OpenLLM-France/wikimedia huggingface dataset:
# ASCII art

ASCII art is a graphic design technique that uses computers for presentation and consists of pictures pieced together from the printable characters defined by the ASCII Standard.

## Resources

* Text Art
# Illustrated Companion to the Latin Dictionary/Abolla

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ABOLLA. A cloak or mantle made of cloth doubled (Serv. ad Virg. Aen. v. 421). and fastened by a brooch under the neck or upon the top of the shoulder. It was originally worn by the military, as in the example (Abolla/1.1) from Trajan's column, and therefore was put on by the inhabitants of the city, instead of the toga, the costume of civilians, during periods of turbulence or foreign invasion (Varro, ap. Non., s. v. p. 538. Mercer); but subsequently it came to be used more commonly, and by all classes, as an article of the ordinary attire. (Juv. iv. 76. Suet. Cal. 35.) It does not differ very materially from the sagum; but was made of finer material, and somewhat smaller dimensions, whence Martial recommends persons addicted to thieving not to wear an abolla, because it was not large enough to conceal the stolen articles beneath it. Mart. Ep. viii. 48.
2. Abolla major. The large wrapping blanket of the Greek philosophers, more especially of the Cynics, who, as they wore no under clothing, enveloped themselves for the sake of decency in a wrapper of very ample dimensions (Mart. Ep. iv. 53.). Hence the expression facinus majoris abollae (Juv. Sat. iii. 115.) means a crime committed by a Greek philosopher, the garment being put for the person who wears it, as we apply our phrase "the long robe" to members of the legal profession. The illustration (Abolla/2.1) represents Heraclitus from an engraved gem.
* Abolla/1.1
* Abolla/2.1
# Illustrated Companion to the Latin Dictionary/Absis

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ABSIS or APSIS. The semicircular termination of any rectangular chamber, forming what is commonly termed in English "an alcove." (Plin. Ep. ii. 17. 8.) A form of this kind was commonly employed in courts of justice (basilicae) in order to make a convenient place for the judges' seats; and sometimes in temples to form a recess for the statue of the deity to whom the edifice was consecrated; as in the illustration (Absis/1.1), which shows the absis, as it now remains, of the temple of Rome and Venus, built by the Emperor Hadrian. Compare also the illustration to ADYTUM, where the ground-plan of a similar member is seen.
# Illustrated Companion to the Latin Dictionary/Acapna

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ACAPNA, sc. Ligna (ἄκαπνα, poet. δανά, κάγκανα). A word adopted from the Greek language and employed to designate fire-wood which had undergone a preparation to prevent it from smoking when placed upon the fire. Smokeless wood of this description was prepared in three different ways: 1st. by peeling off the bark, then soaking it a long time in water, and finally suffering it to dry thoroughly before it was used. (Theophrast. Hist. Plant. xv. 10.) The effect of this process is now well known, as it has been found that wood conveyed by water in floats burns more briskly and throws out less smoke than that which has been transported by land carriage merely: 2d. by soaking it in oil, or oil-lees, or by pouring oil over it (Cato, R.R. 130. Plin. H.N. xv. 8.): 3d. by hardening and scorching it over the fire until it lost the greater part of its moisture, without being entirely reduced to charcoal; this last was also designated by a special name Cocta or Coctilia. Mart. Ep. xiii. 15.
2. Acapnon mel. Honey taken from the hive without smoking the bees, which was considered the best kind of honey. Columell. vi. 33. 2. Plin. H.N. xi. 15.
# Illustrated Companion to the Latin Dictionary/Acatium

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ACAT'IUM (ἀκάτιον). A small, but fast-sailing vessel, belonging to the class termed actuariae, viz. which were worked with oars as well as sails. It was more especially used by the Greek pirates (Thucyd. iv. 67.), was furnished with an armed beak (rostrum). and had the stern rounded and bent inwards (inflexa, Plin. H. N. ix. 49.), a very common form in the marine of the ancients, as will be shown by many illustrations in the course of these pages. (See ACTUARIUS, APHRACTUS.) It is therefore highly probable that the distinctive characteristics of these vessels consisted more in the style of their rigging (see No. 2.) than in the form of the hull.
2. The same word is also used in connection with the rigging of a vessel, being sometimes applied to designate a sail, and sometimes a mast; but which of the sails or which of the masts is nowise apparent. Xenophon (Hellen. vi. 2. 27.) speaks of the acatia as sails, but contradistinct to the larger sails; Hesychius and Isidorus (Orig. xix. 3. 3.) on the contrary assert that the acatium was the largest sail on the ship, and attached to the main mast; while Julius Pollux (i. 91.) and Hesychius in another passage affirm that it was not a sail at all, but a mast, and that one the largest or main mast. Amidst all this apparent contradiction only one thing is certain, that the acatium was especially invented for fast sailing with light winds. If a conjecture might be hazarded all the difficulty would be got over by assuming that it meant both the mast and the sail belonging to it; and that it was a mast rigged after the fashion of the pirate vessels, to which the name properly belonged; a taller and lighter mast for instance than those usually employed, fitted also with smaller sails, probably with a top-sail over the main-sail, which would be handier for working and better for sailing in fair weather than the ordinary heavy mast, with its cumbrous yard. Thus Iphicrates, in the passage of Xenophon already referred to, before commencing his voyage, trimmed his vessels so as to be ready for any emergency. He left behind him the ordinary large set of sails (τἀ μεγάλα ἱστία), and consequently the heavy masts to which they belonged, and fitted the ships with masts and sails (ἀκατίοις), such as the pirates used in their vessels, for the rapidity they afforded in sailing, and the fewer hands they required for working, in case he should be forced to an engagement.
# Illustrated Companion to the Latin Dictionary/Accensus

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ACCENSUS. A civil officer attached to the service of several Roman magistrates, the consuls, praetors, and governors of provinces. (Varro, L. L. vii. 58. Liv. iii. 33.) He was generally the freedman of the person whom he served (Cic. ad Q. Fr. i. 1. 4.), and it was his duty to summon the people to the assemblies, to call the parties engaged in law-suits into court, and preserve order in it (Cic. l. c. 7.), and to proclaim the hour at sunrise, mid-day, and sunset. Plin. H. N. vii. 60.
2. The military ACCENSI were originally a body of supernumeraries enlisted for the purpose of supplying any vacancies which might occur in the legions by death or otherwise (Festus s. v. Adcensi), but subsequently they were formed into a separate corps, belonging to the levis armatura, or light-armed troops, amongst whom they occupied the lowest rank of all. They were selected from the fifth class of the Servian census (Liv. i. 43.), had no body armour nor weapons of attack, properly so called, but fought as they best could, with nothing but their fists and stones (pugnis et lapidibus depugnabant, Varro ap. Non. s. Decuriones, p. 520. Mercer), precisely as shown in the annexed figure (Accensus/2.1), which is copied from the Column of Trajan. On the battle-field they were posted in the rear of the whole army, being drawn up in the last line of all, behind the Rorarii, from whence they could be advanced to assist in desultory attacks as occasion required. Liv. viii. 8. and 10.
# Illustrated Companion to the Latin Dictionary/Accinctus

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ACCINCTUS. In a general sense, girded, equipped, or provided with anything. But the word is more especially applied to the military, and then implies that the soldiers has his sword girded on, or, in other words, that he is accoutred as a soldier on duty ought to be; like the right-hand figure in the illustration (Accinctus/1.1), from Trajan's Column. Hence, miles non accinctus, means a soldier without his sword, or, as we should say, without his "side-arms," which, under a lax system of discipline, the men took off when employed upon field works, fortifications, &c., and piled with their shields and helmets on the ground beside them, like the left-hand figure in the illustration, also from the Column of Trajan. Under a strict system, this was not allowed; the shield and helmet only were laid aside, but the soldier was always accinctus, or had his sword on. Tac. Ann. xi. 18. Veget. Mil. iii. 8.
# Illustrated Companion to the Latin Dictionary/Accubitalia

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ACCUBITA'LIA. Things which belong to a sofa or couch; particularly the furniture of a bed, or a dining couch, including the cushions or pillows, mattress, and coverlet; as seen in the two next illustrations. Valerian ap. Trebell. Claud. 14.
# Illustrated Companion to the Latin Dictionary/Accubitio

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ACCUBIT'IO. The act of reclining at table (Cic. Senect. 13.), as described under ACCUBO.
# Illustrated Companion to the Latin Dictionary/Accubitum

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ACCU'BITUM. A particular kind of couch used to recline upon at meals, which was substituted under the empire for the lectus tricliniaris. (Schol. Vet. ap. Juv. Sat. v. 17. Lamprid. Elagab. 19.) The precise form and character of this piece of furniture is nowhere described; but as the words accubo, accumbo, accubitus, in their strict sense refer to the act of a single person, it is but reasonable to conclude that the accubitum was a sofa intended for the reception of one person only: the more so as the annexed illustration (Accubitum/1.1) from an ancient Roman marble (Symeoni, Epitaffi Antichi, p. 51. Lione, 1558) shows that sofas of such a character were actually used at meals; while the interpretation given explains at the same time the object of their introduction, in order that any number of guests might be accommodated at an entertainment by the addition of extra sofas (Lamprid. Alex. Sev. 34.); whereas the accomodation afforded by a tricliniary couch was limited to nine.
# Illustrated Companion to the Latin Dictionary/Accubitus

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ACCU'BITUS. Same as ACCUBITIO. Stat. Ach. i. 109.
# Illustrated Companion to the Latin Dictionary/Abaculus

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ABAC'ULUS (ἀβακίσκος). A small tile or die of glass, or a composition in imitation of stone, stained of various colours, and used for inlaying patterns in mosaic pavements. (Plin. H.N. xxxvi. 67. Moschus ap. Athen. v. 41.) The illustration (Abaculus/1.1) represents part of the ancient mosaic pavement in the church of S. Groce in Gerusalemme, at Rome.
# Key Signatures

A key signature serves as a guide for the performer of a piece of music. The key signature determines the pattern of accidentals -- sharps and flats -- to be played, and reappears at the beginning of each staff. (In this way it differs from a time signature, which need be written only once). For example, if the key signature consists of only F-sharp, each written note F in the piece should be played as F-sharp, even though no sharp immediately precedes the written note. Often, however, an accidental contradicting the direction of the key signature will appear immediately before the written note. An accidental immediately preceding the written note always takes precedence. (For instance, in our example, if the key signature contains F-sharp but a written note F appears with a natural sign written in front of it, F-natural should be played). In traditional notation, this influence of the new accidental applies for the duration of the measure before the key signature resumes its "dominion", or until canceled by a subsequent new accidental.
Since a the presence of a "key" in music is contingent on a certain pattern of accidentals, the key signature gives a partial indication of the key of a given passage of music. We need more than the key signature to determine the key of a passage, though -- that must be decided on the basis of contextual features to be explained elsewhere in the School of Music. All other things being equal, though, each key signature can represent one of two musical keys: one major, and one minor. Each is termed the "relative" major or minor, respectively, in relation to the other. For example, B-flat major and G minor have the same key signature: the relative minor of the key of B-flat major is G minor, while B-flat major is the relative major of G minor. The following tables illustrate each key signature, along with a listing of their corresponding keys. It is of paramount importance for the practicing musician to memorize these keys and to be able to recall them instantly.
| Key Sig. | Major Key | Minor Key |
| No sharps or flats | C major | A minor |
| Key Sig. | Major Key | Minor Key |
| 1 flat | F major | D minor |
| 2 flats | B♭ major | G minor |
| 3 flats | E♭ major | C minor |
| 4 flats | A♭ major | F minor |
| 5 flats | D♭ major | B♭ minor |
| 6 flats | G♭ major | E♭ minor |
| 7 flats | C♭ major | A♭ minor |
| Key Sig. | Major Key | Minor Key |
| 1 sharp | G major | E minor |
| 2 sharps | D major | B minor |
| 3 sharps | A major | F# minor |
| 4 sharps | E major | C# minor |
| 5 sharps | B major | G# minor |
| 6 sharps | F# major | D# minor |
| 7 sharps | C# major | A# minor |
# K^4/Example for intersection and sum/Bases/2/Exercise

Let $K$ be a field.
a) Show that the linear subspace $U\subseteq K^{4}$ generated by
    ${\begin{pmatrix}5\\3\\-1\\4\end{pmatrix}},\,{\begin{pmatrix}2\\6\\5\\-3\end{pmatrix}},\,{\begin{pmatrix}4\\-2\\-1\\1\end{pmatrix}}$
has dimension $3$.
b) Determine a basis and the dimension of the solution space $L\subseteq K^{4}$ of the linear equation
    $7x_{1}+5x_{2}+3x_{3}-6x_{4}=0\,.$
c) Determine a basis and the dimension of the intersection $U\cap L$.
d) Confirm fact in this example.
# Base change/Transformation matrix/Standard basis and 451/23-8/57-3/Exercise

Determine the transformation matrices $M_{\mathfrak {v}}^{\mathfrak {u}}$ and $M_{\mathfrak {u}}^{\mathfrak {v}}$ for the standard basis ${\mathfrak {u}}$ and the basis ${\mathfrak {v}}$ of $\mathbb {R} ^{3}$ that is given by the vectors
    $v_{1}={\begin{pmatrix}4\\5\\1\end{pmatrix}},\,\,v_{2}={\begin{pmatrix}2\\3\\-8\end{pmatrix}},\,{\text{ and }}\,v_{3}={\begin{pmatrix}5\\7\\-3\end{pmatrix}}$
# Base change/Transformation matrix/R^3/Standard basis and permuted standard basis/Exercise

Determine the transformation matrices $M_{\mathfrak {v}}^{\mathfrak {u}}$ and $M_{\mathfrak {u}}^{\mathfrak {v}}$ for the standard basis ${\mathfrak {u}}$ and the basis ${\mathfrak {v}}$ given by the vectors
    $v_{1}={\begin{pmatrix}0\\1\\0\end{pmatrix}},\,v_{2}={\begin{pmatrix}0\\0\\1\end{pmatrix}},\,{\text{ and }}\,v_{3}={\begin{pmatrix}1\\0\\0\end{pmatrix}}$
in $\mathbb {R} ^{3}$.
# Base change/Transformation matrix/C/Standard basis and 3+5i 1-i/2+3i 4+i/Exercise

Determine the transformation matrices $M_{\mathfrak {v}}^{\mathfrak {u}}$ and $M_{\mathfrak {u}}^{\mathfrak {v}}$ for the standard basis ${\mathfrak {u}}$ and the basis ${\mathfrak {v}}$ of $\mathbb {C} ^{2}$ that is given by the vectors
    $v_{1}={\begin{pmatrix}3+5{\mathrm {i} }\\1-{\mathrm {i} }\end{pmatrix}}{\text{ and }}v_{2}={\begin{pmatrix}2+3{\mathrm {i} }\\4+{\mathrm {i} }\end{pmatrix}}.$
# Base change/Transformation matrix/Standard basis and 237/1-34/569/Exercise

Determine the transformation matrices $M_{\mathfrak {v}}^{\mathfrak {u}}$ and $M_{\mathfrak {u}}^{\mathfrak {v}}$ for the standard basis ${\mathfrak {u}}$ and the basis ${\mathfrak {v}}$ of $\mathbb {R} ^{3}$ given by the vectors
    $v_{1}={\begin{pmatrix}2\\3\\7\end{pmatrix}},\,\,v_{2}={\begin{pmatrix}1\\-3\\4\end{pmatrix}}\,{\text{ and }}\,v_{3}={\begin{pmatrix}5\\6\\9\end{pmatrix}}$
# Base change/Transformation matrix/Polynomial ring/R/Product of linear forms/Exercise

Let $V$ be the vector space of the polynomials of degree $\leq d$. Determine the transformation matrices between the bases ${\mathfrak {u}}=X^{0},X^{1},X^{2},\ldots ,X^{d}$ and ${\mathfrak {v}}=P_{0},P_{1},P_{2},\ldots ,P_{d}$ with $P_{0}=1$ and
    $P_{i}=(X-1)\cdots (X-i)\,$
for $d=0,1,2,3,4$.
# Base change/Three bases/Composition/Fact/Proof/Exercise

Let $K$ be a field, and let $V$ be a $K$-vector space of dimension $n$. Let ${\mathfrak {u}}=u_{1},\ldots ,u_{n},\,{\mathfrak {v}}=v_{1},\ldots ,v_{n},$ and ${\mathfrak {w}}=w_{1},\ldots ,w_{n}$ denote bases of $V$. Show that the transformation matrices fulfill the relation
    $M_{\mathfrak {w}}^{\mathfrak {u}}=M_{\mathfrak {w}}^{\mathfrak {v}}\circ M_{\mathfrak {v}}^{\mathfrak {u}}\,.$
# K^3/Example for intersection and sum/Bases/1/Exercise

Let $K$ be a field.
a) Show that the linear subspace $U\subseteq K^{3}$ generated by
    ${\begin{pmatrix}3\\2\\-4\end{pmatrix}},\,{\begin{pmatrix}2\\8\\-3\end{pmatrix}}$
has dimension $2$.
b) Determine a basis and the dimension of the solution space $L\subseteq K^{3}$ of the linear equation
    $-6x_{1}+4x_{2}+5x_{3}=0\,.$
c) Determine a basis and the dimension of the intersection $U\cap L$.
d) Confirm fact in this example.
# Pairwisely direct sum/No direct sum/Exercise

Give an example of linear subspaces $U_{1},U_{2},U_{3}$ in a vector space $V$ such that $V=U_{1}+U_{2}+U_{3}$, such that $U_{i}\cap U_{j}=0$ for $i\neq j$ holds, and such that the sum is not direct.
# K^3/Plane/Direct complement/1/Exercise

Determine a direct complement of the linear subspace $U\subseteq \mathbb {R} ^{3}$ generated by ${\begin{pmatrix}-5\\4\\9\end{pmatrix}}$ and ${\begin{pmatrix}2\\-7\\3\end{pmatrix}}$
# R to R/Even function/Definition

A function $f\colon \mathbb {R} \rightarrow \mathbb {R}$ is called even if, for all $x\in \mathbb {R}$, the identity
    $f(x)=f(-x)\,$
holds.
# R to R/Odd function/Definition

A function $f\colon \mathbb {R} \rightarrow \mathbb {R}$ is called odd if, for all $x\in \mathbb {R}$, the identity
    $f(x)=-f(-x)\,$
holds.
# Illustrated Companion to the Latin Dictionary/Accubo

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
AC'CUBO (κατακλίνομαι). To recline at table, an attitude usually adopted by the ancients at their meals, instead of our habit of sitting. The posture of reclining, as clearly shown in the illustration (Accubo/1.1), from the Vatican Virgil, was one between lying and sitting, the legs and lower part of the body being stretched out at full length on a sofa, whilst the upper part was slightly raised and supported upon the left elbow, which rested on a pillow, the right arm and hand being left free to reach out and take the food.
The usual method of arranging the sofas, the etiquette of precedence, and position of the different places, is explained under the word LECTUS TRICLINIARIS.
During the later periods of Roman history, the men and women reclined together at their repasts; but the Greeks considered such a posture to be indecorous for females; their women, therefore, either sat at a separate table, or upon one end of the couch on which the men only reclined, as shown in the illustration (Accubo/1.2) copied from a Greek marble in the museum of Verona, representing a funeral repast (coena feralis). The same practice was also observed by the Romans, before the corruption of manners incident upon wealth and conquest had ensued.
* Accubo/1.1
* Accubo/1.2
# Illustrated Companion to the Latin Dictionary/Accumbo

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ACCUM'BO. Properly denotes the taking a place on a dining coach, in contradistinction to Accubo, which refers to a person already reclining; and in allusion to a single person, as distinguished from Discumbo, which has reference to several persons or the whole company. But these distinctions are not always observed.
# Illustrated Companion to the Latin Dictionary/Acerra

This article incorporates text from a publication now in the public domain: Rich, Anthony (1849). The illustrated companion to the Latin dictionary, and Greek lexicon. p. vi. OCLC 894670115. https://archive.org/details/illustratedcompa00rich.
ACERRA (λιβανωτρὶς). A small square box with a lid to it (arca turalis. Serv. ad Virg. Aen. v. 745.), in which the incense used at a sacrifice was contained. (Acerra turis custos. Ovid. Met. xiii. 703. Hor. Od. iii. 8. 2.) The illustration (Acerra/1.1) is copied from a bas-relief in the museum of the Capitol at Rome, on which various implements employed at the sacrifice are sculptured.
The incense itself was not burnt in the acerra, but the box was carried to the altar by an attendant of the priesthood, as shown by the annexed figure (Acerra/1.2), copied from a bas-relief at Rome. The box is carried in his left hand, a jug for pouring out libations of wine (capis) in his right, and the skin of a victim over the left arm. The incense, when used, was taken out of the box, and sprinkled upon the burning altar, for which the expression is libare acerra. Ov. Pont. iv. 8. 39. Pers. Sat. ii. 5.
2. According to Festus (s. v.), the same name was also given to a small portable altar placed before the dead, and on which incense was burnt. See the illustration to ARA TURICREMA, and compare Cic. Leg. ii. 24.
* Acerra/1.1
* Acerra/1.2