion. |
as differing in colour. first, a gay and sprightly fluency; afterwards, a lofty and penetrating subtlety; and lastly, a mature and constant vigour. their names will better express them: ovid, lucan, virgil. |
the same immobility, they say, is produced by the flatness of the surface which the earth presents to the air which underlies it; while the air, not having room enough to change its place because it is underneath the earth, stays there in a mass, like the |
adduced to show which the judge is the most bound to be guided by; or in documents of a wholly contradictory nature, which is the most to be approved. |
ten. in the same case, if o be the middle point of four hundred; prove oo ob od . |
cleinias: they will come from all crete; and of other hellenes, peloponnesians will be most acceptable. |
, and od : five hundred fifty :: pictdn : square dm i. . hence ai : ah :: dn : dm; therefore ai : dn :: ah : dm five. xvi. ; hence abc : def :: ab : de . |
either all things are at rest, or all things are in motion, or some things are at rest and others in motion. |
if it is not one process, it would seem that there is nothing to prevent its being infinite in this sense; e.g. |
even my infancy was trained up after a gentle and free manner, and exempt from any rigorous subjection. |
yes, i said, but for that purpose a very little of either geometry or calculation will be enough; the question relates rather to the greater and more advanced part of geometry-whether that tends in any degree to make more easy the vision of the idea of |
such then is the idea they form of pantheism, and which they ascribe to philosophy. |
but when these same particles, refined by putrefaction, enter into the narrow veins, and are duly proportioned to the particles of earth and air which are there, they set them whirling about one another, and while they are in a whirl cause them to dash |
because it is not divisiable, they say; but both the universal, and the particular or the element, are indivisible. but they are starting-points in different ways, one in definition and the other in time. in which way, then, is one the starting-point? |
you are welcome to hear about them, solon, said the priest, both for your own sake and for that of your city, and above all, for the sake of the goddess who is the common patron and parent and educator of both our cities. |
its work generally-in relation to the extreme of individuality as the multitude of individuals-consists in a double function. |
seventy three. if two sides of a triangle circumscribed to a given circle be given in position, but the third side variable, the circle described about the triangle touches a fixed circle. |
six. therefore the skilful leader subdues the enemy's troops without any fighting; he captures their cities without laying siege to them; he overthrows their kingdom without lengthy operations in the field. |
the narrative the manner of a most brave and valiant death, he took it up and replaced it upon his head. epicurus himself, at his death, consoles himself upon the utility and eternity of his writings: |
he could write in one style, but not in another, and the greek language had not as yet been fashioned by any poet or philosopher to describe physical phenomena. |
nevertheless those who have been wanting as regards good fortune have maintained themselves best. the matter is also facilitated by the prince being obliged to reside personally in his territory, having no others. |
of the numerous company, three only take any serious part in the discussion; nor are we informed whether in the evening they went to the torch-race, or talked, as in the symposium, through the night. |
to begin then, as we said, with motion. we may start by distinguishing (one) what exists in a state of fulfilment only, (two) what exists as potential, (three) what exists as potential and also in fulfilment-one being a 'this', another 'so much', a third |
the dead and for the most part unmerchantable wood behind my house, and the driftwood from the pond, have supplied the remainder of my fuel. i was obliged to hire a team and a man for the ploughing, though i held the plough myself. |
psychology-taken in this high philosophical acceptation-thus leads on to ethics; and ethics is parted by no impassable line from psychology. |
hence the rectangle ac.cb is equal to the figure ad, and the square on cb is the figure ce. hence the rectangle ac.cb, together with the square on cb, is equal to the figure ae. |
nor will that admirable, and incredible, and almost godlike skill of his in interpreting the laws and explaining the principles of equity be buried in silence. |
fifty five. express the sides of a triangle in terms of the radii of its escribed circles. |
not long after, they surrounded the house with armed men, thrust cato out of the forum, killed some that made resistance, and decreed caesar his command for five years longer, and provinces for themselves, syria, and both the spains, which being divided |
but how will our conclusion work out in the case of the circle and the straight line? |
now, because the points b, one hundred are in this second plane, the line bc i., def. vi. is in it. therefore the two right lines abc, abd lying in one plane have a common segment ab, which is impossible. therefore, c. |
by the term analytic of conceptions, i do not understand the analysis of these, or the usual process in philosophical investigations of dissecting the conceptions which present themselves, according to their content, and so making them clear; but i mean |
having all the night dreamed that he had horns on his head, did, by the force of imagination, really cause them to grow there. passion gave to the son of croesus the voice which nature had denied him. |
solicitations of his son aruns, who was earnest for the roman interest, made a peace on these conditions, that they should resign the land they had taken from the tuscans, and restore all prisoners and receive back their deserters. |
private aggrandizement, as theopompus in his history relates, whom anyone may rather give credit to when he commends, than when he finds fault, as it is more agreeable to him to blame than to praise. |
still, notwithstanding the absurdities of polus and others, rhetoric has great power in public assemblies. this power, however, is not given by any technical rules, but is the gift of genius. |
besides this, to be able to undertake greater enterprises, and always under the pretext of religion, he had recourse to a pious cruelty, driving out the moors from his kingdom and despoiling them. no more admirable or rare example can be found. |
the distinctions are three, namely, above and below, front and its opposite, right and left-all these three oppositions we expect to find in the perfect body-and each may be called a principle. |
sect. one hundred fifty seven. things of this world are in so constant a flux, that nothing remains long in the same state. |
thirty six. of the word of god, and of prophets |
soft that it fitted him like the skin of an onion, and glistened in the sunlight to the admiration of all the women who beheld it. |
secondly, in an assembly of many, there cannot choose but be some whose interests are contrary to that of the publique; and these their interests make passionate, and passion eloquent, and eloquence drawes others into the same advice. |
such a one may have a sight clear enough who looks asquint, and consequently sees what is good, but does not follow it, and sees knowledge, but makes no use of it. |
eight. the perimeter of a quadrilateral is greater than the sum of its diagonals. |
ignorance of the soveraign power, in the place of a mans ordinary residence, excuseth him not; because he ought to take notice of the power, by which he hath been protected there. |
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