OpenLLM-France/wikimedia huggingface dataset:
# Pan: Double Villanelle

I
O GOAT-FOOT God of Arcady! This modern world is grey and old, And what remains to us of thee?
No more the shepherd lads in glee Throw apples at thy wattled fold, O goat-foot God of Arcady!
Nor through the laurels can one see Thy soft brown limbs, thy beard of gold, And what remains to us of thee?
And dull and dead our Thames would be, For here the winds are chill and cold, O goat-foot God of Arcady!
Then keep the tomb of Helice, Thine olive-woods, thy vine-clad wold, And what remains to us of thee?
Though many an unsung elegy Sleeps in the reeds our rivers hold, O goat-foot Glod of Arcady! Ah, what remains to us of thee?
II
AH, leave the hills of Arcady, Thy satyrs and their wanton play, This modern world hath need of thee.
No nymph or Faun indeed have we, For Faun and nymph are old and grey, Ah, leave the hills of Arcady!
This is the land where liberty Lit grave-browed Milton on his way, This modern world hath need of thee!
A land of ancient chivalry Where gentle Sidney saw the day, Ah, leave the hills of Arcady!
This fierce sea-lion of the sea, This England lacks some stronger lay, This modern world hath need of thee!
Then blow some trumpet loud and free, And give thine oaten pipe away, Ah, leave the hills of Arcady! This modern world hath need of thee!
This work was published before January 1, 1929, and is in the public domain worldwide because the author died at least 100 years ago.
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# 1911 Encyclopædia Britannica/Number/The Theorems of Fermat and Wilson

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28. The Theorems of Fermat and Wilson.—Let $r_{1},r_{2},\dots r_{t}$ where $t=\phi (m)$, be a complete set of residues prime to the modulus $m$. Then if $x$ is any number prime to $m$, the residues $xr_{1},xr_{2},\dots xr_{t}$ also form a complete set prime to $m$ (§ 27). Consequently $xr_{1}\cdot xr_{2},\dots xr_{t}\equiv r_{1}r_{2}\dots r_{t}$, and dividing by $r_{1}r_{2}\dots r_{t}$, which is prime to the modulus, we infer that
    $x^{\phi (m)}\equiv 1{\pmod {m}}$
which is the general statement of Fermat's theorem. If $m$ is a prime $p$, it becomes $x^{p-1}\equiv 1{\pmod {p}}$.
For a prime modulus $p$ there will be among the set $x,2x,3x,\dots (p-l)x$ just one and no more that is congruent to $1$: let this be $xy$. If $y\equiv x$, we must have $x^{2}-1=(x-1)(x+1)\equiv 0$, and hence $x\equiv \pm 1$: consequently the residues $2,3,4,...(p-2)$ can be arranged in ${\tfrac {1}{2}}(p-3)$ pairs $(x,y)$ such that $xy\equiv 1$. Multiplying them all together, we conclude that $2.3.4.\dots (p-2)\equiv l$ and hence, since $1.(p-1)\equiv -1$,
    $(p-1)!\equiv -1{\pmod {p}}$.
which is Wilson's theorem. It may be generalized, like that of Fermat, but the result is not very interesting. If $m$ is composite $(m-1)!+1$ cannot be a multiple of $m$: because $m$ will have a prime factor $p$ which is less than $m$, so that $(m-1)!\equiv 0{\pmod {p}}$. Hence Wilson’s theorem is invertible: but it does not supply any practical test to decide whether a given number is prime.
# 1911 Encyclopædia Britannica/Number/Normal Fields

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51. Normal Fields.—The special properties of a particular field $\Omega$ are closely connected with its relations to the conjugate fields $\Omega ',\Omega '',\dots \Omega ^{(n-1)})$. The most important case is when each of the conjugate fields is identical with $\Omega$: the field is then said to be Galoisian or normal. The aggregate $\mathrm {R} (\Omega ,\Omega ',\dots \Omega ^{(n-1)}))$ of all rational functions of $\theta$ and its conjugates is a normal field: hence every arithmetical field of order $n$ is either normal, or contained in a normal field of a higher order. The roots of an equation $f(\theta )=0$ which defines a normal field are associated with a group of substitutions: if this is Abelian, the field is called Abelian; if it is cyclic, the field is called cyclic. A cyclotomic field is one the elements of which are all expressible as rational functions of roots of unity; in particular the complete cyclotomic field $\mathrm {C} _{m}$, of order $\phi (m)$, is the aggregate of all rational functions of a primitive mth root of unity. To Kronecker is due the very remarkable theorem that all Abelian (including cyclic) fields are cyclotomic: the first published proof of this was given by Weber, and another is due to D. Hubert.
Many important theorems concerning a normal field have been established by Hilbert. He shows that if $\Omega$ is a given normal field of order $m$, and ${\mathfrak {p}}$ any of its prime ideals, there is a finite series of associated fields $\Omega _{1},\Omega _{2},\!\And \!\!\!\!\mathrm {c} .$, of orders $m_{1},m_{2},\!\And \!\!\!\!\mathrm {c} .$, such that $m_{i}\equiv 0{\pmod {m_{i+1}}}$, and that if $r_{i}=m/m_{i}$, ${\mathfrak {p}}^{r_{i}}={\mathfrak {p}}_{i}$, a prime ideal in $\Omega _{i}$. If $\Omega _{l}$ is the last of this series, it is called the field of inertia (Trägheitskörper) for ${\mathfrak {p}}$: next after this comes another field of still lower order called the resolving field (Zerlegungskörper) for ${\mathfrak {p}}$, and in this field there is a prime of the first degree, ${\mathfrak {p}}_{l+1}$, such that ${\mathfrak {p}}_{l+1}={\mathfrak {p}}^{k}$, where $k=m/m_{l}$. In the field of inertia ${\mathfrak {p}}_{l+1}$ remains a prime, but becomes of higher degree; in $\Omega _{l-1}$, which is called the branch-field (Verzweigungskörper) it becomes a power of a prime, and by going on in this way from the resolving field to $\Omega$, we obtain $(l+2)$ representations for any prime ideal of the resolving field. By means of these theorems, Hilbert finds an expression for the exact power to which a rational prime $p$ occurs in the discriminant of $\Omega$, and in other ways the structure of $\Omega$ becomes more evident. It may be observed that when $m$ is prime the whole series reduces to $\Omega$ and the rational field, and we conclude that every prime ideal in $\Omega$ is of the first or mth degree: this is the case, for instance, when $m=2$, and is one of the reasons why quadratic fields are comparatively so simple in character.
# 1911 Encyclopædia Britannica/Number/Problem of Representation

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34. Problem of Representation.—It is required to find out whether a given number $m'$ can be represented by the given form $(a',b',c')$. One condition is clearly that the divisor of the form must be a factor of $m'$. Suppose this is the case; and let $m,(a,b,c)$ be the quotients of $m'$ and $(a',b',c')$ by the divisor in question. Then we have now to discover whether $m$ can be represented by the primitive form $(a,b,c)$. First of all we will consider proper representations
    $m=(a,b,c)(\alpha ,\gamma )^{2}$
where $\alpha ,\gamma$ are co-primes. Determine integers $\beta ,\delta$ such that $\alpha \delta -\beta \gamma =l$, and apply to $(a,b,c)$ the substitution ${\begin{pmatrix}\alpha ,&\beta \\\gamma ,&\delta \end{pmatrix}}$; the new form will be $(m,n,l)$, where
    $n^{2}-4ml=\mathrm {D} =b^{2}-4ac$.
Consequently $n^{2}=\mathrm {D} {\pmod {4m}}$, and $\mathrm {D}$ must be a quadratic residue of $m$. Unless this condition is satisfied, there is no proper representation of $m$ by any form of determinant $\mathrm {D}$. Suppose, however, that $n^{2}=\mathrm {D} {\pmod {4m}}$ is soluble and that $n_{1},n_{2},\!\!\And \!\!\!\!\mathrm {c} .$ are its roots. Taking any one of these, say $n_{i}$, we can find out whether $(m,n_{i},l_{i})$ and $(a,b,c)$ are equivalent; if they are, there is a substitution ${\begin{pmatrix}\alpha ,&\beta \\\gamma ,&\delta \end{pmatrix}}$ which converts the latter into the former, and then $m=a\alpha ^{2}+b\alpha \gamma +c\gamma ^{2}$. As to derived representations, if $m=(a,b,c)(tx,ty)^{2}$, then $m$ must have the square factor $t^{2}$, and $m/t^{2}=(a,b,c)(x,y)^{2}$; hence everything may be made to depend on proper representation by primitive forms.
# 1911 Encyclopædia Britannica/Number/Quadratic Fields

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52. Quadratic Fields.—Let $m$ be an ordinary integer different from $+1$, and not divisible by any square: then if $x,y$ assume all ordinary rational values the expressions $x+y\surd m$ are the elements of a field which may be called $\Omega (\surd m)$. It should be observed that $\surd m$ means one definite root of $x^{2}-m=0$, it does not matter which: it is convenient, however, to agree that $\surd m$ is positive when $m$ is positive, and $i\surd m$ is negative when $m$ is negative. The principal results relating to $\Omega$ will now be stated, and will serve as illustrations of §§ 44–51.
In the notation previously used
    ${\mathfrak {o}}=[1,{\tfrac {1}{2}}(1+\surd m)]{\mbox{ or }}[1,\surd m]$
according as $m\equiv 1{\pmod {4}}$ or not. In the first case $\Delta =m$, in the second $\Delta =4m$. The field $\Omega$ is normal, and every ideal prime in it is of the first degree.
Let $q$ be any odd prime factor of $m$; then $q={\mathfrak {q}}^{2}$, where ${\mathfrak {q}}$ is the prime ideal $[q,{\tfrac {1}{2}}(q+\surd m)]$ when $m\equiv 1{\pmod {4}}$ and in other cases $[q,\surd m]$. An odd prime $p$ of which $m$ is a quadratic residue is the product of two prime ideals ${\mathfrak {p}},{\mathfrak {p}}'$, which may be written in the form $[p,{\tfrac {1}{2}}(a+\surd m)],[p,{\tfrac {1}{2}}(a-\surd m)]$ or $[p,a+\surd m],[p,a-\surd m]$, according as $m\equiv 1{\pmod {4}}$ or not: here $a$ is a root of $x^{2}\equiv m{\pmod {p}}$, taken so as to be odd in the first of the two cases. All other rational odd primes are primes in $\Omega$. For the exceptional prime $2$ there are four cases to consider: (i.) If $m\equiv 1{\pmod {8}}$, then $2=[2,{\tfrac {1}{2}}(1+\surd m)]\times [2,{\tfrac {1}{2}}(1-\surd m)]$. ( ii.) If $m\equiv 5{\pmod {8}}$, then $2$ is prime: (iii.) if $m\equiv 2{\pmod {4}},2=[2,\surd m]^{2}$: (iv.) if $m\equiv 3{\pmod {4}},2=[2,1+\surd m]^{2}$. Illustrations will be found in § 44 for the case $m=23$.
# 1911 Encyclopædia Britannica/Number/Theory of Numbers

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24. Theory of Numbers.—The theory of numbers is that branch of mathematics which deals with the properties of the natural numbers. As Dirichlet observed long ago, the whole of the subject would be coextensive with mathematical analysis in general; but it is convenient to restrict it to certain fields where the appropriateness of the above definition is fairly obvious. Even so, the domain of the subject is becoming more and more comprehensive, as the methods of analysis become more systematic and more exact.
The first noteworthy classification of the natural numbers is into those which are prime and those which are composite. A prime number is one which is not exactly divisible by any number except itself and 1; all others are composite. The number of primes is infinite (Eucl. Elem. ix. 20), and consequently, if n is an assigned number, however large, there is an infinite number (a) of primes greater than n.
If m, n are any two numbers, and m>n, we can always find a definite chain of positive integers (q$_1$, r$_1$), (q$_2$, r$_2$), &c., such that
m＝q$_1$n+r$_1$, n＝q$_2$r$_1$+r$_2$, r$_1$＝q$_3$r$_2$+r$_3$, &c.
with n>r$_1$>r$_2$>r$_3$ . . .; the process by which they are calculated will be called residuation. Since there is only a finite number of positive integers less than n, the process must terminate with two equalities of the form
r$_{h−2}$＝q$_h$r$_{h−1}$+r$_h$,  r$_{h−1}$＝q$_{h+1}$r$_h$.
Hence we infer successively that $r_{h}$ is a divisor of $r_{h-1},r_{h-2},\dots r_{1}$, and finally of $m\$ and $n\$. Also $r_{h}$ is the greatest common factor of $m,n$: because any common factor must divide $r_{1},r_{2},$ and so on down to $r_{h}$; and the highest factor of $r_{h}$ is $r_{h}$ itself. It will be convenient to write $r_{h}=\operatorname {dv} (m,n)$. If $r_{h}=1$, the numbers $m,n$ are said to be prime to each other, or co-primes.
25. The foregoing theorem of residuation is of the greatest importance; with the help of it we can prove three other fundamental propositions, namely:—
(1) If $m,n$ are any two natural numbers, we can always find two other natural numbers $x,y$ such that
    $\operatorname {dv} (m,n)=xm-yn$.
(2) If $m,n$ are prime to each other, and $p\$ is a prime factor of $mn$, then $p$ must be a factor of either $m\$ or $n\$.
(3) Every number may be uniquely expressed as a product of prime factors.
Hence if $n=p^{\alpha }q^{\beta }r^{\gamma }\dots$ is the representation of any number $n\$ as the product of powers of different primes, the divisors of $n\$ are the terms of the product $(1+p+p^{2}+\dots +p^{\alpha })(1+q+\dots +q^{\beta })(1+r+\dots +r^{\gamma })\dots$ their number is $(\alpha +1)(\beta +1)(\gamma +1)\dots$ ; and their sum is $\textstyle \prod (p^{\alpha +1}-1)\div \prod (p-1)$. This includes $1$ and $n$ among the divisors of $n$.
# 1911 Encyclopædia Britannica/Number/Residues and congruences

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27. Residues and congruences.—It will now be convenient to include in the term “number” both zero and negative integers. Two numbers $a,b$ are said to be congruent with respect to the modulus $m$, when $(a-b)$ is divisible by $m$. This is expressed by the notation $a\equiv b{\pmod {m}}$, which was invented by Gauss. The fundamental theorems relating to congruences are
    If $a\equiv b$ and $c\equiv d{\pmod {m}}$, then $a\pm c\equiv b\pm d$, and $ac\equiv bd$.
    If $ha\equiv hb{\pmod {m}}$ then $a\equiv b{\pmod {m/d}}$, where $d=\operatorname {dv} (h,m)$.
Thus the theory of congruences is very nearly, but not quite, similar to that of algebraic equations. With respect to a given modulus $m$ the scale of relative integers may be distributed into $m$ classes, any two elements of each class being congruent with respect to $m$. Among these will be $\phi (m)$ classes containing numbers prime to $m$. By taking any one number from each class we obtain a complete system of residues to the modulus $m$. Supposing (as we shall always do) that $m$ is positive, the numbers $0,1,2,\dots (m-1)$ form a system of least positive residues; according as m is odd or even, $0,\pm 1,\pm 2,\dots \pm {\tfrac {1}{2}}(m-1)$, or $0,\pm 1,\pm 2,\dots \pm {\tfrac {1}{2}}(m-2),{\tfrac {1}{2}}m$ form a system of absolutely least residues.
# Chill and harsh the year draws to its close

From A Hundred and Seventy Chinese Poems (Alfred A. Knopf, 1919).
Chill and harsh the year draws to its close: In my cotton dress I seek sunlight on the porch. In the southern orchard all the leaves are gone: In the north garden rotting boughs lie heaped. I empty my cup and drink it down to the dregs: I look towards the kitchen, but no smoke rises. Poems and books lie piled beside my chair: But the light is going and I shall not have time to read them. My life here is not like the Agony in Ch'ēn, But often I have to bear bitter reproaches. Let me then remember, to calm my heart's distress, That the Sages of old were often in like case.
This work is a translation and has a separate copyright status to the applicable copyright protections of the original content.
# Reading the Book of Hills and Seas

From A Hundred and Seventy Chinese Poems (Alfred A. Knopf, 1919).
In the month of June the grass grows high And round my cottage thick-leaved branches sway. There is not a bird but delights in the place where it rests: And I too—love my thatched cottage. I have done my ploughing: I have sown my seed. Again I have time to sit and read my books. In the narrow lane there are no deep ruts: Often my friends' carriages turn back. In high spirits I pour out my spring wine And pluck the lettuce growing in my garden. A gentle rain comes stealing up from the east And a sweet wind bears it company. My thoughts float idly over the story of King Chou My eyes wander over the pictures of Hills and Seas. At a single glance I survey the whole Universe. He will never be happy, whom such pleasures fail to please!
This work is a translation and has a separate copyright status to the applicable copyright protections of the original content.
# It is no dream of mine

from Walden; or, Life in the Woods (1854) pp. 209-210.
It is no dream of mine, To ornament a line; I cannot come nearer to God and Heaven Than I live to Walden even. I am its stony shore, And the breeze that passes o'er; ​In the hollow of my hand Are its water and its sand, And its deepest resort Lies high in my thought.
# The Minister's Daughter

In the minister's morning sermon He had told of the primal fall, And how thenceforth the wrath of God Rested on each and all.
And how of His will and pleasure, All souls, save a chosen few, Were doomed to the quenchless burning, And held in the way thereto.
Yet never by faith's unreason A saintlier soul was tried, And never the harsh old lesson A tenderer heart belied.
And, after the painful service On that pleasant Sabbath day, He walked with his little daughter Through the apple-bloom of May.
Sweet in the fresh green meadows Sparrow and blackbird sung; Above him their tinted petals The blossoming orchards hung.
Around on the wonderful glory The minister looked and smiled; "How good is the Lord who gives us These gifts from His hand, my child.
"Behold in the bloom of apples And the violets in the sward A hint of the old, lost beauty Of the Garden of the Lord!"
Then up spake the little maiden, Treading on snow and pink "O father! these pretty blossoms Are very wicked, I think.
"Had there been no Garden of Eden There never had been a fall; And if never a tree had blossomed God would have loved us all."
"Hush, child!" the father answered, "By His decree man fell; His ways are in clouds and darkness, But He doeth all things well.
"And whether by His ordaining To us cometh good or ill, Joy or pain, or light or shadow, We must fear and love Him still."
"Oh, I fear Him!" said the daughter, "And I try to love Him, too; But I wish He was good and gentle, Kind and loving as you."
The minister groaned in spirit As the tremulous lips of pain And wide, wet eyes uplifted Questioned his own in vain.
Bowing his head he pondered The words of the little one; Had he erred in his life-long teaching? Had he wrong to his Master done?
To what grim and dreadful idol Had he lent the holiest name? Did his own heart, loving and human, The God of his worship shame?
And lo! from the bloom and greenness, From the tender skies above, And the face of his little daughter, He read a lesson of love.
No more as the cloudy terror Of Sinai's mount of law, But as Christ in the Syrian lilies The vision of God he saw.
And, as when, in the clefts of Horeb, Of old was His presence known, The dread Ineffable Glory Was Infinite Goodness alone.
Thereafter his hearers noted In his prayers a tenderer strain, And never the gospel of hatred Burned on his lips again.
And the scoffing tongue was prayerful, And the blinded eyes found sight, And hearts, as flint aforetime, Grew soft in his warmth and light.
This work was published before January 1, 1929, and is in the public domain worldwide because the author died at least 100 years ago.
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# Encyclopædia Britannica, Ninth Edition/Thomas A Kempis

From volume XXIII of the work. See also the Project Disclaimer.
THOMAS A KEMPIS. See Kempis.
# Inherited Memories

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From Popular Science Monthly Volume 29, October 1886 Popular Miscellany
​Inherited Memories.—Dr. H. D. Yalin has communicated to "Mind in Nature" (Chicago) some instances in which specific memories appear to have been transmitted by inheritance. He believes that they are the first cases that have been published, for even Ribot confesses to have had but little success in establishing instances of the kind.
The most striking case is that of a little girl fifteen months old, the child of a French Canadian father, whose principal traits of character and appearance she seems to have received, and of an American mother of German descent. She has had only the English and German languages spoken to her; yet the first word she ever spoke—when five months old was—mouman, the French Canadian form of maman, mother. Her first words of assent and dissent were oui and non—French—when eight months of age, "and she does not yet know yes or ya, though she seems to have forgotten oui. When a year old she was presented with a poodle-dog named Venus, which she called Nanan—candy, "one of the very first words that a French child talks." At about the same age she used freely the words bon, good, and pus, French Canadian for plus, no more. These six French words are the very ones that her father is likely to have exclusively used when a babe. The u of the last word was sounded as in French, as also were the nasal sounds of non and Nanan, things which her mother could not have done. Inheritance of memory has been observed in the case of birds, which soon learn to avoid the telegraph-wires, while their young seem equally ready in keeping away from them. Chauncey Wright is quoted as saying of those dreams of strange places and events that often recur to one in his sleep, with the intimation of being familiar though never seen in a wakeful state, that they are inherited memories. Dr. Valin also relates of his own personal experience: "My mother was brought up and educated in a most romantic country village, which she revisited a few months before I was born. The first time I visited it I remembered vividly having been there before. In fact, I could tell at that time what next would follow in the scenery, and I argued with my relatives who were denying my former knowledge of that place; my mother having died when I was about nine months old, and I had not had any description of it from any one, or conversed with any one in regard to the village scenery." A little girl in Burlington, Vermont, with whose family Dr. Valin at one time resided, "had inherited so good a memory of an uncle, whose funeral had been attended by her mother not long before this little girl's birth, that she could give a full description of him, and knew his picture at once the first time that she ever saw it." Some of these cases may have been maternal impressions, but the first one was undoubtedly one of inherited memory.