OpenLLM-France/wikimedia huggingface dataset:
# Illustrated Companion to the Latin Dictionary/Corbis

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.
COR'BIS. A basket of wicker-work, made in a pyramidical or conical shape (Varro, L. L. v. 139. Id. R. R. i. 22. 1. Isidor. Orig. xx. 9. Compare Arrian. Anab. v. 7. 8. πλέγμα ἐκ λύγου πυραμοειδές), and used for a variety of agricultural purposes, the particular application being generally marked by a characteristic epithet, as: —
1. Corbis messoria; a basket used for measuring corn in the ear, as opposed to the modius, in which it was measured after it had been threshed out (Cic. Sext. 38. Cato, R. R. 136.); or in which the ears of corn (spicas) were collected by the reaper, when each ear was nicked off from the top of the stalk by a serrated instrument (see the illustration and description s. Falx denticulata), instead of being cut with the straw. Varro, R. R. i. 50. 1. Propert. iv. 11. 28. Ov. Met. xiv. 643.
2. Corbis pabulatorius; a basket of the same character, which contained a certain measure of green food for cattle. Columell. vi. 3. 5. Id. xi. 2. 99.
3. Corbis constricta; a basket of similar character, employed as a muzzle for horses (Veget. Mulom. iii. 23. 2.), but here the reading is doubtful; Schneider has curcuma.
The example (Corbis/0.1) introduced above is copied from a fresco painting in the sepulchre of the Nasonian family on the Flaminian Way, near Rome, where it appears several times in the hands of figures engaged in rural occupations; and is given as a genuine specimen of the Roman corbis or corbula, on account of the uses to which it is there applied, its affinity in form to the descriptions cited at the head of this article, and because a basket of exactly the same shape and materials is now employed by the Neapolitan peasantry for similar purposes, and called by a diminutive of the same name, la corbella.
# Illustrated Companion to the Latin Dictionary/Corbita

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.
COR'BITA (πλοῖον σιταγωγόν or σιτηγόν). A merchantman; but more accurately, a ship employed solely for the transport of corn, and so termed, because it carried a corbis at the mast-head. (Festus, s. v.) These were large and heavy sailing vessels (Plaut. Poen. iii. 1. 4. Lucil. ap. Non. s. v. p. 533. Compare Cic. Att. xvi. 6.), with two masts, as proved by the annexed example (Corbita/1.1) from a medal of Commodus, struck in commemoration of his having chartered a number of vessels to bring corn to Rome from Africa and Egypt, as narrated by Lampridius in his life. The corbis is seen at the top of the main mast; and it may be remarked that the modern name corvette originated in this word.
# Illustrated Companion to the Latin Dictionary/Corbula

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.
COR'BULA. Diminutive of CORBIS; a small basket employed in fruit gathering (Cato, R. R. ii. 5.); as a bread basket (Caecil. ap. Non. s. v. p. 197.); and for carrying up dishes from the kitchen to the dining room. Plaut. Aul. ii. 7. 4.
# Illustrated Companion to the Latin Dictionary/Cordax

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.
CORDAX (κόρδαξ). A dance of the old Greek comedy, at once highly ridiculous, and so indecent that it was considered a mark of drunkenness or great want of self-respect to dance it off the stage. (Pet. Sat. 52. 9. Hesych. s. v. Aristoph. Nub. 540.) A dance of this kind is represented on the marble tazza in the Vatican (Visconti, Mus. Pio-Clem. iv. 29.), where it is performed by ten figures, five Fauns, and five Bacchanals; but their movements, though extremely lively and energetic, are not marked by any particular indelicacy; certainly not so much as is exhibited in the Neapolitan tarantella, which is thought to preserve the vestiges of the Greek cordax.
# Illustrated Companion to the Latin Dictionary/Coriarius

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.
CORIA'RIUS. One who prepares hides and skins; a tanner or a carrier. Plin. H. N. xvii. 6. Inscript. ap. Grut. 648. 8. and 283. 1.
# Illustrated Companion to the Latin Dictionary/Cornicen

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.
COR'NICEN (κεραταύλης or κεραύλης). A trumpeter; i. e. who blows the large circular horn called cornu, as shown by the annexed illustration (Cornicen/1.1), from the arch of Constantine at Rome. Liv. ii. 64. Juv. x. 214.
# Illustrated Companion to the Latin Dictionary/Cornicularius

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.
CORNICULA'RIUS. Strictly, a soldier who had been presented by his general with the corniculum; whence the name was given as a title to an assistant officer, or adjutant, who acted for the consul or tribune; probably because the person so promoted was always selected from amongst those who had received the above-named reward. Suet. Dom. 17. Val. Max. vi. 1. 11.
2. Hence the word came also to be applied in civil matters to a clerk or secretary, who acted as the assistant of a magistrate. Cod. Theodos. 7. 4. 32.
# Illustrated Companion to the Latin Dictionary/Corniculum

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.
CORNIC'ULUM. Diminutive of CORNU, any small horn; but, in a more special sense, an ornament bestowed upon meritorious soldiers by their commanding officer, as a mark of distinction (Liv. x. 44.), supposed to have been in the form of a horn, and worn upon the helmet, either as a support for the crest, like the left-hand figure in the engraving (Corniculum/1.1) annexed, from a bas-relief; or affixed to the sides, like the one on the right, from a painting at Pompeii.
# Illustrated Companion to the Latin Dictionary/Cornu copiae

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.
CORNU CO'PIAE (κέρας Ἀμαλθείας). The horn of plenty; a symbol composed of the primitive drinking-horn (CORNU, 4.), filled with corn and fruit, to indicate the two kinds of nourishment essential to mankind, whence commonly employed by poets and artists as a symbol of Happiness, of Concord, and of Fortune. (Plaut. Pseud. ii. 3. 5. Compare Hor. Epist. i. 12. 29. Od. i. 17. 15. The example (Cornu_copiae/1.1) is from a terra-cotta lamp, where it accompanies an image of Fortune.
# Illustrated Companion to the Latin Dictionary/Corollarium

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.
COROLLA'RIUM. Also a diminutive from CORONA; but more specially applied to a light wreath made of very thin leaves of metal plated or gilt, which the Romans used to give away as a present to favourite actors. Plin. H. N. xxi. 3. Varro, L. L. v. 178.
# Illustrated Companion to the Latin Dictionary/Corolla

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.
COROL'LA (στεφανίσκος). As a general diminutive of CORONA, means any kind of small chaplet or garland (Prop. ii. 34. 59. Catull. 63. 66.); but the word is used in a more special sense to designate a wreath of artificial flowers made out of thin horn shavings, tinged with different colours, to imitate the tints required, and worn in the winter season. Plin. H. N. xxi. 3.
# Illustrated Companion to the Latin Dictionary/Coronaria

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.
CORONA'RIA. A female who makes garlands and chaplets. Plin. H. N. xxi. 3. See next illustration.
# Illustrated Companion to the Latin Dictionary/Coronarius

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.
CORONA'RIUS (στεφανηπλόκος). One who makes and sells garlands, wreaths, chaplets, or crowns, of real or artificial flowers. (Front. ad M. Caes. Ep. i. 6. Plin. H. N. xxxiv. 26.) The illustration (Coronarius/1.1) is from a Pompeian painting, and represents male and female genii engaged in this operation.
2. Aurum coronarium. A sum of gold sent by the provinces to a commander, for making a golden triumphal crown. (Cic. Pis. 37.) See CORONA, 1. (3.).
3. Opus coronarium. Stucco-work employed in the decoration of cornices. Vitruv. vii. 6. CORONA, 14. and 15.
# Illustrated Companion to the Latin Dictionary/Coronatus

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.
CORONA'TUS (στεφανηφόρος). Wearing a wreath, chaplet, or crown. See the illustrations to CORONA.
2. Also, decorated with garlands or festoons; applied to things, as to ships (Ov. Fast. iv. 335.); to altars (Prop. iii. 10. 19.); to cattle (Prop. iii. 1. 10. Id. iv. 1. 21.).
# Unitary vector space/Isometry/Eigenvalues/Fact

Let $V$ be a finite-dimensional ${\mathbb {K} }$-vector space, and let
    $\varphi \colon V\longrightarrow V$
denote a linear isometry.
modulus of every eigenvalue
$\varphi$
$1$
In case ${\mathbb {K} }=\mathbb {R}$, only the eigenvalues $1$ and $-1$ are possible.
# Illustrated Companion to the Latin Dictionary/Corrigia

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.
CORRIG'IA (ἱμάς, σφαιρωτήρ). A shoe-string and boot-lace (Cic. Div. ii. 40.); which were sometimes made of dog's skin. (Plin. H. N. xxx. 12.) The examples (Corrigia/1.1) are from Pompeian paintings.
# Illustrated Companion to the Latin Dictionary/Corrugis

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.
CORRU'GIS. Literally wrinkled; but it is applied to the plaits of a loose garment (sinus corrugis, Nemes. Cyneg. 93.), produced by tieing a girdle round it (see the figures in the opposite column); or to the irregular and transverse folds created by throwing up a portion over the shoulder, instead of leaving it pendant, as seen on the right side of the figure s. CONTABULATIO.
# Illustrated Companion to the Latin Dictionary/Corsae

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.
CORSAE. Fillets or mouldings employed to decorate the external face of a marble door-post. (Vitruv. iv. 6.) See the illustration s. ANTEPAGMENTUM.
# Illustrated Companion to the Latin Dictionary/Cortinale

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.
CORTINA'LE. A cellar in which new-made wine was boiled down in caldrons (cortinae). Columell. i. 6. 19.
# Illustrated Companion to the Latin Dictionary/Cortina

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.
CORTI'NA. A deep circular vessel, or caldron, employed for boiling meat, melting pitch (Plin. H. N. xvi. 22.), making paint (Id. xxxv. 42.), and a variety of other purposes, for which its form and character rendered it convenient, and which, when placed over the fire, was either raised upon a trivet, or supported upon large stones put under it. (Plin. H. N. xxxvi. 65.) The example (Cortina/1.1) is copied from a bronze original found at Pompeii.
2. (ὅλμος, κύκλος, ἐπίθημα τοῦ τρίποδος). The lid or covering placed over the caldron or hollow part of the Delphic tripod (Virg. Aen. vi. 347. Prudent. Apoth. 506. tripodas cortina tegit, Jul. Pollux. x. 81.), upon which the priestess sat to receive the divine afflatus, and pronounce her responses. It had the form of a half globe, and is frequently represented in that manner by sculptors, lying by itself upon the ground at the feet of Apollo; but when placed upon the caldron, the two together made a complete globe; as shown in the illustration (Cortina/2.1), from a bas-relief upon an altar in the Villa Borghese. In the original, the raven, sacred to Apollo, is sitting on its top; in one of Hamilton's vases, Apollo himself is seen sitting upon the cup, without any lid, and in another, upon a lid like the present.
3. An altar in the form of a tripod, made of marble, bronze, or the precious metals, often intended to be dedicated as an offering in the temples of the gods, and likewise preserved as a piece of ornamental furniture in the houses of great and wealthy persons. (Plin. H. N. xxxiv. 8. Suet. Aug. 52. Compare Mart. xii. 66.) The illustration (Cortina/3.1) is copied from an original of marble in the Vatican.
4. The vault or ceiling over the stage in a theatre, from its resemblance to the covering of the tripod, No. 2. Sever. Aetn. 294.
* Cortina/1.1
* Cortina/2.1
* Cortina/3.1
# Illustrated Companion to the Latin Dictionary/Cortinula

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.
CORTIN'ULA. Diminutive of CORTINA. Ammian. xxix. 1.
# Illustrated Companion to the Latin Dictionary/Corvus

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.
CORVUS (κόραξ). The name given to several machines employed in naval and military operations, and in the attack or defence of fortified places; each of which was so called either from its resemblance in form to the raven's beak, or from the manner of its application, like the raven darting down, and carrying off its prey; consequently, the word may be translated as a crane, a grappling-iron, a crow-bar, as best suits the context in the passages where it occurs. Quin. Curt. iv. 2. Id. iv. 4. Vitruv. x. 19.
2. A cutting instrument used in surgical operations, because the blade was shaped like a raven's beak. Celsus, vii. 19.
# Illustrated Companion to the Latin Dictionary/Corycaeum

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.
CORYCAE'UM. An apartment in the gymnasium and in large bathing establishments, such as the Roman Thermae, appropriated for playing a particular kind of game, which consisted in buffetting backwards and forwards a large sack (κώρυκος), filled with fig grains, olive husks, bran, or sand, suspended from the ceiling. Anthyll. ap. Oribas. Coll. Med. 6. Vitruv. v. 11.
# Illustrated Companion to the Latin Dictionary/Corymbium

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.
CORYM'BIUM. A wig of false hair, dressed in imitation of the corymbus (Pet. Sat. 110. 1. and 5.), — a fashion which is explained in the next article, No. 2.
# Illustrated Companion to the Latin Dictionary/Corymbus

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.
CORYM'BUS (κόρυμβος). A bunch of ivy berries, and likewise of other kinds of fruit which grow in the same conical-shaped clusters; afterwards, a wreath or chaplet made with the leaves and clusters of the ivy, which the ancients used as a festive ornament on many occasions, but especially as an appropriate decoration for Bacchus and his followers, as in the annexed illustration (Corymbus/1.1), from a marble bust, supposed to represent Ariadne. Tibull. i. 7. 45. Prop. ii. 30. 39. Juv. vi. 52.
2. A peculiar manner of arranging the hair, more especially characteristic of the early population of Athens (Heraclid. ap. Athen. xii. 5. Compare CROBYLUS), and of the female sex amongst them. (Schol. ad Thucyd. i. 6.) It was produced by turning the hair backwards all round the head, and drawing it up to a point at the top, where it was tied with a band, so as to have a sort of resemblance in general form to a cluster of ivy berries, as shown by the example (Corymbus/2.1), from a bas-relief in Greek marble. When the hair was too long or too abundant to be tied thus simply, it was fastened in a double bow across the top of the head, as in the well-known statue of Apollo Belvedere, and a bust of Diana in the British Museum. In Cicero (Ep. Att. xiv. 3.) Corymbus is a proper name, arising out of the custom of arranging the hair in the manner described. Ernesti, Clav. Cic. s. v.
3. The elevated ornament on the stern of a ship (Val. Flacc. i. 272.); for which the special name is APLUSTRE; which see.
* Corymbus/1.1
* Corymbus/2.1
# Illustrated Companion to the Latin Dictionary/Corytus

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.
CORY'TUS (γωρυτός). Properly, and accurately a bow-case (Serv. ad Virg. Aen. x. 168.), as contradistinguished from the quiver for arrows (pharetra); although the same case was sometimes used to carry both the bow and arrows, when it is distinguished by a characteristic epithet (sagittiferi coryti, Sil. Ital. xv. 773.). An example of both kinds is given in the engraving (Corytus/1.1), the simple bow-case from a fictile vase, the one containing the bow and arrows from an engraved gem.
# Illustrated Companion to the Latin Dictionary/Cosmetae

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.
COSME'TAE. Ladies' maids; slaves whose duty it was to attend the toilet of the Roman ladies, and assist in dressing and adorning their mistresses. Juv. Sat. vi. 477. Heindorf. ad Hor. Sat. i. 2. 98.
# Illustrated Companion to the Latin Dictionary/Cos

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.
COS (ἀκόνη). A hone, whetstone, or grindstone; worked with water and oil (Plin. H. N. xxxvi. 47.), and by the same sort of machinery as now employed. The illustration (Cos/1.1), from an engraved gem, represents Cupid sharpening his arrows on a grindstone, exactly as described by Horace (Od. ii. 8. 15. ardentes acuens sagittas Cote cruenta).
# Illustrated Companion to the Latin Dictionary/Cothurnatus

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.
COTHURNATUS. Wearing the cothurnus, as explained and illustrated in the next word.
# Unitary vector space/Isometry/Eigenvalues/Fact/Proof

Let $\varphi (v)=\lambda v$ with $v\neq 0$, that is, $v$ is an eigenvector for the eigenvalue $\lambda \in {\mathbb {K} }$. Due to the isometry property, we have
    $\Vert {v}\Vert =\Vert {\varphi (v)}\Vert =\Vert {\lambda v}\Vert =\vert {\lambda }\vert \cdot \Vert {v}\Vert \,.$
Because of $\Vert {v}\Vert \neq 0$, this implies $\vert {\lambda }\vert =1$. In the real case this means $\lambda =\pm 1$.