Misplaced Pages

#469530

98-595: Only very specific elements may be offered at the Divine Liturgy : The bread used for the Liturgy is referred to as prosphora . A prosphoron is a round loaf of leavened bread baked in two layers to represent the two natures of Christ. It has a square seal on the top side which has inscribed on it a cross and the Greek letters IC (an abbreviation in Greek for "Jesus") XC ("Christ") and NIKA ("Conquers"). The portion of

196-403: A 3 {\displaystyle a{\sqrt {3}}} . Both formulas can be determined by using Pythagorean theorem . The surface area of a cube A {\displaystyle A} is six times the area of a square: A = 6 a 2 . {\displaystyle A=6a^{2}.} The volume of a cuboid is the product of its length, width, and height. Because all

294-450: A {\displaystyle 2a} is the locus of all points ( x , y , z ) {\displaystyle (x,y,z)} such that max { | x − x 0 | , | y − y 0 | , | z − z 0 | } = a . {\displaystyle \max\{|x-x_{0}|,|y-y_{0}|,|z-z_{0}|\}=a.} The cube

392-442: A compass and straightedge solely. Ancient mathematicians could not solve this old problem until French mathematician Pierre Wantzel in 1837 proved it was impossible. With edge length a {\displaystyle a} , the inscribed sphere of a cube is the sphere tangent to the faces of a cube at their centroids, with radius 1 2 a {\textstyle {\frac {1}{2}}a} . The midsphere of

490-406: A rhombohedron , with congruent edges, and a rectangular cuboid , with right angles between pairs of intersecting faces and pairs of intersecting edges. It is an example of many classes of polyhedra: Platonic solid , regular polyhedron , parallelohedron , zonohedron , and plesiohedron . The dual polyhedron of a cube is the regular octahedron . The cube is the three-dimensional hypercube ,

588-674: A confession of faith. The partaking of the Eucharist follows, first the Body of Christ given to the celebrants, to the deacons and to the faithful who approach the sanctuary without shoes and then the Blood of Christ in the same order. Psalm 150 is sung in the meantime. The distribution of the Eucharist ends with a blessing with the Paten . The dismissal rites include The Prayer of Laying the Hands and

686-404: A cube has four vertices, each of which connects with three congruent lines. These edges form square faces, making the dihedral angle of a cube between every two adjacent squares being the interior angle of a square, 90°. Hence, the cube has six faces, twelve edges, and eight vertices. Because of such properties, it is categorized as one of the five Platonic solids , a polyhedron in which all

784-445: A cube is the sphere tangent to the edges of a cube, with radius 1 2 a {\textstyle {\frac {1}{\sqrt {2}}}a} . The circumscribed sphere of a cube is the sphere tangent to the vertices of a cube, with radius 3 2 a {\textstyle {\frac {\sqrt {3}}{2}}a} . For a cube whose circumscribed sphere has radius R {\displaystyle R} , and for

882-475: A family of polytopes also including the two-dimensional square and four-dimensional tesseract . A cube with unit side length is the canonical unit of volume in three-dimensional space, relative to which other solid objects are measured. The cube can be represented in many ways, one of which is the graph known as the cubical graph . It can be constructed by using the Cartesian product of graphs . The cube

980-488: A gap. The cube can be represented as the cell , and examples of a honeycomb are cubic honeycomb , order-5 cubic honeycomb , order-6 cubic honeycomb , and order-7 cubic honeycomb . The cube can be constructed with six square pyramids , tiling space by attaching their apices. Polycube is a polyhedron in which the faces of many cubes are attached. Analogously, it can be interpreted as the polyominoes in three-dimensional space. When four cubes are stacked vertically, and

1078-783: A given point in its three-dimensional space with distances d i {\displaystyle d_{i}} from the cube's eight vertices, it is: 1 8 ∑ i = 1 8 d i 4 + 16 R 4 9 = ( 1 8 ∑ i = 1 8 d i 2 + 2 R 2 3 ) 2 . {\displaystyle {\frac {1}{8}}\sum _{i=1}^{8}d_{i}^{4}+{\frac {16R^{4}}{9}}=\left({\frac {1}{8}}\sum _{i=1}^{8}d_{i}^{2}+{\frac {2R^{2}}{3}}\right)^{2}.} The cube has octahedral symmetry O h {\displaystyle \mathrm {O} _{\mathrm {h} }} . It

SECTION 10

#1732765033470

1176-602: A line below the Lamb and the particles for the Theotokos and saints. Only Orthodox Christians may be commemorated on the diskos at the Proskomedia. From the prosphoron of the departed the priest takes a larger particle as a general memorial of the departed hierarchs , rulers and the founders of the local church or monastery. He then takes out smaller particles in commemoration of departed Orthodox Christians. He commemorates

1274-419: A little water with the wine that is poured in the chalice and presents it to the priest for him to bless. The deacon then pours the wine and water into the chalice, as the priest says, "Blessed be the union of Thy holy things, now and ever, and unto the ages of ages. Amen." Next the priest takes up the second prosphoron, blesses it with the spear, and cuts a large, triangular particle from it, which he places on

1372-417: A part of the hypercube graph, it is also an example of a unit distance graph . Like other graphs of cuboids, the cubical graph is also classified as a prism graph . An object illuminated by parallel rays of light casts a shadow on a plane perpendicular to those rays, called an orthogonal projection . A polyhedron is considered equiprojective if, for some position of the light, its orthogonal projection

1470-456: A plane by the process known as polar reciprocation . One property of dual polyhedrons generally is that the polyhedron and its dual share their three-dimensional symmetry point group . In this case, the dual polyhedron of a cube is the regular octahedron , and both of these polyhedron has the same symmetry, the octahedral symmetry. The cube is face-transitive , meaning its two squares are alike and can be mapped by rotation and reflection. It

1568-1013: A polyhedron by connecting along the edges of those polygons. Eleven nets for the cube are shown here. In analytic geometry , a cube may be constructed using the Cartesian coordinate systems . For a cube centered at the origin, with edges parallel to the axes and with an edge length of 2, the Cartesian coordinates of the vertices are ( ± 1 , ± 1 , ± 1 ) {\displaystyle (\pm 1,\pm 1,\pm 1)} . Its interior consists of all points ( x 0 , x 1 , x 2 ) {\displaystyle (x_{0},x_{1},x_{2})} with − 1 < x i < 1 {\displaystyle -1<x_{i}<1} for all i {\displaystyle i} . A cube's surface with center ( x 0 , y 0 , z 0 ) {\displaystyle (x_{0},y_{0},z_{0})} and edge length of 2

1666-802: A single anaphora (the Athanasius -Anaphora) for the liturgy: Holy Patarag or in Western Armenian Holy Badarak, meaning 'sacrifice'. This is in distinction from the other liturgies of the Oriental Orthodox Churches (Coptic, West Syrian, Ethiopic) which have retained multiple anaphora. This means that the text of the Patarag can be contained in a single, unified liturgical book, the Պատարագամատոյց ( Pataragamatooyts , Western Armenian Badarakamadooyts , meaning 'the offering of sacrifice'). This book contains all of

1764-445: A space—called honeycomb —in which each face of any of its copies is attached to a like face of another copy. There are five kinds of parallelohedra, one of which is the cuboid. Every three-dimensional parallelohedron is zonohedron , a centrally symmetric polyhedron whose faces are centrally symmetric polygons , An elementary way to construct a cube is using its net , an arrangement of edge-joining polygons constructing

1862-731: A veil. In the Liturgy of the Catechumens the readings from the New Testament are proclaimed. This portion was in ancient times the beginning of the liturgy, and the only part which could be attended by the catechumens . It is roughly equivalent to the Liturgy of the Word in the Western Rites. It begins with a Penitential Rite in which first the priest prays inaudibly to Christ for the forgiveness of sins ( The Absolution to

1960-412: Is Hanner polytope , because it can be constructed by using Cartesian product of three line segments. Its dual polyhedron, the regular octahedron, is constructed by direct sum of three line segments. According to Steinitz's theorem , the graph can be represented as the skeleton of a polyhedron; roughly speaking, a framework of a polyhedron. Such a graph has two properties. It is planar , meaning

2058-452: Is vertex-transitive , meaning all of its vertices are equivalent and can be mapped isometrically under its symmetry. It is also edge-transitive , meaning the same kind of faces surround each of its vertices in the same or reverse order, all two adjacent faces have the same dihedral angle . Therefore, the cube is regular polyhedron because it requires those properties. The cube is a special case among every cuboids . As mentioned above,

SECTION 20

#1732765033470

2156-407: Is a regular polygon. The cube is equiprojective because, if the light is parallel to one of the four lines joining a vertex to the opposite vertex, its projection is a regular hexagon . Conventionally, the cube is 6-equiprojective. The cube can be represented as configuration matrix . A configuration matrix is a matrix in which the rows and columns correspond to the elements of a polyhedron as in

2254-479: Is a set of polyhedrons known since antiquity. It was named after Plato in his Timaeus dialogue, who attributed these solids with nature. One of them, the cube, represented the classical element of earth because of its stability. Euclid 's Elements defined the Platonic solids, including the cube, and using these solids with the problem involving to find the ratio of the circumscribed sphere's diameter to

2352-886: Is called "Liturgy of the Faithful". Eastern Christians believe that the Eucharist is the central part of the service in which they participate, as they believe the bread and wine truly become the real Body and Blood of Christ , and that by partaking of it they jointly become the Body of Christ (that is, the Church ). Each Liturgy has its differences from others, but most are very similar to each other with adaptations based on tradition, purpose, culture and theology. Autocephaly recognized by some autocephalous Churches de jure : Autocephaly and canonicity recognized by Constantinople and 3 other autocephalous Churches: Spiritual independence recognized by Georgian Orthodox Church: Semi-Autonomous: Three Divine Liturgies are in common use in

2450-474: Is composed of reflection symmetry , a symmetry by cutting into two halves by a plane. There are nine reflection symmetries: the five are cut the cube from the midpoints of its edges, and the four are cut diagonally. It is also composed of rotational symmetry , a symmetry by rotating it around the axis, from which the appearance is interchangeable. It has octahedral rotation symmetry O {\displaystyle \mathrm {O} } : three axes pass through

2548-528: Is fixed, although the specific readings and hymns vary with season and feast. The Divine Liturgy consists of three interrelated parts; when not in conjunction with vespers, the liturgies of John Chrysostom and Basil the Great are structured thus: A typical celebration of the Byzantine Liturgy consists of: This part of the Liturgy is private, performed only by the priest and deacon. It symbolizes

2646-535: Is named among the saints. The term Liturgy of Saint Basil may refer also to the whole Eucharistic Liturgy which in the Coptic Church has the following structure: Offertory (or Prothesis ) is the part of the liturgy in which the Sacramental bread ( qorban ) and wine ( abarkah ) are chosen and placed on the altar. All these rites are Middle-ages developments. It begins with the dressing of

2744-667: Is present, he, rather than the priest, may bless their vestments. After vesting, the priest and deacon wash their hands, saying the Prayer of the Washing of Hands (Psalm 26:6-12) They then go to the Prothesis (Table of Oblation) where the Gifts are to be prepared. If there are several priests concelebrating, usually only one—traditionally, the most junior— celebrates the Proskomedia. Others may assist in taking out particles for

2842-468: Is the core of the Liturgy, where are placed the proper Eucharistic rites. It begins with the prayer of the Veil, in which the priest offers the liturgical sacrifice to God. The Long Litanies follows, where all pray for the peace, for the ecclesiastic hierarchy and for the congregation. The Nicean Creed is proclaimed, the priest washes his hands three times and sprinkles water on the congregation reciting

2940-522: Is the largest cube that can pass through a hole cut into the unit cube, despite having sides approximately 6% longer. A polyhedron that can pass through a copy of itself of the same size or smaller is said to have the Rupert property . A geometric problem of doubling the cube —alternatively known as the Delian problem —requires the construction of a cube with a volume twice the original by using

3038-579: Is the usual name used in most Eastern Christian rites for the Eucharistic service. The Greek Catholic and Orthodox Churches see the Divine Liturgy as transcending time and the world. All believers are seen as united in worship in the Kingdom of God along with the departed saints and the angels of heaven. Everything in the liturgy is seen as symbolic, but not merely so, for it makes present

Liturgy of Preparation - Misplaced Pages Continue

3136-525: Is usually used during the feasts of the Church but not exclusively. In addition the clergy performing the liturgy can combine extracts of the Liturgies of St. Cyril and St. Gregory to the more frequently used St. Basil at the discretion of the priest or bishop. The main liturgy used by the Coptic Church is known as Liturgy of Saint Basil. The term Liturgies of Saint Basil in a Coptic context means not only

3234-769: The Byzantine Rite apply it to their Eucharistic services but, while in English the same word (as also the word "Mass") is at times used to speak of the corresponding services of the Oriental Orthodox Churches , the normal names used in those Churches refers either to the aspect of offering/sacrifice ( Qurobo Alohoyo in the Syriac Orthodox Church ), Badarak in the Armenian Apostolic Church , Prosfora in

3332-540: The Byzantine Rite : As well as these, there are two others that are used locally and rarely, the Liturgy of St. James and the Liturgy of Saint Mark . As numbers in a diocese increased dramatically, the bishop who presides over the Eucharistic assembly appointed presbyters to act as celebrants in the local communities (the parishes). Still, the Church is understood in Eastern Orthodoxy in terms not of

3430-602: The Coptic Orthodox Church ) or of sanctifying ( Keddase in the Ethiopian Orthodox Tewahedo Church ). The Oriental Orthodox Churches own a richness of different liturgies, which are named after the anaphora included. At present, the Coptic Orthodox Church and Coptic Catholic Church have three Liturgies: The Liturgy of St. Basil is celebrated on most Sundays and contains the shortest anaphora. The Liturgy of St. Gregory

3528-508: The Father for the forgiveness of sins ( The Absolution to the Father ). The Elevation is similar to that in the Byzantine Rite , with the celebrant who raises the portion of the Lamb engraved with a cross (the ispadikon ) crying: " The holy things for the holy ones ". The priest makes a second consignation and puts gently the ispakidon in the chalice (the commixture), then he recites aloud

3626-503: The Kyrie eleison , the priest checks the wine and chooses among the bread one loaf which will be consecrated (the Lamb ). The Lamb is cleaned with a napkin and blessed with the priest's thumb wet with wine. Afterwards the priest takes the Lamb in procession around the altar and the deacon follows with the wine and a candle. At the altar, the priest, with appropriate prayers, blesses the Lamb and

3724-451: The Psalms . The deacon brings his vestments to the priest to bless, kisses the priest's hand, and likewise for each vestment kisses the cross on it and dons it, but only for the sticharion recites a verse, the same verse for it as does the priest. Each subdeacon , reader , and server vests in the same manner as a deacon, except for not reciting anything. If a bishop who is not celebrating

3822-776: The Second Vatican Council (1962–1965) by Pope Paul VI in 1969 and revised by Pope John Paul II in 2002, largely replacing the usage of the Tridentine Mass form originally promulgated in 1570 in accordance with decrees of the Council of Trent in its closing session (1545–46). The 1962 form of the Tridentine Mass, in the Latin language alone, may be employed where authorized by the Holy See or, in

3920-680: The Trisagion is sung three times, each time with a different reference to the Incarnation , Passion , Resurrection , thus addressing the Trisagion to Christ only. After the Trisagion follows a litany , the recital of a Psalm and the singing of the Alleluia , and finally the proclamation of the Gospel from the doors of the sanctuary. The sermon may follow. The Liturgy of the Faithful

4018-412: The regular polygons are congruent and the same number of faces meet at each vertex. Given a cube with edge length a {\displaystyle a} . The face diagonal of a cube is the diagonal of a square a 2 {\displaystyle a{\sqrt {2}}} , and the space diagonal of a cube is a line connecting two vertices that is not in the same face, formulated as

Liturgy of Preparation - Misplaced Pages Continue

4116-517: The thief , and on the Throne with the Father and the Spirit , wast thou, O Christ, who art everywhere present and fillest all things. When a bishop is serving the divine liturgy, one of the priests and the deacons and lower clergy vest and the Liturgy of Preparation is performed as normal with a few omissions which are later performed by the bishop: the other clergy who are serving are not commemorated,

4214-727: The Annunciation's case, during Easter Week)), Maundy Thursday and Holy Saturday ) after the Old Testament readings the Little Litany is said and the liturgy continues from this point: In the early Church, only baptized members who could receive Holy Communion were allowed to attend this portion of the Liturgy. In common contemporary practice, with very few local exceptions (e.g., Mount Athos ), all may stay. However, in some places, catechumens are formally dismissed for further study. Almost all texts are chanted throughout

4312-520: The Bishop who ordained him (if he is still among the living), the clergy who are concelebrating with him, and any living Orthodox Christian whom he wishes. Churches and monasteries often have diptychs (memorial books) of the living and departed who should be commemorated at every Liturgy. Among the Slavic peoples, it is customary for the laity to offer small prosphora in commemoration of those living and

4410-634: The Bohairic text: the manuscript, incomplete in its first part, begins with the Post Sanctus , and is followed by a terse Institution narrative , by a pithy Anamnesis which simply lists the themes and ends with the oblation . The next Epiclesis consists only of the prayer to the Holy Spirit to come and manifest the gifts, without any explicit request to change the gifts in the Body and Blood of Christ. The intercessions are shorter and only Mary

4508-622: The Divine Liturgy, not only hymns but litanies, prayers, creed confession and even readings from the Bible, depending on tradition. In ancient rubrics, and contemporary Greek practice, the sermon, Nicene Creed and the Lord's Prayer are spoken/read, rather than chanted. Slavic traditions chant or sing everything except the sermon. "Divine Liturgy" is the normal word for church service in Oriental Orthodoxy. In their own languages, followers of

4606-628: The Living. He takes out a larger particle in commemoration of the Patriarch (or Synod of Bishops), and a second larger particle in commemoration of the Ruler (in former times, this would have been the Emperor, but nowadays it reflects the government of the local nation in which the church is located). He then takes out smaller particles in commemoration of others among the living. He must always commemorate

4704-482: The Patarag. However, the celebration of a short memorial service for one or more departed persons (Հոգեհանգիստ hogehangist , Western Armenian hokehankist , meaning 'rest of the spirit') is quite prevalent in parishes and replaces the reading of the last Gospel. The following description of the celebration of Mass, usually in the local vernacular language, is limited to the form of the Roman Rite promulgated after

4802-528: The Prayer of Reconciliation which is a prayer of worthiness for all who attend the liturgy. Next is the Kiss of peace during which the faithful sing the Aspasmos Adam ( Rejoice O Mary ) hymn. The Anaphora is conducted. After the anaphora takes place the consignation, i.e. the moistening of the Lamb with some drops of the consecrated Wine, which is shown for the worship of the faithful. The Fraction of

4900-559: The Son ) and then all the participants kneel in front of the altar and the celebrant, or the bishop if present, recites a prayer of absolution ( The Absolution to the Ministers ). The reading from the Pauline epistles is preceded by the offering of incense at the four sides of the altar, at the iconostasis , at the book of the Gospel and at the faithfuls in the nave ; in the meantime

4998-579: The Sunday before, the priest must cut out extra Lambs for each Presanctified Liturgy that there will be during that week. During Bright Week (The week following Easter Sunday) most of the services are quite radically different than during the rest of the year. However, at the Liturgy of Preparation, only the Entrance Prayers change; everything else remains the same. The various Oriental Orthodox Churches also have Liturgies of Preparation before

SECTION 50

#1732765033470

5096-570: The Theotokos are sometimes used. The wine used must be red grape wine, and it must be fermented. Orthodox tend to favor altar wine that is somewhat sweet, though this is not a requirement. These elements are referred to collectively as the "Gifts", both before and after the Consecration. The Priest's Service Book states that, before celebrating the Divine Liturgy, the priest must be reconciled to all men, keep his heart from evil thoughts, and be fasting since midnight. The same rules apply to

5194-534: The bishop and kissing the bishop's right shoulder says his own name, by which the bishop takes out a particle commemorating him. Finally, the bishop censes the offerings. During Great Lent it is not permitted to celebrate the Divine Liturgy on weekdays. However, on Wednesdays and Fridays the faithful may receive Holy Communion from the reserved Mysteries (Sacrament) at the Liturgy of the Presanctified Gifts . In order to provide for these services, on

5292-406: The bishop who ordained him (if he is departed) and any of the departed whom he will, as well as the names in the diptychs and those presented by the faithful. All of the particles for the departed are placed in a line below the particles for the living. Before the conclusion, any concelebrating priests who would like to make their own commemorations of the living and the departed may do so. For

5390-526: The church in Jerusalem. A special prayer of repentance is sung by the clergy on the morning of Palm Sunday (Armenian: Ծաղկազարդ tsaghkazard , Western Armenian dzaghgazard ), after which the curtain is opened for the first time since the last Sunday before the Great Fast. One element which almost certainly derives from the influence of Western liturgy is the reading of a last Gospel at the conclusion of

5488-411: The circumstances indicated in the 2021 document Traditionis custodes , by the diocesan bishop. Cube In geometry , a cube or regular hexahedron is a three-dimensional solid object bounded by six congruent square faces, a type of polyhedron . It has twelve congruent edges and eight vertices. It is a type of parallelepiped , with pairs of parallel opposite faces, and more specifically

5586-401: The commencement of the public portion of the Divine Liturgy. `Some of these are very simple, and some are more complex. They all involve the entry of the clergy, vesting and preparing the Gifts of bread and wine, accompanied by appropriate prayers. Divine Liturgy Divine Liturgy ( ‹See Tfd› Greek : Θεία Λειτουργία , translit.   Theia Leitourgia ) or Holy Liturgy

5684-414: The concluding Prayer of Offering is not said, and the offerings are not censed. When the liturgy neither immediately follows matins nor is in conjunction with vespers, the reading of the hours generally does not commence until after the arrival of the bishop. When it is time, the bishop enters formally into the church and the deacons recite the Entrance Prayers and he is then vested by the subdeacons while

5782-529: The consecrated Lamb ensues, during which the priest says a prayer which varies according to the Coptic calendar . All of the congregation stands and prays with open hands the Lord's Prayer . To be prepared for partaking of the Eucharist, the faithful bow while the celebrant says in low voice the prayer of submission, then the priest and the participants offer each other a wish of peace and the priest inaudibly prays to

5880-780: The consecration of churches, and the first liturgies offered by newly ordained priests. Due to the long isolation of the Saint Thomas Christians the rite of the Syro-Malankara Catholic Church shows some differences, so that this rite is called the Malankara Rite . The Armenian Apostolic Church and the Armenian Catholic Church have at present a single liturgical structure, called the Armenian Rite , with

5978-455: The cross over it with the liturgical spear . Then, cutting on all four sides of the square seal on the prosphoron, he removes a cube (the Lamb), taking from both layers of the loaf, and places it in the center of the diskos . He then cuts the underside of the Lamb, making a cross, then turns the Lamb right side up and pierces it with the spear, saying the words from the Gospel ( John 19:34–35 ). (See Lamb for more details). The deacon mingles

SECTION 60

#1732765033470

6076-462: The cube can be represented as the rectangular cuboid with edges equal in length and all of its faces are all squares. The cube may be considered as the parallelepiped in which all of its edges are equal edges. The cube is a plesiohedron , a special kind of space-filling polyhedron that can be defined as the Voronoi cell of a symmetric Delone set . The plesiohedra include the parallelohedrons , which can be translated without rotating to fill

6174-417: The cube's opposite faces centroid, six through the cube's opposite edges midpoints, and four through the cube's opposite vertices; each of these axes is respectively four-fold rotational symmetry (0°, 90°, 180°, and 270°), two-fold rotational symmetry (0° and 180°), and three-fold rotational symmetry (0°, 120°, and 240°). The dual polyhedron can be obtained from each of the polyhedron's vertices tangent to

6272-410: The cube, twelve vertices and eight edges. The cubical graph is a special case of hypercube graph or n {\displaystyle n} - cube—denoted as Q n {\displaystyle Q_{n}} —because it can be constructed by using the operation known as the Cartesian product of graphs . To put it in a plain, its construction involves two graphs connecting

6370-416: The deacon and censes the covered Gifts. He then says the concluding Prayer of Offering (unless a bishop is celebrating; see below). Afterwards, the deacon performs a full censing of the prothesis, the holy table, the sanctuary, the entire church and the people while he recites the following hymn and Psalm 50 quietly to himself: In the Tomb with the body, and in Hades with the soul, in Paradise with

6468-430: The deacon. The beginning of the Liturgy of Preparation should be timed so that it is concluded slightly before the Reader finishes reading the Third Hour and Sixth Hour . The priests and deacons celebrating the liturgy stand together in front of the holy doors of the iconostasis , venerate the icons , and say special entrance prayers before they enter into the altar. At the end of these prayers, they bow to

6566-480: The deacons read the Vesting Prayers. Then the Reader begins the Little Hours or vespers commences or matins conclude, as the case may be. During the great litany the bishop himself recites the Prayer of Offering omitted earlier from the usual order of the prothesis. Just before the Great Entrance , the bishop commemorates those whom he wishes, taking out particles from a special prosphoron that has been prepared for him. Then each priest, deacon, and server approaches

6664-415: The departed whom they would like to have prayed for during the Liturgy. These often are smaller than the five prosphora used by the priest. They hand these to the priest together with their list of names, and he takes particles out (living from the top of the loaf, departed from the bottom) and place them on the diskos. The loaves are returned to the faithful. All of the particles for the living are placed in

6762-454: The diskos next to the Lamb in commemoration of the Theotokos. This loaf (if it is a separate loaf) is sometimes sealed with an icon of the Mother of God, or with her monogram. Next, the priest takes up the prosphoron of the Nine Ranks. From this loaf are taken smaller triangular particles in commemoration of the various ranks of saints . There are some differences between the Greek and the Slavic texts as to which particular saints are named, but

6860-412: The diskos, saying: "And the star came and stood over the place where the young child was." He then holds each of the smaller veils over the censer and places them on the discos and the chalice, respectively, saying appropriate prayers for each. Then he takes the larger veil, called the Aër , wraps it around the censer and then covers the chalice and diskos together. Finally, he takes the censer from

6958-442: The edge length. Following its attribution with nature by Plato, Johannes Kepler in his Harmonices Mundi sketched each of the Platonic solids, one of them is a cube in which Kepler decorated a tree on it. In his Mysterium Cosmographicum , Kepler also proposed the Solar System by using the Platonic solids setting into another one and separating them with six spheres resembling the six planets. The ordered solids started from

7056-456: The edges of a cube are equal in length, it is: V = a 3 . {\displaystyle V=a^{3}.} One special case is the unit cube , so-named for measuring a single unit of length along each edge. It follows that each face is a unit square and that the entire figure has a volume of 1 cubic unit. Prince Rupert's cube , named after Prince Rupert of the Rhine ,

7154-405: The edges of a graph are connected to every vertex without crossing other edges. It is also a 3-connected graph , meaning that, whenever a graph with more than three vertices, and two of the vertices are removed, the edges remain connected. The skeleton of a cube can be represented as the graph, and it is called the cubical graph , a Platonic graph . It has the same number of vertices and edges as

7252-552: The elevated altar area (Armenian խորան khoran ) is never opened – even for the reading of the Gospel, certain movable parts of the liturgy are omitted, the parts of the liturgy sung by the choir are said or chanted simply without adornment, there is no general confession, and there is no distribution of Communion to the faithful. This practice of fasting from the Communion bread in preparation for Easter may reflect an ancient custom of

7350-757: The faithful sing a hymn to Mary and a hymn of intercession. The Pauline epistle is followed by a reading from the Catholic epistles and by one from the Acts of the Apostles . Another offering of incense is conduced (the Praxis Incense ), similar to the Pauline incense except that only the first row of the faithful is incensed. A reading from the Coptic Synaxarium can follow. After these readings,

7448-723: The final blessing. The Syriac Orthodox Church , the Syriac Catholic Church , the Syriac Maronite Church of Antioch and the Syro-Malankara Catholic Church of the West Syriac Rite which is developed from the Antiochene Rite use a version of the Divine Liturgy of Saint James which differs substantially from its Byzantine Rite counterpart, most notably in being substantially shorter (it can be completed in under two hours, whereas

7546-492: The hidden years of Christ's earthly life. This is the public part of the Liturgy, in which both catechumens and baptized faithful would be in the nave: When the liturgy is at the usual time (following matins or the sixth hour), this order is followed: But when the liturgy is joined to vespers (on Christmas Eve , Theophany Eve , the feast of the Annunciation (except when these days fall on Saturday or Sunday (or, in

7644-480: The historic form of the Byzantine Rite liturgy prior to the revisions of St. Basil and St. John Chrysostom took more than four hours), and in that it can be used with more than eighty different anaphoras; the most commonly used are those of Mar Bar Salibi (which is the shortest), and that of St. James, which resembles that of the Byzantine Rite liturgy, and is mandated on certain occasions, such as major feasts,

7742-464: The innermost to the outermost: regular octahedron , regular icosahedron , regular dodecahedron , regular tetrahedron , and cube. The cube can appear in the construction of a polyhedron, and some of its types can be derived differently in the following: The honeycomb is the space-filling or tessellation in three-dimensional space, meaning it is an object in which the construction begins by attaching any polyhedrons onto their faces without leaving

7840-524: The intent is that all of the saints are included. Saint John the Forerunner and the Patron Saint of the church or monastery are always named. The number nine was chosen because that is the traditional number of the ranks of angels . These nine particles are placed to the left of the Lamb (i.e., to the priest's right, as he looks down on the diskos). Then the priest takes up the prosphoron for

7938-539: The last commemoration, the priest takes out a particle for himself, saying: "Remember, O Lord, mine unworthy self, and pardon me every transgression, whether voluntary or involuntary." The deacon places incense in the censer and holds it up for the priest to bless. The priest blesses the incense saying the Prayer of the Censer. Next, the priest takes the Asterisk (star cover), holds it over the censer and then places it on

8036-614: The latter and has its own peculiarities: its text is more brief, with less Scriptural and allusive enhancements, and it lacks well-defined Trinitarian references, which are typical of other versions and reflect the theology of the First Council of Constantinople of 381. The structure of the Bohairic Coptic version used today in the Coptic Church can be summarized as follows: The 7th-century Sahidic Coptic version found in 1960 shows an earlier and more sober form of

8134-467: The liturgy. Then comes the prayer of covering said inaudibly by the priest, which has the form of an epiclesis asking God to show his face on the gifts, and to change them in order that the bread and wine may became the Body and Blood of Christ . This text might come from an ancient anaphora or simply be a later High Middle Ages creation. The paten and the ark with the chalice inside are here covered with

8232-403: The living and the dead. In the Greek traditions (Constantinople, Antioch, etc.) all particles are frequently taken from one large prosphoron which is stamped with a seal that serves as a template, but in the Slavic traditions there are several (usually five) prosphora, from which particles are taken as described below. The priest takes a prosphoron and blesses it three times, making the sign of

8330-421: The loaf that is cut out along this seal is the Lamb (Host), from which all are communicated, and therefore must be proportionately large for the number of communicants. Prosphora must be made using only the finest wheat flour, water, salt, and yeast. It should be freshly baked and without blemish. The Greeks use one large loaf for the Liturgy of Preparation, with a large round seal on it inscribed not only with

8428-525: The middle row indicates that there are two vertices in (i.e., at the extremes of) each edge, denoted as 2; the middle column of the first row indicates that three edges meet at each vertex, denoted as 3. The following matrix is: [ 8 3 3 2 12 2 4 4 6 ] {\displaystyle {\begin{bmatrix}{\begin{matrix}8&3&3\\2&12&2\\4&4&6\end{matrix}}\end{bmatrix}}} The Platonic solid

8526-453: The pair of vertices with an edge to form a new graph. In the case of the cubical graph, it is the product of two Q 2 {\displaystyle Q_{2}} ; roughly speaking, it is a graph resembling a square. In other words, the cubical graph is constructed by connecting each vertex of two squares with an edge. Notationally, the cubical graph can be denoted as Q 3 {\displaystyle Q_{3}} . As

8624-605: The prayers for the Patarag assigned to the bishop (if celebrating as a bishop), the celebrating priest, the deacon(s), and the people, the last typically led by a choir with accompaniment. Before the end of the 10th century there were also other liturgical forms, such as the Anaphora of St. Basil , the Anaphora of St. Gregory the Illuminator and others in use. The elements of the Armenian eucharistic liturgy reflect

8722-399: The presbyter, but the diocesan bishop. When the latter celebrates the liturgy personally, the service is more complex and festive. To demonstrate unity with the greater Orthodox community, the hierarch commemorates the hierarch he is subordinate to or, if he is head of an autocephalous church, he commemorates all his peers, whose names he reads from a diptych . The format of Divine Liturgy

8820-571: The priest with vestments and the preparation of the altar, along with prayers of worthiness for the celebrant. At this point is chanted the appropriate hour of the Canonical hours , followed by the washing of the hands with its prayer of worthiness, and by the proclamation of the Nicean Creed . Then takes place the elaborate rite of the choosing of the Lamb: while the congregation sing 41 times

8918-814: The rich set of influences on Armenian culture. The roots of the liturgy lie in the West Syrian and Byzantine forms, with the influence of the Roman Catholic Mass, the latter having arrived likely during the period of the Fourth Crusade or shortly thereafter. Among the distinctive practices of the Armenian Patarag is the tradition that on the Sundays of the fast before Easter (the Great Fast) the curtain which hangs down in front of

9016-542: The sole anaphora with or without the related prayers, but also the general order of the Alexandrine Rite liturgy. The Egyptian (or Coptic) anaphora of Saint Basil, even if related and using the same Antiochene (or "West Syrian" ) structure, represents a different group from the Byzantine , West Syrian and Armenian grouping of anaphoras of Saint Basil. The Egyptian version does not derive directly from

9114-532: The square seal mentioned above (from which the Lamb is taken), but also markings indicating where the portions for the Theotokos , the Ranks, the Living and Dead are removed (see Proskomedie , below). Those churches which follow Slavic usage use five small loaves, recalling the five loaves from which Christ fed the multitude ( John 6:5–14 ). Normally all are stamped with a small square seal, though special seals for

9212-402: The throne of the bishop who oversees the church, or, if it is a monastery, the abbot , acknowledging the authority of their spiritual superiors, without whose permission they may not celebrate the divine services. Next The priests and deacons venerate the holy table and vest . For each vestment, the priest blesses it, kisses the cross on it, and dons it reciting a Biblical verse, usually from

9310-485: The unseen reality. According to Eastern tradition and belief, the liturgy's roots go back to the adaptation of Jewish liturgy by Early Christians . The first part, termed the "Liturgy of the Catechumens", includes like a synagogue service the reading of scriptures and, in some places, perhaps a sermon/homily. The second half is based on the Last Supper and the first Eucharistic celebrations by Early Christians and it

9408-405: The vertices, edges, and faces. The diagonal of a matrix denotes the number of each element that appears in a polyhedron, whereas the non-diagonal of a matrix denotes the number of the column's elements that occur in or at the row's element. As mentioned above, the cube has eight vertices, twelve edges, and six faces; each element in a matrix's diagonal is denoted as 8, 12, and 6. The first column of

9506-402: The wine, places the Lamb on the Paten and pours wine and a few drops of water in the chalice (the chalice is placed on the altar in a wooden box named ark ). The last part of the offertory resembles an anaphora: after a dialogue, the priest blesses the congregation and proclaims a prayer of thanksgiving, giving thanks to God for his support to us, and asking him for a worthy participation to

9604-515: Was discovered in antiquity. It was associated with the nature of earth by Plato , the founder of Platonic solid. It was used as the part of the Solar System , proposed by Johannes Kepler . It can be derived differently to create more polyhedrons, and it has applications to construct a new polyhedron by attaching others. A cube is a special case of rectangular cuboid in which the edges are equal in length. Like other cuboids, every face of

#469530