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72-406: The vesica piscis is a type of lens , a mathematical shape formed by the intersection of two disks with the same radius, intersecting in such a way that the center of each disk lies on the perimeter of the other. In Latin, " vesica piscis " literally means "bladder of a fish", reflecting the shape's resemblance to the conjoined dual air bladders ( swim bladder ) found in most fish. In Italian,

144-411: A r {\displaystyle 2a_{r}} and 2 a R {\displaystyle 2a_{R}} have areas 2 a r r 2 {\displaystyle 2a_{r}r^{2}} and 2 a R R 2 {\displaystyle 2a_{R}R^{2}} . Their union covers the triangle, the flipped triangle with corner at (x,-y), and twice

216-547: A Freemason to explore Masonry further through other degrees, administered separately from the basic Craft or "Blue Lodge" degrees described here, but generally having a similar structure and meetings. There is much diversity and little consistency in Freemasonry because each Masonic jurisdiction is independent and sets its own rules and procedures while Grand Lodges have limited jurisdiction over their constituent member Lodges, which are ultimately private clubs. The wording of

288-524: A Mason, he is qualified to join various "Concordant bodies" which offer additional degrees. These organisations are usually administered separately from the Grand Lodges who administer the Craft degrees. The extra degrees vary with locality and jurisdiction . In addition to these bodies, there are further organizations outside of the more traditional Rites of Freemasonry, that require an individual to be

360-734: A Master Mason before they can join (such as the Rosicrucian Society of England ). Throughout its history, Freemasonry has received criticism and opposition on religious and political grounds. The Catholic Church, some Protestant denominations, and certain Islamic countries or entities have expressed opposition to or banned membership in Free-Masonry. Opposition to Freemasonry is sometimes rooted in anti-Semitism or conspiracy theories , and Freemasons have historically been persecuted by authoritarian states. The Masonic lodge

432-645: A given country, state or geographical area (termed a jurisdiction ). There is no single overarching governing body that presides over worldwide Freemasonry; connections between different jurisdictions depend solely on mutual recognition. Estimates of the worldwide membership of Freemasonry in the early 21st century ranged from about two million to more than six million. The fraternity is administratively organised into independent Grand Lodges (or sometimes Grand Orients), each of which governs its own Masonic jurisdiction, which consists of subordinate (or constituent ) Lodges. The United Grand Lodge of England remains

504-508: A lecture, which is usually on some aspect of Masonic history or ritual. At the conclusion of the meeting, the Lodge may hold a formal dinner , or festive board , sometimes involving toasting and song. The bulk of Masonic ritual consists of degree ceremonies. Candidates for Freemasonry are progressively initiated into Freemasonry, first in the degree of Entered Apprentice . At some later time, in separate ceremonies, they will be passed to

576-547: A precedent for "shared jurisdiction" between mainstream and Prince Hall Grand Lodges, effectively modifying the traditional interpretation of Exclusive Jurisdiction. By 2024, most U.S. Grand Lodges have recognized their Prince Hall counterparts, establishing a new norm where two Grand Lodges can legitimately operate within the same geographical area, provided they maintain mutual recognition and amity. The evolution of this practice demonstrates how traditional Masonic principles can adapt to accommodate social progress while maintaining

648-450: A sector of one sixth of the circle (60°). The area of the sector is then: 1 6 π r 2 {\displaystyle {\frac {1}{6}}\pi r^{2}} . Since the side of the equilateral triangle has length r , its area is 3 4 r 2 {\displaystyle {\frac {\sqrt {3}}{4}}r^{2}} . The area of the segment is the difference between those two areas: By summing

720-453: A series of approximations to this value, each with the property that no better approximation can be obtained with smaller whole numbers. Archimedes of Syracuse , in his Measurement of a Circle , uses these ratios as upper and lower bounds: The area of the vesica piscis is formed by two equilateral triangles and four equal circular segments . In the drawing, one triangle and one segment appear in blue. One triangle and one segment form

792-453: Is where is the area of a triangle with sides d , r , and R . The two circles overlap if d < r + R {\displaystyle d<r+R} . For sufficiently large d {\displaystyle d} , the coordinate x {\displaystyle x} of the lens centre lies between the coordinates of the two circle centers: [REDACTED] For small d {\displaystyle d}

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864-514: Is 18, but university lodges are given dispensations to initiate undergraduates below that age.) Additionally, most Grand Lodges require a candidate to declare a belief in a Supreme Being (although every candidate must interpret this condition in his own way, as all religious discussion is commonly prohibited). In a few cases, the candidate may be required to be of a specific religion. The form of Freemasonry most common in Scandinavia (known as

936-476: Is Regular and what is Irregular (and the definitions do not necessarily agree between Grand Lodges). Essentially, every Grand Lodge will hold that its landmarks (its requirements, tenets and rituals) are Regular, and judge other Grand Lodges based on those. If the differences are significant, one Grand Lodge may declare the other "Irregular" and withdraw or withhold recognition. The most commonly shared rules for Recognition (based on Regularity) are those given by

1008-464: Is a historically African-American branch of Freemasonry that maintains its own separate Grand Lodge system parallel to the state Grand Lodge system. Together, these two systems - the conservative Grand Lodges and Prince Hall Grand Lodges make up for a total of 97 UGLE recognized Grand Lodges, sharing jurisdictions in the United States. They represent the main bodies of Masonic governance in

1080-690: Is a system of 33 degrees, including the three Blue Lodge degrees administered by a local or national Supreme Council. This system is popular in North America, South America and in Continental Europe . In America, the York Rite , with a similar range, administers three orders of Masonry, namely the Royal Arch , Cryptic Masonry , and Knights Templar . In Britain, separate bodies administer each order. Freemasons are encouraged to join

1152-433: Is an asymmetric lens . The vesica piscis is one form of a symmetric lens, formed by arcs of two circles whose centers each lie on the opposite arc. The arcs meet at angles of 120° at their endpoints. The area of a symmetric lens can be expressed in terms of the radius R and arc lengths θ in radians: The area of an asymmetric lens formed from circles of radii R and r with distance d between their centers

1224-536: Is in amity with the Prince Hall Grand Lodge of Connecticut, the principle of Exclusive Jurisdiction does not apply, and other Grand Lodges may recognise both. Likewise, the five distinct kinds of lodges in Germany have nominally united under one Grand Lodge in order to obtain international recognition. The concept of Exclusive Jurisdiction has been significantly challenged in the United States with

1296-456: Is not allowed. There are many reasons one Grand Lodge will withhold or withdraw recognition from another, but the two most common are Exclusive Jurisdiction and Regularity . Exclusive Jurisdiction is a concept whereby normally only one Grand Lodge will be recognised in any geographical area. If two Grand Lodges claim jurisdiction over the same area, the other Grand Lodges will have to choose between them, and they may not all decide to recognise

1368-434: Is progressively taught the meanings of the symbols of Freemasonry and entrusted with grips, signs, and words to signify to other members that he has been so initiated. The degrees are part allegorical morality play and part lecture. These three degrees form Craft (or Blue Lodge) Freemasonry, and members of any of these degrees are known as Free-Masons , Freemasons or Masons . Once the Craft degrees have been conferred upon

1440-481: Is that each candidate must be "free and of good reputation". The question of freedom, a standard feudal requirement of mediaeval guilds, is nowadays one of independence: the object is that every Mason should be a proper and responsible person. Thus, each Grand Lodge has a standard minimum age, varying greatly and often subject to dispensation in particular cases. (For example, in England the standard minimum age to join

1512-548: Is the Lodge . These private Lodges are usually supervised at the regional level (usually coterminous with a state, province, or national border) by a Grand Lodge or Grand Orient. There is no international, worldwide Grand Lodge that supervises all of Freemasonry; each Grand Lodge is independent, and they do not necessarily recognise each other as being legitimate. Lodges are found around the world and on all populated continents; however due to anti-Masonry and laws that effectively ban

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1584-457: Is the annual installation of the Master of the Lodge and his appointed or elected officers. In some jurisdictions, an Installed Master elected, obligated, and invested to preside over a Lodge, is valued as a separate rank with its own secrets and distinctive title and attributes; after each full year in the chair the Master invests his elected successor and becomes a Past Master with privileges in

1656-424: Is the basic organisational unit of Freemasonry. The Lodge meets regularly and conducts the usual formal business of any small organisation (approve minutes , elect new members, appoint officers and take their reports, consider correspondence, bills and annual accounts, organise social and charitable events, etc.). In addition to such business, the meeting may perform a ceremony to confer a Masonic degree or receive

1728-485: Is the ordinate of the intersection. The branch of the arcsin with a r > π / 2 {\displaystyle a_{r}>\pi /2} is to be taken if d 2 < R 2 − r 2 {\displaystyle d^{2}<R^{2}-r^{2}} . The area of the triangle is Δ = 1 2 y d {\displaystyle \Delta ={\frac {1}{2}}yd} . The area of

1800-432: Is upon candidates to ask to join; while they may be encouraged to ask, they may not be invited. Once the initial inquiry is made, a formal application may be proposed and seconded or announced in open Lodge and a more or less formal interview usually follows. If the candidate wishes to proceed, references are taken up during a period of notice so that members may enquire into the candidate's suitability and discuss it. Finally,

1872-531: The Bible , the Quran , or other religious scripture be open in a working lodge, that every member professes belief in a Supreme Being , that no women be admitted, and that the discussion of religion and politics do not take place within the lodge; and Continental Freemasonry , which consists of the jurisdictions that have removed some, or all, of these restrictions. The basic, local organisational unit of Freemasonry

1944-631: The Holy Royal Arch , which is linked to Mark Masonry in Scotland and Ireland, but completely separate in England. In England, the Royal Arch is closely associated with the Craft, automatically having many Grand Officers in common, including H.R.H the Duke of Kent as both Grand Master of the Craft and First Grand Principal of the Royal Arch. The English Knights Templar and Cryptic Masonry share

2016-547: The Landmarks of Freemasonry , which elude any universally accepted definition. Candidates for Freemasonry will usually have met the most active members of the Lodge they are joining before being elected for initiation. The process varies among Grand Lodges, but in modern times interested people often look up a local Lodge through the Internet and will typically be introduced to a Lodge social function or open evening. The onus

2088-497: The Lodge of Edinburgh (Mary's Chapel) No. 1 in Scotland show a continuity from an operative lodge in 1598 to a modern speculative Lodge. It is reputed to be the oldest Masonic Lodge in the world. Alternatively, Thomas De Quincey in his work titled Rosicrucians and Freemasonry put forward the theory that suggested that Freemasonry may have been an outgrowth of Rosicrucianism . The theory had also been postulated in 1803 by German professor; J. G. Buhle . The first Grand Lodge,

2160-595: The Nordic countries , the Swedish Rite is dominant; a variation of it is also used in parts of Germany. Freemasonry describes itself as a "beautiful system of morality, veiled in allegory and illustrated by symbols". The symbolism is mainly, but not exclusively, drawn from the tools of stonemasons – the square and compasses , the level and plumb rule, the trowel , the rough and smooth ashlars , among others. Moral lessons are attributed to each of these tools, although

2232-479: The Swedish Rite ), for example, accepts only Christians. At the other end of the spectrum, "Liberal" or Continental Freemasonry , exemplified by the Grand Orient de France , does not require a declaration of belief in any deity and accepts atheists (the cause of the distinction from the rest of Freemasonry). During the ceremony of initiation, the candidate is required to undertake an obligation, swearing on

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2304-608: The United Grand Lodge of England . The Grand Lodge of Ireland and the Grand Lodge of Scotland were formed in 1725 and 1736, respectively, although neither persuaded all of the existing lodges in their countries to join for many years. The earliest known American lodges were in Pennsylvania . The collector for the port of Pennsylvania, John Moore, wrote of attending lodges there in 1715, two years before

2376-760: The United States , Masonic membership is organized in two systems, first through 51 Conservative Grand Lodges - one for each state plus the District of Columbia . While these Grand Lodges once boasted over 4 million members in 1957, membership has declined sharply. According to the Masonic Service Association of North America, current combined membership across these jurisdictions stands at approximately 875,000 members. Additionally, there are 46 Prince Hall Grand Lodges in amity with UGLE, operating across various U.S. states. Prince Hall Masonry

2448-404: The abscissa of the intersecting rims is The sign of x , i.e., d 2 {\displaystyle d^{2}} being larger or smaller than R 2 − r 2 {\displaystyle R^{2}-r^{2}} , distinguishes the two cases shown in the images. The ordinate of the intersection is Negative values under the square root indicate that

2520-524: The seals of ecclesiastical organizations can be enclosed within a vertically oriented vesica piscis (instead of the more usual circular enclosure). Also, the ichthys symbol incorporates the vesica piscis shape. Ecclesiastical heraldry of the Catholic Church appeared first in seals, nearly all vesica-shaped. The vesica piscis has been used within Freemasonry , most notably in the shapes of

2592-529: The second world war from 33,000 in 1960 to 53,000 in 2023. Relations between Grand Lodges are determined by the concept of Recognition . Each Grand Lodge maintains a list of other Grand Lodges that it recognises. When two Grand Lodges recognise and are in Masonic communication with each other, they are said to be in amity , and the brethren of each may visit each other's Lodges and interact Masonically. When two Grand Lodges are not in amity, inter-visitation

2664-404: The "craft" by being progressively "initiated", "passed" and "raised" into the three degrees of Craft, or Blue Lodge Masonry. During these three rituals, the candidate is progressively taught the Masonic symbols, and entrusted with grips or tokens, signs, and words to signify to other Masons which degrees he has taken. The dramatic allegorical ceremonies include explanatory lectures and revolve around

2736-473: The Grand Lodge of London and Westminster, later called the Grand Lodge of England , was founded on St John's Day , 24 June 1717, when four existing London Lodges met for a joint dinner. Over the next decade, most of the existing Lodges in England joined the new regulatory body, which itself entered a period of self-publicity and expansion. New lodges were created, and the fraternity began to grow. During

2808-583: The Lodge and Grand Lodge. In other jurisdictions, the grade is not recognised, and no inner ceremony conveys new secrets during the installation of a new Master of the Lodge. Most Lodges have some sort of social functions, allowing members, their partners, and non-Masonic guests to meet openly. Often coupled with these events is the discharge of every Mason's and Lodge's collective obligation to contribute to charity. This occurs at many levels, including in annual dues, subscriptions, fundraising events, Lodges and Grand Lodges. Masons and their charities contribute for

2880-427: The Lodge takes an officially secret ballot on each application before a candidate is either initiated or rejected. The exact number of adverse ballots ("blackballs") required to reject a candidate varies between Masonic jurisdictions. As an example, the United Grand Lodge of England only requires a single "blackball", while the Grand Lodge of New York requires three. A minimum requirement of every body of Freemasons

2952-791: The Mark Grand Lodge offices and staff at Mark Masons Hall. The Ancient and Accepted Rite (similar to the Scottish Rite), requires a member to proclaim the Trinitarian Christian faith, and is administered from Duke Street in London. Conversely, the Societas Rosicruciana in Anglia is a fully independent esoteric organization that requires members be United Grand Lodge of England Master Masons . In

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3024-552: The Premiere Grand Lodge had adopted. As an insult, the self proclaimed "Antient Grand Lodge" coined the term "modern" to designate the Premiere Grand Lodge (historians now use Premiere Grand Lodge and Antient Grand Lodge – to differentiate the two bodies). These two Grand Lodges vied for supremacy until the Premiere Grand Lodge made a compromise with the antient Grand Lodge to return to a ritual that worked for both Grand Lodges. They re-united on 27 December 1813 to form

3096-652: The United Grand Lodge of England in 1929: Blue Lodges, known as Craft Lodges in the United Kingdom, offer only the three traditional degrees. In most jurisdictions, the rank of past or installed master is also conferred in Blue/Craft Lodges. Master Masons are able to extend their Masonic experience by taking further degrees, in appendant or other bodies whether or not approved by their own Grand Lodge. The Ancient and Accepted Scottish Rite

3168-460: The United States, though both have experienced significant membership declines since their mid-20th century peaks. Grand Orient de France , the largest jurisdiction in Continental or Liberal Freemasonry in terms of membership, is over 53,000 members spread across approximately 1,381 lodges for an average of 38 members per Lodges. The Grand Orient de France has been growing in membership since

3240-526: The areas of two triangles and four segments, we obtain the area of the vesica piscis: The two circles of the vesica piscis, or three circles forming in pairs three vesicae, are commonly used in Venn diagrams . Arcs of the same three circles can also be used to form the triquetra symbol, and the Reuleaux triangle . In Christian art , some aureolas are in the shape of a vertically oriented vesica piscis, and

3312-414: The assignment is by no means consistent. The meaning of the symbolism is taught and explored through ritual, and in lectures and articles by individual Masons who offer their personal insights and opinions. According to the scholar of Western esotericism Jan A. M. Snoek: "the best way to characterize Freemasonry is in terms of what it is not, rather than what it is". All Freemasons begin their journey in

3384-465: The asymmetric lens is A = a r r 2 + a R R 2 − y d {\displaystyle A=a_{r}r^{2}+a_{R}R^{2}-yd} , where the two angles are measured in radians. [This is an application of the Inclusion-exclusion principle : the two circular sectors centered at (0,0) and (d,0) with central angles 2

3456-554: The collars worn by officiants of the Masonic rituals. It was also considered the proper shape for the enclosure of the seals of Masonic lodges. The vesica piscis is also used as a proportioning system in architecture, in particular Gothic architecture . The system was illustrated in Cesare Cesariano 's 1521 version of Vitruvius 's De architectura , which he called "the rule of the German architects". The vesica piscis

3528-510: The construction of the Temple of Solomon , and the artistry and death of the chief architect, Hiram Abiff . The degrees are those of "Entered apprentice", "Fellowcraft" and "Master Mason". While many different versions of these rituals exist, with various lodge layouts and versions of the Hiramic legend, each version is recognizable to any Freemason from any jurisdiction. In some jurisdictions,

3600-472: The coordinate x {\displaystyle x} of the lens centre lies outside the line that connects the circle centres: [REDACTED] By eliminating y from the circle equations x 2 + y 2 = r 2 {\displaystyle x^{2}+y^{2}=r^{2}} and ( x − d ) 2 + y 2 = R 2 {\displaystyle (x-d)^{2}+y^{2}=R^{2}}

3672-593: The course of the 18th century, as aristocrats and artists crowded out the craftsmen originally associated with the organization, Freemasonry became fashionable throughout Europe and the American colonies . Between 1730 and 1750, the Grand Lodge endorsed several significant changes that some Lodges could not endorse. A rival Grand Lodge was formed on 17 July 1751, which called itself the " Antient Grand Lodge of England " to signify that, in their opinion, these lodges were maintaining older traditions and rejected changes that

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3744-487: The degree of Fellowcraft ; and then raised to the degree of Master Mason . In each of these ceremonies, the candidate must first take the new obligations of the degree, and is then entrusted with secret knowledge including passwords, signs and grips ( secret handshakes ) confined to his new rank. Although these symbols and gestures are nominally secret, they are readily found in public sources, including those published by Masonic organizations themselves. Another ceremony

3816-457: The first evidence of ceremonial regalia. There is no clear mechanism by which these local trade organisations became today's Masonic Lodges. The earliest rituals and passwords known, from operative lodges around the turn of the 17th–18th centuries, show continuity with the rituals developed in the later 18th century by accepted or speculative Masons, as those members who did not practice the physical craft gradually came to be known. The minutes of

3888-406: The fundamental aims of regular Freemasonry. Some jurisdictions have formalized this arrangement through written agreements that specifically outline the terms of shared jurisdiction. Regularity is a concept based on adherence to Masonic Landmarks , the basic membership requirements, tenets and rituals of the craft. Each Grand Lodge sets its own definition of what these landmarks are, and thus what

3960-448: The increasing recognition of Prince Hall Grand Lodges , a branch of Freemasonry created for African Americans. Historically, many "mainstream" or conservative U.S. Grand Lodges refused to recognize Prince Hall Grand Lodges operating in their states, citing Exclusive Jurisdiction. However, this began to change in 1989 when the Grand Lodge of Connecticut extended recognition to its Prince Hall counterpart. This initial recognition created

4032-419: The largest Masonic jurisdiction worldwide. However, its membership has declined dramatically - from about 500,000 members in the 1960s to approximately 175,000 in 2021. The organization is structured into various Provincial Grand Lodges at the local level. Similarly, the Grand Lodge of Ireland has experienced a steep decline, with membership falling from 100,000 in 1960 to around 19,000 members currently. In

4104-558: The law. In most Lodges, the oath or obligation is taken on a Volume of Sacred Law , whichever book of divine revelation is appropriate to the religious beliefs of the individual brother (usually the Bible in the Anglo-American tradition). In Progressive continental Freemasonry, books other than scripture are permissible, a cause of rupture between Grand Lodges. Since the middle of the 19th century, Masonic historians have sought

4176-518: The lens area.] A lens with a different shape forms the answer to Mrs. Miniver's problem , on finding a lens with half the area of the union of the two circles. Lenses are used to define beta skeletons , geometric graphs defined on a set of points by connecting pairs of points by an edge whenever a lens determined by the two points is empty. Freemasonry Freemasonry (sometimes spelled Free-Masonry ) or simply Masonry includes various fraternal organisations that trace their origins to

4248-425: The local guilds of stonemasons that, from the end of the 14th century, regulated the qualifications of stonemasons and their interaction with authorities and clients. Freemasonry is the oldest fraternity in the world and among the oldest continued organizations in history. Modern Freemasonry broadly consists of two main recognition groups: Regular Freemasonry , which insists that a “volume of sacred law”, such as

4320-536: The main themes of each degree are illustrated by tracing boards . These painted depictions of Masonic themes are exhibited in the lodge according to which degree is being worked and are explained to the candidate to illustrate the legend and symbolism of each degree. The idea of Masonic brotherhood probably descends from a 16th-century legal definition of a "brother" as one who has taken an oath of mutual support to another. Accordingly, Masons swear at each degree to support and protect their brethren unless they have broken

4392-478: The manner they find most satisfying. Some will simply enjoy the dramatics, or the management and administration of the lodge, others will explore the history, ritual and symbolism of the craft, others will focus their involvement on their Lodge's sociopolitical side, perhaps in association with other lodges, while still others will concentrate on the lodge's charitable functions. Grand Lodges and Grand Orients are independent and sovereign bodies that govern Masonry in

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4464-531: The origins of the movement in a series of similar documents known as the Old Charges , dating from the Regius Poem in about 1425 to the beginning of the 18th century. Alluding to the membership of a lodge of operative masons , they relate it to a mythologised history of the craft, the duties of its grades, and the manner in which oaths of fidelity are to be taken on joining. The 15th century also sees

4536-566: The putative formation of the first Grand Lodge in London. The Grand Lodge of England appointed a Provincial Grand Master for North America in 1731, based in Pennsylvania, leading to the creation of the Grand Lodge of Pennsylvania . In Canada, Erasmus James Philipps became a Freemason while working on a commission to resolve boundaries in New England and, in 1739, he became provincial Grand Master for Nova Scotia ; Philipps founded

4608-533: The relief of need in many fields, such as education, health and old age. Private Lodges form the backbone of Freemasonry, with the sole right to elect their own candidates for initiation as Masons or admission as joining Masons, and sometimes with exclusive rights over residents local to their premises. There are non-local Lodges where Masons meet for wider or narrower purposes, such or in association with some hobby, sport, Masonic research, business, profession, regiment or college. The rank of Master Mason also entitles

4680-404: The religious volume sacred to his personal faith to do good as a Mason. In the course of three degrees, Masons will promise to keep the secrets of their degree from lower degrees and outsiders, as far as practicality and the law permit, and to support a fellow Mason in distress. There is formal instruction as to the duties of a Freemason, but on the whole, Freemasons are left to explore the craft in

4752-415: The rims of the two circles do not touch because the circles are too far apart or one circle lies entirely within the other. The value under the square root is a biquadratic polynomial of d . The four roots of this polynomial are associated with y=0 and with the four values of d where the two circles have only one point in common. The angles in the blue triangle of sides d , r and R are where y

4824-519: The ritual, the number of officers present, the layout of the meeting room, etc. varies from jurisdiction to jurisdiction. Almost all officers of a Lodge are elected or appointed annually. Every Masonic Lodge has a Master, two Wardens, a treasurer and a secretary. There is also always a Tyler , or outer guard, outside the door of a working Lodge, who may be paid to secure its privacy. Other offices vary between jurisdictions. Each Masonic Lodge exists and operates according to ancient principles known as

4896-402: The same one. (In 1849, for example, the Grand Lodge of New York split into two rival factions, each claiming to be the legitimate Grand Lodge. Other Grand Lodges had to choose between them until the schism was healed. ) Exclusive Jurisdiction can be waived when the two overlapping Grand Lodges are themselves in amity and agree to share jurisdiction. For example, since the Grand Lodge of Connecticut

4968-413: The shape's name is mandorla (" almond "). A similar shape in three dimensions is the lemon . This figure appears in the first proposition of Euclid's Elements , where it forms the first step in constructing an equilateral triangle using a compass and straightedge . The triangle has as its vertices the two disk centers and one of the two sharp corners of the vesica piscis. Mathematically,

5040-661: The tradition, it does not have a presence in every country. In the spirit of brotherhood and hopefulness, however, Freemasons usually presume that clandestine lodges may nonetheless exist in those countries in which it is banned, even if they may not actually exist. The degrees of Freemasonry are the three grades of medieval craft guilds : Entered Apprentice , Journeyman or Fellow of the craft (now called either “Fellowcraft” or “Fellow Craft” in English speaking jurisdictions, and “Companion” in non-English speaking jurisdictions), and Master Mason . The candidate of these three degrees

5112-499: The vesica piscis is a special case of a lens , the shape formed by the intersection of two disks. The mathematical ratio of the height of the vesica piscis to the width across its center is the square root of 3 , or 1.7320508... (since if straight lines are drawn connecting the centers of the two circles with each other and with the two points where the circles intersect, two equilateral triangles join along an edge). The ratios 265:153 = 1.7320261... and 1351:780 = 1.7320513... are two of

5184-515: Was a leitmotif of architect Carlo Scarpa and is used as a "viewing device" in Tomba Brion ( Brion Cemetery ) in San Vito d'Altivole , Italy. Several other artworks or designs have also featured this shape: Various symbolic meanings have been associated with the vesica piscis: Lens (geometry) If the two arcs of a lens have equal radius, it is called a symmetric lens , otherwise

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