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

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.
FAT'UI and FAT'UAE. Idiots of both sexes, who were purchased as slaves, and kept in great Roman families for the purpose of exciting merriment by their stupidity. Senec. Ep. 50.
# Illustrated Companion to the Latin Dictionary/Faux

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.
FAUX. From its original meaning, the gullet or entrance to the stomach, is used to designate any narrow pass or confined entrance either in natural or artificial objects; and expressly to a narrow passage which formed a communication between the two principal divisions of a Roman house, the atrium and peristylium. It was situated by the side of the tablinum; and as there were frequently two of these, one on each side of the above-named apartment, the word is commonly used in the plural (fauces, Vitruv. vi. 3. 6.) The object of it was to obviate the inconvenience of making a passage room of the tablinum, as well as to afford a ready access from one part of the house to the other, when that apartment was closed in with screens. The relative position which it bore to the other members of the house will be understood by referring to the ground-plan at p. 248., where it is marked E, and its general appearance in elevation by the annexed engraving (Faux/1.1), which presents a view from the house of the Dioscuri at Pompeii, with the ceiling only restored. The foreground shows the interior of the atrium, with its impluvium in the floor; the large deep recess on the left at the back is an open tablinum, showing the peristyle through it; and the low dark door at the side is the faux, which opens at its further end into the peristyle in the same way as it does upon the atrium on the side here shown.
2. Also in the plural; the stalls or stables for the horses and chariots in the Circus. (Ennius ap. Cic. Div. i. 48. Cassiodor. Var. Ep. iii. 51.) See CARCER, 2., where the object is described and illustrated.
# Illustrated Companion to the Latin Dictionary/Favissae

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.
FAVIS'SAE. Pits, or cellars constructed underneath a temple, in which the sacred implements, ornaments, furniture, or other property belonging to the edifice were stowed away after they had become unfit for use. (Varro, ap. Gell. ii. 10. Brocchi, Suola di Roma p. 152.) Three pits of this nature were discovered under the ruins of an ancient temple at Fiesole, filled with broken musical instruments, various implements and utensils in ivory and bronze, as well as idols, lamps, and fictile vases, all damaged and mutilated. Giornal. Arcad. tom. iii. p. 119.
# Illustrated Companion to the Latin Dictionary/Favus

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.
FAVUS. A flag, tile, or slab of marble cut into a six-cornered figure of the same shape as the cell in a honey-comb (favus), used for making pavements of the kind termed sectilia. (Vitruv. vii. 1. 4.) The illustration (Favus/1.1) represents a piece of pavement in the Thermae of Titus at Rome; the honeycomb pattern is laid with slabs of fine marble, of the kind called pavonazzetto.
# Illustrated Companion to the Latin Dictionary/Fax

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.
FAX (φανός). A torch; which was made out of a piece of resinous wood cut into a point, and dipped into oil or pitch; or of tow impregnated with wax, tallow, pitch, rosin, or any inflammable materials enclosed in a tube of metal, or in a bundle of wattled laths (faculae), as shown by the illustration (Fax/1.1), from the Column of Antoninus. Virg. Georg. i. 291. Liv. xxii. 16. Plin. H. N. xix. 7.
# Illustrated Companion to the Latin Dictionary/Fecialis

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.
FECIA'LIS. See FETIALIS.
# Illustrated Companion to the Latin Dictionary/Feminalia

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.
FEMINA'LIA or FEMORA'LIA. Short breeches, or drawers which covered the thighs (femora), being fastened round the waist, and terminating a little below the knee (Suet. Aug. 82. Isidor. Orig. xix. 22. 29.), like the annexed figure (Feminalia/1.1), from the Column of Trajan. They were not, however, usually worn by the Romans in early times, except, perhaps, by some few individuals of delicate constitution, like Augustus; as in ordinary cases the long and ample toga rendered such a precaution unnecessary. But when that garment fell into disuse, they seem to have been very generally adopted; particularly by the troops engaged on foreign service in cold and northerly climates; for they appear invariably on all the figures of the triumphal arches and columns, both officers and men.
# Illustrated Companion to the Latin Dictionary/Femur

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.
FEMUR (μηρός). In architecture, the long flat projecting face between each channel (canaliculus) of a triglyph (Vitruv. iv. 3. 5.); three of which are seen in the annexed engraving (Femur/1.1), from the frieze of a Doric temple formerly existing at Rome.
# Illustrated Companion to the Latin Dictionary/Fenestella

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.
FENESTEL'LA or FENESTREL'LA. Diminutive of FENESTRA. A small window, or one which is less than the usual size. (Columell. viii. 3. 3. Pallad. i. 24.) The annexed illustration (Fenestella/1.1) represents two of the windows in the house of the Tragic Poet at Pompeii, on the street side. They are situated on the ground floor, at a height of six feet six inches above the pavement, and are not quite three feet by two in size. By the side of each is a wooden frame for the shutter to slide into when the window was opened.
# Illustrated Companion to the Latin Dictionary/Fenestra

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.
FENES'TRA (θυρίς). A window; inclusive of the aperture (lumen) in the wall, through which the light is admitted, and the casement or shutters, whether glazed, or otherwise by which it is closed. The illustration (Fenestra/1.1) represents three ancient windows of different designs; the one on the left hand, from a Greek bas-relief in the British Museum; that on the right from the Vatican Virgil; and the centre one from a marble sarcophagus of a later period, found in the Vatican cemetery.
2. Fenestra biforis (θυρίς δικλίς). A window opening in two leaves from top to bottom, such as well call a French window. Ovid. Pont. iii. 3. 5.
3. A loop hole in the walls of a fortress, from which missiles were discharged. (Caes. B. C. ii. 9.) The illustration (Fenestra/3.1), which presents a view of the Porta asinaria at Rome, constructed by Honorius, shows several of these apertures. The low-roofed building in front is a modern structure.
4. A hole pierced in the lobe of the ear for the purpose of receiving the ring of a pendant or ear-ring. (Juv. i. 104.) Many statues have been discovered with holes bored in the marble, into which real ear-rings were inserted; of which the annexed engraving (Fenestra/4.1), from a bust found at Herculaneum affords an example. The holes in the ears still remain, and the pupil of the eye is also hollowed to receive an artificial one.
* Fenestra/1.1
* Fenestra/3.1
* Fenestra/4.1
# Illustrated Companion to the Latin Dictionary/Fenestrula

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.
FENES'TRULA. Same as FENESTELLA. Apul. Met. ix. p. 208.
# Illustrated Companion to the Latin Dictionary/Ferculum

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.
FER'CULUM. In a general sense, that on which anything is borne; a contracted form for FERICULUM; especially a tray, on which a number of dishes were brought up at once from the kitchen into the eating room (Pet. Sat. 36. 2. Id. 39. 1. Suet. Aug. 74.); whence the same word frequently implies the dishes displayed upon it, constituting what we term a course or remove. Hor. Sat. ii. 6. 104. Plin. H. N. xxxiii. 47. Juv. i. 94.
2. A sort of portable platform borne by a number of men upon their shoulders, in solemn processions and other pageants, upon which any object of attraction was placed in order that it might be exposed to the general gaze from an elevated position; as, for example, the images of the gods at the Circensian procession (Suet. Jul. 76. Compare Cic. Off. i. 36.); the spoils of conquered nations at a triumph (Suet. Jul. 37.); and even the captives themselves, when of sufficient consequence, were subjected to this cruel exposure. (Senec. Herc. Oet. 110.) The illustration (Ferculum/2.1), from a bas-relief on the Arch of Titus, represents eight Roman soldiers at the triumph of that emperor, after the conquest of Jerusalem, carrying the spoils of the temple, the "table of gold" (1 Kings, vii. 48.) and trumpets on a ferculum; another bas-relief on the same arch represents a group transporting the golden candlestick in the same manner; a frieze shows a statue of the River Jordan personified, similarly transported; and a sarcophagus of the Pio-Clementine Museum affords an example of three captives, two males and a female, borne aloft upon a ferculum of the same description, by six supporters.
# Euclidean plan/Proper isometry/Rotation/Fact/Proof

Let $(x,y)$ and $(u,v)$ be the images of the standard vectors $(1,0)$ and $(0,1)$. An isometry preserves the length of a vector; therefore,
    $\Vert {\begin{pmatrix}x\\y\end{pmatrix}}\Vert ={\sqrt {x^{2}+y^{2}}}=1\,.$
Hence, $x$ is a real number between $-1$ and $+1$, and $y=\pm {\sqrt {1-x^{2}}}$, that is, $(x,y)$ is a point on the real unit circle. The unit circle is parametrized by the trigonometric functions, that is, there exists a uniquely determined angle $\theta$, $0\leq \theta <2\pi$, such that
    $(x,y)=(\operatorname {cos} \,\theta ,\operatorname {sin} \,\theta )\,.$
Since an isometry preserves orthogonality, we have
    $\left\langle {\begin{pmatrix}x\\y\end{pmatrix}},{\begin{pmatrix}u\\v\end{pmatrix}}\right\rangle =xu+yv=0\,.$
In case $y=0$, this implies (because of $x=\pm 1$) $u=0$. Then $v=\pm 1$, and, due to the properness assumption, the sign must be that of $x$.
So let $y\neq 0$. Then
    ${\begin{pmatrix}-v\\u\end{pmatrix}}={\frac {u}{y}}{\begin{pmatrix}x\\y\end{pmatrix}}\,.$
Since both vectors have the length $1$, the modulus of the scalar factor $u/y$ is $1$. In case $u=y$, we had $v=-x$ and the determinant were $-1$. Therefore, $u=-y$ and $v=x$, yielding the claim.
# Illustrated Companion to the Latin Dictionary/Ferentarii

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.
FERENTA'RII. A corps of soldiers in the Roman armies, classed amongst the levis armatura, or light-armed troops. (Veg. Mil. i. 20. Non. s. v. p. 554.) They were not armed for close conflict, having no defensive weapons, and only such offensive ones as were intended to be discharged from a distance (quae ferrentur, non quae tenerentur. Non. s. Decuriones, p. 520. Festus, s. v.), whence they are sometimes ranked with the Accensi. They were posted on the wings in the battle array; and were chiefly employed to commence the attack by a discharge of missiles (Sal. Cat. 60. Veg. l. c.); or sometimes, like the Rorarii, to annoy the enemy from between the ranks of the heavy-armed troops. Tac. Ann. xii. 35.
2. Equites ferentarii. A mounted corps of the same description, furnished with javelins for throwing at a distance, instead of the fixed cavalry lance; qui ea modo habebant arma quae ferrentur, ut jaculum. Varro, L. L. vii. 57.
# Illustrated Companion to the Latin Dictionary/Feretrum

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.
FER'ETRUM and FERET'RUM (φέρετρον). Strictly speaking, a Greek word, which the Romans expressed by capulus (Serv. ad Virg. Aen. vi. 222.); the bier, on which a dead body was carried to the grave, or to the funeral pile (Virg. Aen. vi. 222. Ov. Met. iii. 508.), represented by the illustration (Feretrum/1.1), from a marble tomb at Rome.
2. Same as FERCULUM, 2. Sil. Ital. x. 566. Id. xvii. 630.
# Illustrated Companion to the Latin Dictionary/Ferraria

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.
FERRA'RIA, sc. fodina and officina. An iron mine; an iron foundry; and a blacksmith's workshop. Caes. B. G. vii. 22. Liv. xxxiv. 21.
# Illustrated Companion to the Latin Dictionary/Ferrarius

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.
FERRA'RIUS, sc. faber, or absolutely. A smith, blacksmith, armourer, who works in iron, as contradistinguished from other metals. (Plaut. Rud. ii. 6. 47. Inscript. ap. Spon. Miscell. Antiq. p. 66.) The engraving (Ferrarius/1.1) represents Vulcan and his companions at their forge, from a Roman bas-relief.
# Illustrated Companion to the Latin Dictionary/Ferriterium

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.
FERRITER'IUM. A prison where slaves were kept in chains. Plaut. Most. iii. 2. 55. Same as ERGASTULUM.
# Illustrated Companion to the Latin Dictionary/Ferriterus

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.
FERRIT'ERUS. A slave kept in chains. Plaut. Trin. iv. 3. 4. See COMPEDITUS.
# Illustrated Companion to the Latin Dictionary/Ferritribax

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.
FERRIT'RIBAX. (Plaut. Most. ii. 1. 9.) Same as preceding.
# Illustrated Companion to the Latin Dictionary/Ferula

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.
FERULA (νάρθηξ). The fennel; a plant much used by the ancients for the infliction of slight punishments; as a schoolmaster's ferule for chastising boys on the hand (Juv. Sat. i. 15.), or the back (Apul. Met. ix. p. 196.); a riding switch (Ov. A. Am. i. 546.); and a cane for punishing slaves guilty of minor offences. (Hor. Sat. i. 3. 119. Juv. vi. 479.) As an instrument of punishment, the ferula was thus the mildest of those employed by the ancients.
# Illustrated Companion to the Latin Dictionary/Festra

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.
FES'TRA. An antiquated form of writing FENESTRA. (Festus, s. v. Pet. Fragm. xxi. 6.)
# Illustrated Companion to the Latin Dictionary/Festuca

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.
FESTU'CA. A slight rod, with which the lictor of a praetor touched the head of a slave whose owner had restored him to freedom. (Plaut. Mil. iv. i. 15. Id. Pers. v. 174.) Also called VINDICTA.
# Illustrated Companion to the Latin Dictionary/Fetiales

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.
FETIA'LES (φετιάλεις and φητιάλεις). The members of a college of heralds at Rome to whom was entrusted the duty of seeking redress of grievances from hostile states, carrying declarations of war, and assisting in the conclusion of treaties of peace. They carried with them a wand (caduceus), as the emblem of amity, and a spear, as the token of war, which they hurled across the hostile frontier when hostilities were decided on. (Gell. x. 27.) The annexed figure (Fetiales/1.1), from an engraved gem, is supposed to represent a Fetialis about to depart upon a hostile mission from the columna bellica, on which the figure of Minerva is seen in the act of discharging a spear, as above described.
# Illustrated Companion to the Latin Dictionary/Fictile

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.
FIC'TILE (κέραμον). A general name given to any thing made of earthenware or potter's clay; including vessels, moulds, or casts in terra-cotta, bricks, tiles, &c.
# Illustrated Companion to the Latin Dictionary/Fictor

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.
FICTOR (πλάστης). A general term for any artist who models in clay, wax, or any plastic material, as contradistinguished from one who works in bronze, marble, wood, ivory, or other solid substances. (Cic. Fragm. ap. Lactant. ii. 8. Plin. Ep. i. 10.) The annexed figure (Fictor/1.1), from a bas-relief of the Villa Albani, represents an artist of this description, as is manifest from the small wooden stick held in the left hand, which artists still universally make use of to form their models in clay; the very fine or delicate contours were also finished with the fingers and nails, which gave rise to the expression ad unguem factus homo (Hor. Sat. i. 5. 32.), meaning a finished gentleman.
2. A sort of confectioner, or artiste, who executed models in pastry or wax of different animals required for sacrifice in certain religious rites, but which could not be themselves procured for the purpose. Ennius ap. Varro, L. L. vii. 4. Serv. ad Virg. Aen. ii. 116.
# Illustrated Companion to the Latin Dictionary/Fidelia

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.
FIDE'LIA. A sort of vessel, jar, or pot made of earthenware, or glass (Columell. xii. 38. 1.), the distinctive properties of which are not known; further than that it was employed for holding cement (Cic. Fam. vii. 29.), as well as various other things. Plaut. Aul. iv. 2. 15. Pers. Sat. v. 183. Columell. xii. 10. 4.
# Illustrated Companion to the Latin Dictionary/Fides

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.
FIDES or FIDIS. Apparently from the Greek σφίδη, cat-gut; whence used as a general term for stringed instrument, such as the lyra, chelys, cithara. Varro, R. R. ii. 5. 12. Ov. Fast. v. 104.
# Illustrated Companion to the Latin Dictionary/Fidicen

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.
FID'ICEN. A general term for a male performer on any stringed instrument. Cic. Fam. ix. 22.
# Illustrated Companion to the Latin Dictionary/Fidicina

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.
FIDIC'INA. A general term for a female performer on any stringed instrument. Ter. Phorm. i. 2. 59.
# Illustrated Companion to the Latin Dictionary/Fidicula

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.
FIDIC'ULA. Diminutive of FIDIS. A small or thin musical string. Cic. N. D. ii. 8.
2. Mostly in the plural, FIDICULAE; a contrivance for torturing slaves, consisting of a number of thin cords; but the exact nature of the apparatus, as well as the manner in which it was applied, is involed in uncertainty. Suet. Cal. 33. Seneca, Ira, iii. 3. and 19.