OpenLLM-France/wikimedia huggingface dataset:
# Philosophy and Fun of Algebra/Chapter 5

CHAPTER V MATHEMATICAL CERTAINTY AND REDUCTIO AD ABSURDUM
It is very often said that we cannot have mathematical certainty about anything except a few special subjects, such as number, or quantity, or dimensions.
Mathematical certainty depends, not on the subject matter of our investigation, but upon three conditions. The first is a constant recognition of the limits of our own knowledge and the fact of our own ignorance. The second is reverence for the As-Yet-Unknown. The third is absolute fearlessness in meeting the reductio ad absurdum. In mathematics we are always delighted when we come to any such conclusion as 2 + 3 = 7. We feel that we have absolutely cleared out of the way one among the several possible hypotheses, and are ready to try another.
We may be still groping in the dark, but we know that one stumbling-block has been cleared ​out of our path, and that we are one step "for-rader " on the right road. We wish to arrive at truth about the state of our balance sheet, the number of acres in our farm, the time it will take us to get from London to Liverpool, The height of Snowdon, the distance of the moon, and the weight of the sun. We have no desire to deceive ourselves upon any of these points, and therefore we have no superstitious shrinking from the rigid reductio ad absurdum. On some other subjects people do wish to be deceived. They dislike the operation of correcting the hypothetical data which they have taken as basis. Therefore, when they begin to see looming ahead some such ridiculous result as 2 + 3 = 7, they shrink into themselves and try to find some process of twisting the logic, and tinkering the equation, which will make the answer come out a truism instead of an absurdity; and then they say, "Our hypothetical premiss is most likely true because the conclusion to which it brings us is obviously and indisputably true."
If anyone points out that there seems to be a flaw in the argument, they say, "You cannot ​expect to get mathematical certainty in this world," or "You must not push logic too far," or "Everything is more or less compromise," and so on.
Of course, there is no mathematical certainty to be had on those terms. You could have no mathematical certainty about the amount you owed your grocer if you tinkered the process of adding up his bill. I wish to call your attention to the fact that even in this world there is a good deal of mathematical certainty to be had by whosoever has endless patience, scrupulous accuracy in stating his own ignorance, reverence for the As-Yet-Unknown, and perfect fearlessness in meeting the reductio ad absurdum.
# Philosophy and Fun of Algebra/Chapter 4

CHAPTER IV PARTIAL SOLUTIONS AND THE PROVISIONAL ELIMINATION OF ELEMENTS OF COMPLEXITY
Suppose that we never find out for certain whether x is unity or zero or something else, we then begin to experiment in a different direction. We try to find out which of the hypothetical values of x throw most light on other questions, and if we find that some particular value of x—for instance, unity—makes it easier than does any other value to understand things about y and z we have to be very careful not to slip into asserting that x is unity. But the teacher would be quite right in saying to the class, "For the present we will leave alone thinking about what would happen if x were something different from unity, and attend only to such questions as can be solved on the supposition that x is unity." This is what is called in Algebra "provisional elimination of some elements of complexity."
It might happen that one of the older pupils, ​specially clever at mathematics, but not very well disciplined, should start some point connected with the supposition that x is something different than unity. It would be the teacher's business to remind her: "At present we are dealing with the supposition that x is unity. When we have exhausted that subject we will investigate your question. But, till then, please do not distract the attention of the class by talking about what is not the business on hand at present."
If the girl forgot, the teacher might say: "I should very much like you to try your own suggestion in private, but please do not talk about it in class till I give you leave."
If she forgot again, the teacher might say,—I think I should be inclined to say:—"If you cannot remember not to distract the class by talking about what is irrelevant to the business on hand, I shall have to request you to keep outside my class-room till you can."
In an orderly school the teachers have time to be polite, and it is their business to set the example of being so. In history, especially such history as ​that of half-civilised countries 3000 years ago, teachers were under too much strain to cultivate either a polite manner of saying things, or, what is of far more consequence, that genuine intellectual courtesy which is the absolutely necessary condition for the development of any really perfect mathematical system. The great Hebrew Algebra, therefore, never became quite perfect. It was only rough hewn, so to speak; and its manners and customs were rough too. The teachers had ways of saying, "Hold your tongue, or else go out of my class-room," which perhaps we should now call bigoted and brutal. But what I want you to notice is that "Hold your tongue, or get out of my class-room," is not the same thing as "My hypothesis is right, and yours ought not to be tried anywhere."
This latter is contrary to the essential basis of Algebra, viz., a recognition of one's own ignorance.
The other, a rough way of saying "Get out of my class-room," is only contrary to that fine intellectual courtesy which is essential to the perfection of mathematical method.
# Philp v. Nock

* related portals: Supreme Court of the United States.
* sister projects: Wikidata item.
United States Supreme Court
84 U.S. 460
Philp v. Nock
ERROR to the Supreme Court of the District of Columbia.
Nock brought an action in the court below against Philp and others to recover damages for the infringement of a patent granted to him by the United States for an improvement touching the lids of inkstands and the hinge whereby such lids are attached. The case came on to be tried in March, 1870, and therefore while the Patent Act of July 4th, 1836, which in suits against infringers gives to patentees 'the actual damages sustained' by them, was in force; a similar provision, however, being made in the subsequent Patent Act of July 8th, 1870. The bill of exceptions showed that the plaintiff gave in evidence that during the term of the patent 'the defendants had sold inkstands having hinges that were infringements of the plaintiff's patent, to the number of seventy-five dozen, and that the royalty which the plaintiff received for the use of his patent was at the rate of $2 per gross.' The testimony being closed, the court instructed the jury as follows:
'If the jury shall find a verdict for the plaintiff under the foregoing instructions, they will award him such sum as they shall find to be required to remunerate him for the loss sustained by the wrongful act of the defendants, and to reimburse him for all such expenditures as have been necessarily incurred by him in order to establish his right.'
To this instruction the defendant excepted.
A verdict and judgment having been given for the plaintiff in the sum of $500 the defendants brought the case here.
Mr. R. D. Mussey, for the plaintiff in error:
All the injury proved was that the defendants withheld royalty to the amount of $12.50. There was no evidence of any 'expenditure' by Nock, and the instruction had no foundation in the evidence. Its inevitable effect upon the minds of the jury was to lead them to believe they might lump counsel fees, and such other expenditures as they inferred, and out of them make a total. The jury followed this evident lead of the court, and returned a verdict for forty times the amount proven.
Mr. G. W. Paschall, contra:
The bill of exceptions does not show all the evidence in the case, but it may be gathered that the plaintiff below proved that the defendants had infringed his right by selling seventy-five dozen inkstands. What further facts he proved is not stated.
Mr. Justice SWAYNE delivered the opinion of the court.

## Notes

* ↑ 5 Stat. at Large, 123.
* ↑ 16 Id. 207.
This work is in the public domain in the United States because it is a work of the United States federal government (see 17 U.S.C. 105).
Public domainPublic domainfalsefalse
# Poems Written During the Progress of the Abolition Question In the United States/Hymn

HYMN Sung on the 4th of July, 1834, at the Chatham Street Chapel, New-York.
Oh, Thou, whose presence went before Our fathers in their weary way, As with Thy chosen moved of youre The fire by night—the cloud by day!
When from each temple of the free, A nation's song ascends to Heaven, Most Holy Father! unto Thee May not our humble prayer be given?
Thy children all—though hue and form Are varied in Thine own good will— With Thy own holy breathings warm, And fashioned in Thine image still. ​We thank Thee, Father!—hill and plain Around us wave their fruits once more, And clustered vine, and blossomed grain, Are bending round each cottage door.
And peace is here—and hope and love Are round us as a mantle thrown, And unto Thee, supreme above, The knee of prayer is bowed alone.
But, Oh, for those, this day can bring, As unto us, no joyful thrill— For those, who, under Freedom's wing, Are bound in Slavery's fetters still:—
For those to whom Thy living word Of light and love is never given— For those whose ears have never heard The promise and the hope of heaven!
For broken heart—and clouded mind, Whereon no human mercies fall— Oh, be thy gracious love inclined, Who, as a father, pitiest all!—
And grant, Oh, Father! that the time Of Earth's deliverance may be near, When every land, and tongue, and clime, The message of Thy love shall hear— ​When, smitten as with fire from Heaven, The captive's chain shall sink in dust, And to this fettered soul be given The glorious freedom of the just!
# Poems Written During the Progress of the Abolition Question In the United States/Note

NOTE.
In compliance with the urgent request of a large number of the admirers of Whittier, this volume was issued from the press, with very little time for revision, while the author was absent from Boston. By a strange oversight, the following articles were omitted. As soon as the work appeared, however, the omission was at once discovered, and they are here inserted, that the volume may not disappoint its readers.
Publisher.
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# Poems Written During the Progress of the Abolition Question In the United States/Plead for the Slave

PLEAD FOR THE SLAVE! WRITTEN IN AN ALBUM.
Oh, Woman! from thy happy hearth, Extend thy gentle hand to save The poor and perishing of earth— The chained and stricken slave! Oh! plead for all the sufferings of thy kind— For the crushed body and darkened mind!
So shall the ancient Earth have not A nobler name than thine shall be:— The deeds my martial manhood wrought— The lofty energies of thought— The spell of poesy— These are but frail and fading honors—thine Shall Time unto Eternity consign!
Yea, and when thrones shall crumble down, And human pride and grandeur fall, ​The herald's line of long renown, The mitre and the kingly crown,— Perishing glories all! The pure devotion of thy generous heart Shall live in Heaven, of which it is a part!
# Poems Written During the Progress of the Abolition Question In the United States/Clerical Oppression

CLERICAL OPPRESSORS.
In the Report of the celebrated Pro-Slavery Meeting in Charleston, S. C., on the 4th of the 9th mo., 1835, published in the courier of that city, it is stated, 'The CLERGY of all denominations attended in a body, lending their sanction to the proceedings; and adding by their presence to the impressive character of the scene!'
Just God!—and these are they Who minister at Thine altar, God of Right! Men who their hands with prayer and blessing lay On Israel's Ark of light!
What! preach and kidnap men? Give thanks—and rob Thy own afflicted poor? Talk of Thy glorious liberty, and then Bolt hard the captive's door?
What! servants of thy own Merciful Son, who came to seek and save The homeless and the outcast—, fettering down The tasked and plundered slave! ​Pilate and Herod, friends! Chief priests and rulers, as of old, combine! Just God and holy! is that church which lends Strength to the spoiler, Thine?
Paid hypocrites, who turn Judgment aside, and rob the Holy Book Of those high words of truth which search and burn In warning and rebuke.
Feed fat, ye locusts, feed! And, in your tasselled pulpits, thank the Lord That, from the toiling bondsman's utter need, Ye pile your own full board.
How long, oh Lord! how long Shall such a Priesthood barter Truth away, And, in Thy name, for robbery and wrong At thy own altars pray?
Is not Thy hand stretched forth Visibly in the heavens to awe and smite? Shall not the living God of all the earth, And heaven above, do right?
Woe, then, to all who grind Their brethren of a Common Father down! To all who plunder from th' immortal mind Its bright and glorious crown!
Woe to the Priesthood! woe To those whose hire is with the price of blood— ​Perverting, darkening, changing as they go, The searching truths of God!
Their glory and their might Shall perish; and their very names shall be Vile before all the people, in the light Of a world's liberty.
Oh! speed the moment on When Wrong shall cease—and Liberty, and Love, And Truth, and Right, throughout the earth are known, As in their home above.
# Poems Written During the Progress of the Abolition Question In the United States/Lines, on reading 'Right and Wrong in Boston'

LINES
WRITTEN ON READING
'RIGHT AND WRONG IN BOSTON:'
Containing an account of the meeting of the Boston Female Anti-Slavery Society, and the mob which followed, on the 21st October, 1835.
Unshrinking from the storm, Well have ye borne your part, With woman's fragile form, But more than manhood's heart! Faithful to Freedom, when Its name was held accursed— Faithful, midst ruffian men, Unto your holy trust.
Oh—steadfast in the Truth! Not for yourselves alone, Matron and gentle youth— Your lofty zeal was shown: For the bondman of all climes— For freedom's last abode— For the hope of future times— For the birthright gift of God. ​For scorned and broken laws— For honor and the right— For staked and periled cause Of liberty and light. For holy eyes above On a world of evil cast— For the children of our love— For the mothers of the past!
Worthy of them are ye— The Pilgrim wives who dared The waste and unknown sea, And the hunter's perils shared. Worthy of her, whose mind Triumphant over all, Ruler nor priest could bind, Nor banishment appal.
Worthy of her who died Martyr of Freedom, where Your 'Common's' verdant pride Opens to sun and air: Upheld at that dread hour By strength which could not fail; Before whose holy power, Bigot and priest turned pale. ​God give ye strength to run, Unawed by earth or hell, The race ye have begun So gloriously and well— Until the trumpet call Of Freedom has gone forth, With joy and life to all The bondmen of the earth!
Until immortal mind Unshackled walks abroad, And chains no longer bind The image of our God: Until no captive one Murmurs on land or wave; And, in his course, the sun Looks down upon no slave!
* ↑ Mrs. Hutchinson, who was banished from the Massachusetts Colony, as the easiest method of confuting her doctrines.
* ↑ Mary Dyer, the Quaker Martyr, who was hanged in Boston in 1659, for worshipping God according to the dictates of her conscience.
# Poems Written During the Progress of the Abolition Question In the United States/Apology

APOLOGY
Most chivalrous gentlemen—pardon us, pray, And pity our present condition— The lady fanatics have carried the day, And openly preach Abolition! The petticoat-plotters, with might and with main, Are tearing the bonds of the Union in twain!
We knew, to our sorrow, that over their tea, These ladies, for months, had been brewing A plot to dismember the Union, and free Your slaves, to their positive ruin: But who would have dreamed that they ever would dare, In the face of New Hampshire, their purpose declare!
Oh, where had the fear of the P*****t gone From the eyes of these turbulent ladies? And where Parson F**k's indignation and scorn Which overwhelmed all, when he made his
Great speech at our democrat gathering, when Abolition was working its way with the men?
Alack and alas! that we live to relate How these Amazons gathered together, Consulting each other, in solemn debate, About loosing the slave from his tether; And gravely resolving your negroes to be Created like all of us—equal and free.
But think not, dear sirs, that with conduct so base, 'The democracy' rested in quiet— No—it rose in its strength to redeem from disgrace The town, by a regular riot! And, surrounding the house where the mischief went on, Plied well the 'fanatics' with brickbat and stone.
Through door and through window our missiles went in, Disturbing the laces and trimming— Oh, would that 'our dear southern brethren' had seen How 'democracy' pelted the women! And had heard, midst the crashing of brickbats, its shout— 'Hurra for the Union!—you women, clear out!'
Yet, it grieves us to say, that in spite of our great And most patriotic exertion, These petticoat-traitors regarded our feat As merely a cause of diversion;
And still they went on, without let or disaster, To spoil 'the relations of servant and master.'
But, though foiled in its efforts to drive away This bevy of gossip and beauty, 'The democracy' feels, and rejoices to say, That it fully performed its duty; And it trusts that its friends will with cheerfulness own, That all that it could do, in safety, was done!
We are sadly disheartened, and all in a fret— Parson F**k is about to absquatalize, And B—t—n beneath the States Prison debt Is hiding himself from mortal eyes; Even H**l cannot help us—his hands are too full, Making C**h**n a 'democrat dyed in the wool.'
White Slave, Doughface, &, Co.
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# Poems: Second Series (Dickinson)/The Oriole

XIII.
THE ORIOLE.
ONE of the ones that Midas touched, Who failed to touch us all, Was that confiding prodigal, The blissful oriole.
So drunk, he disavows it With badinage divine; So dazzling, we mistake him For an alighting mine.
A pleader, a dissembler, An epicure, a thief,— Betimes an oratorio, An ecstasy in chief;
The Jesuit of orchards, He cheats as he enchants Of an entire attar For his decamping wants.
The splendor of a Burmah, The meteor of birds, Departing like a pageant Of ballads and of bards.
I never thought that Jason sought For any golden fleece; But then I am a rural man, With thoughts that make for peace.
But if there were a Jason, Tradition suffer me Behold his lost emolument Upon the apple-tree.
# Poems: Second Series (Dickinson)/The Shelter

XLIV.
THE SHELTER.
THE body grows outside,— The more convenient way,— That if the spirit like to hide, Its temple stands alway
Ajar, secure, inviting; It never did betray The soul that asked its shelter
In timid honesty.
# Poems: Second Series (Dickinson)/The Preacher

XXXVIII.
THE PREACHER.
HE preached upon "breadth" till it argued him narrow,— The broad are too broad to define; And of "truth" until it proclaimed him a liar,— The truth never flaunted a sign.
Simplicity fled from his counterfeit presence As gold the pyrites would shun. What confusion would cover the innocent Jesus To meet so enabled a man!
# Poems: Second Series (Dickinson)/The Sea

​ POEMS. 139
AN everywhere of silver,
With ropes of sand
To keep it from effacing
The track called land.
# Poems: Second Series (Dickinson)/The Robin

VI.
THE ROBIN
THE robin is the one That interrupts the morn With hurried, few, express reports When March is scarcely on.
The robin is the one That overflows the noon With her cherubic quantity, An April but begun.
The robin is the one That speechless from her nest Submits that home and certainty And sanctity are best.
# Poems: Second Series (Dickinson)/The Show

XVIII. THE SHOW.
THE show is not the show,
But they that go.
Menagerie to me
My neighbor be.
Fair play — Both went to see.
# Poems: Second Series (Dickinson)/The Railway Train

XVII. THE RAILWAY TRAIN.
I LIKE to see it lap the miles,
And lick the valleys up,
And stop to feed itself at tanks;
And then, prodigious, step
Around a pile of mountains,
And, supercilious, peer
In shanties by the sides of roads;
And then a quarry pare
To fit its sides, and crawl between,
Complaining all the while
In horrid, hooting stanza;
Then chase itself down hill
And neigh like Boanerges;
Then, punctual as a star,
Stop — docile and omnipotent — At its own stable door.
# Poems: Second Series (Dickinson)/The Rat

XXXV.
THE RAT.
The rat is the concisest tenant. He pays no rent,— Repudiates the obligation, On schemes intent.
Balking our wit To sound or circumvent, Hate cannot harm A foe so reticent.
Neither decree Prohibits him, Lawful as Equilibrium.
# Poems: Second Series (Dickinson)/The Return

XXII.
The Return.
Though I get home how late, how late !
So I get home, 't will compensate.
Better will be the ecstasy
That they have done expecting me,
When, night descending, dumb and dark,
They hear my unexpected knock.
Transporting must the moment be,
Brewed from decades of agony !
To think just how the fire will burn,
Just how long-cheated eyes will turn
To wonder what myself will say,
And what itself will say to me,
Beguiles the centuries of way!
# Poems: Second Series (Dickinson)/The Oriole's Secret

XII.
THE ORIOLE’S SECRET.
TO hear an oriole sing May be a common thing, Or only a divine.
It is not of the bird Who sings the same, unheard, As unto crowd.
The fashion of the ear Attireth that it hear In dun or fair.
So whether it be rune, Or whether it be none, Is of within;
The "tune is in the tree," The sceptic showeth me; "No, sir! In thee!"
# Opticks (2nd Ed)

Opticks is a book written by English physicist Isaac Newton that was released to the public in 1704. It is about optics and the refraction of light, and is considered one of the great works of science in history.Warning: template has been deprecated.

### Contents

* Advertisement
* The First Book
** Part I
** Part II
* The Second Book
** Part I
** Part II
** Part III
** Part IV
* The Third Book
** Part I