Euclid (c. 325 BC – 265 BC) – Greek Mathematician considered the “Father of Geometry”. His textbook ‘Elements’ remained a highly influential mathematics teaching book until the late 19th Century and is one of the most widely published books in the world. It has had a lasting influence on the sciences -, especially in mathematics. […]
Delve into the world of Euclid, the renowned mathematician, and uncover 11 facts about his life, contributions, and enduring legacy.
August 8, 2010 (updated September 3, 2010) by Tim Barker The "Seal of Melchizedek" is becoming a popular icon within modern Latter-day Saint culture, generally popularized by stories regarding the design of the San Diego Temple, and briefly discussed by Hugh Nibley, in his Temple and Cosmos: Beyond This Ignorant Present. Brother Nibley includes an illustration by Michael Lyon of the below mosaic, and describes it as follows: Another Ravenna mosaic, c. A.D. 520, shows the priest-king Melchizedek in a purple cloak, offering bread and wine at the altar (Genesis 14:18-20). The white altar cloth is decorated with two sets of gammadia, as well as the so-called "seal of Melchizedek," two interlocked squares in gold. Abel offers his lamb as Abraham gently pushes Isaac forward. The hand of God reaches down to this sacred meeting through the red veils adorned with golden gammadia on either side. The theme is the great sacrifice of Christ, which brings together the righteous prophets from the past as well as the four corners of the present world, thereby uniting all time and space."1 The Three Sacrifices of the Old Testament. Abel, Melchisedec, and Abraham (6th-7th century). Mosaic, Ravenna, Basilica of Sant'Apollinare in Classe.2 This mosaic is particularly interesting since the imagery so strongly depicts symbols of Christ in the temple setting. Righteous Abel is shown offering a lamb at the altar, a similitude of Christ who is the "Lamb of God."3 Abraham offers Isaac at the altar, illustrating his willing obedience to keep God's commandment in sacrificing his only son. Isaac symbolizes Christ as the sacrifice of the Only Begotten Son, and Abraham symbolizes God the Father in sacrificing his only son.4 Melchizedek stands at the head of the altar with bread and wine, foreshadowing the institution of the sacrament as taught by Christ to his disciples, who were to partake of the sacraments in remembrance of the Lord's body and blood which was offered in the great atoning sacrifice.5 In addition, Melchizedek himself was a significant symbol of Christ as the High Priest and King, this however, will be treated more fully in another post. This gathered offering is taking place at the altar before the veil of the temple, where the curtains are parted and the hand of God reaches through. The open veil illustrates the fulfillment of Christ's atonement wherein the temple veil was rent in twain from top to bottom so that all can potentially come unto God and enter into the holy of holies.6 Additionally, the rent veil "figured also the pierced body of the Saviour..."7 A number of other symbols of Christ exist within the mural, however, it is not within the scope of this study to delve into every detail. Amidst all of these symbols, however, the "so-called seal of Melchizedek" is at the forefront. After noting the commonalities between each of these symbols, it can hardly be doubted whether this "seal" also has a Christmatic connection. One apocryphal source connects Melchizedek's seal directly with the Priesthood. Translated from Slavonic in 1896, The Book of the Secrets of Enoch, discusses the birth and life of Melchizedek. This apocryphal source is believed to date back to some time between 50 B.C. and 70 A.D. Nir is identified as Lamech's son, Noah's brother ("Noe"), and the father of Melchizedek, although he did not father Melchizedek (the birth of Melchizedek without an earthly father is another type of Christ). At Melchizedek's birth, it is stated: And Noe, and Nir were tempted with a great fear, for the child was complete in its body, like one of three years old; and spake with its lips, and blessed the Lord. And Noe, and Nir gazed upon it; and lo! the seal of the priesthood was on its breast, and it was glorious in countenance.8 While the validity of this apocryphal text cannot be entirely measured, it is interesting to note that the seal is directly linked to the priesthood. In the scriptures, Melchizedek is refered to as a High Priest, which is an office belonging to the highest order of the priesthood. Paul declared that Jesus was "made an high priest forever after the order of Melchisedec," and Alma, the son of Alma, stated that Melchizedek was a High Priest after the Order of the Son. This order, according to latter-day revelation was called the "Melchizedek Priesthood," because "Melchizedek was such a great high priest. Before his day it was called the Holy Priesthood, after the Order of the Son of God."9 In the Joseph Smith Translation, the scriptures are given added clarity in that this order of priesthood, rather than Melchizedek, was "without father, without mother, without descent, having neither beginning of days, nor end of life." It is additionally stated that, "all those who are ordained unto this priesthood are made like unto the Son of God, abiding a priest continually."10 As Christ is eternal, so is this priesthood, which is after His Order. It appears reasonable that there is a distinct connection between Melchizedek's seal of the priesthood, and the Holy Priesthood after the Order of the Son. With this connection we can better understand Alma's teachings (which directly precedes his discourse on Melchizedek), regarding the ordination to the holy priesthood being a type of Christ, as Christ was foreordained to be from Eternity to all Eternity, so were those priests after His Order.11 Another mosaic shows Melchizedek and Abel in an outdoor setting. This mosaic is from a different Basilica in Ravenna, Italy. In this case, the hand of God reaches down from the heavens, rather than through the veil. The presence of the altar of God lends the scenario to being another temple motif. Abel and Melchizedek, Ravenna mosaic, Basilica of San Vitale In this image the lamb and the sacramental offerings are present. We can better see the seal of Melchizedek in this image, and note that two concentric circles are included within the interlocked squares. It is provided below for a closer (although fuzzier) look: Another version of the eight-pointed star associated with Melchizedek appears in a Masonic work in 1905, based on the "47th Problem of Euclid." Euclid of Alexandria is commonly known as the "Father of Geometry." Around 300 B.C., he produced a thirteen volume work, entitled Elements, which became the standard mathematical textbook for approximately two-thousand years. These volumes included a collection of "geometry, proportion, and number theory." The 47th problem was extracted from Book 1 of Euclid's tome.12 The 47th proposition postulates that "in a right-angled triangle the square on the side subtending the right-angle is equal to the (sum of the) squares on the sides surrounding the right-angle." For anybody who has taken a geometry course, this should seem familiar since it is equivalent to the pythagorean theorem, which is illustrated by the equation a2 + b2 = c2. "Most of the theorems appearing in the Elements were not discovered by Euclid himself, but were the work of earlier Greek mathematicians such as Pythagoras (and his school), Hippocrates of Chios, Theaetetus of Athens, and Eudoxus of Cnidos."13 Freemasons have made particular mention of Euclid's 47th problem in numerous publications, including its connection with Pythagoras, the Egyptians, and its symbol of morality, representing "the ideal of perfection."14 It has been noted as one of the emblems of the Masonic third degree, and serves to teach Masons to be "lovers of the arts and sciences."15 Euclidean Geometry is recognized by Masons because it has been thought that this "system embraces the Masonic philosophy expressed in mathematical terms."16 This is explained by noting that "the geometrical constructions employed in the Elements are restricted to those which can be achieved using a straght-rule and a compass."17 Obviously, the compass and square (straight-rule) figure predominantly in Freemasonry. In 1905, Henry Pelham Holmes Bromwell published his Restorations of Masonic Geometry and Symbolry Being a Dissertation on the Lost Knowledges of the Lodge, wherein this equation from Euclidean geometry was extrapolated to construct an eight-pointed star. As the geometric problem illustrates above, the triangle is made up of three angles, one angle being 90 degrees and the other two are both 45 degrees. By eliminating the 90 degree angle, and inserting in it's place another 45 degree angle (all lines being equal in length), an eight-pointed star is created that continues infinitely. This star, Bromwell explains, is identified as the "Signet of Melchizedek."18 Bromwell gives us some meaning as to its significance, but doesn't elaborate on its connection specifically with Melchizedek. The famous Masonic encyclopedia compiled by Albert Gallatin Mackey states that "in Masonry, Melchizedek is connected with the order or degree of High Priesthood, and some of the high degrees...[and] was the founder of an Order of Priesthood."19 Perhaps H.P.H. Bromwell was familiar with the eight-pointed star constructed by the two interlocking squares, and simply redesigned the symbol by incorporating Euclidean geometry to connect Melchizedek into this ideal of perfection. In any case, it is interesting that another version of the eight-pointed star has a direct connection with Melchizedek, and in this case also, Masonry connects him with the Order or High Priesthood of Melchizedek. All of this leaves us curious. What further meaning do these symbols have? Are they recorded in ancient history? Why is there no mention of this iconography within the scriptures? My discussion of the subject at this point is far from conclusive, but rather, I hope it opens a door for further research. Symbols are significant within Mormon culture and always carry theological implications. Any study of the connection of the eight-pointed star and its connection with Melchizedek can only garner further light and educate us in relation to this interesting curiosity. A historical study regarding the documentation of this symbol in art or writing may prove fruitful since it appears to have survived through the ages. It would make for an interesting study if the artist who created these 6th-7th century mosaics had documented anything in connection with these motifs (it appears to be the same artist in either case). What particular meaning did he attach to the seal? Likewise, an investigation into the existence of other known illustrations or descriptions of the seal from different time periods may provide further enlightenment. Lastly, there seems to be a connection between the Star of David (or Seal of Solomon) with Melchizedek. At this point, I have been unable to find anything substantial in connecting the two. Perhaps a further study of this connection may prove fruitful as well. From a Latter-day Saint perspective, it is interesting to note that Melchizedek is seen in a temple setting as a type of Christ, and that he is identified as a High Priest holding the Priesthood after the Order of the Son of God. It is no wonder that his seal is represented on Latter-day temples where the fullness of the Melchizedek priesthood ordinances are administered for those who are willing to take upon them the name of Christ and keep His commandments.20 Joseph Smith taught that "if a man gets a fullness of the priesthood of God he has to get it in the same way that Jesus Christ obtained it, and that was by keeping all the commandments and obeying all the ordinances of the house of the Lord."21 In the temple, all of these elements come together wherein the Holy Priesthood can seal us to eternal life and we become one with Him who is from all Eternity to all Eternity. ____________________________ 1 Hugh Nibley, Temple and Cosmos: Beyond This Ignorant Present, ed. Don Norton (The Collected Works of Hugh Nibley, 19 Vols.; Salt Lake City: Deseret Book Company, and Provo, UT: Foundation for Ancient Research and Mormon Studies [FARMS], 1992), 12:109 2 William J. Hamblin and David Rolph Seely, Solomon's Temple: Myth and History (London: Thames & Hudson, 2007), 111 3 See the following scriptures: Leviticus 3:6-7, Isaiah 53:7, Jeremiah 11:29, John 1:29, Revelations 12:11 and 13:8, 1 Nephi 11-14, Alma 7:14, and Moses 7:47 4 See the following scriptures: Genesis 22:2-14, Hebrews 11:17-19, and Jacob 4:5. Abraham also serves as a symbol of Christ since he sought to be a "prince of peace" and a High Priest, and as a symbol of the Father since he sought to be a "father" of many nations (Abraham 1:2). It is also interesting to note that Isaac was to be offered as a burnt offering (Genesis 22:3, 7-8), the same as the lamb was offered as a burnt offering (Numbers 7, 28, 29). These offerings were known as sacrifice offerings since they occurred on the altar of sacrifice. The offering of his own life by the Savior was the great sacrifice that all other sacrifices represented. 5 See the following scriptures: Luke 22:19-20, Moroni 4:1-3, and Moroni 5:1-2 6 See the following scriptures: Matthew 27:51, Hebrew 6:19. Among many studies on this subject, it has been stated, that "the solemn ritual of the great Day of Atonement was fulfilled in the one Sacrifice now offered upon the cross. Such rituals were no longer needed. God himself opens the way into the most holy place. His people may draw near, very near, into his immediate presence. All may come, not the high priest only, but all faithful Christians; for he who washed us from our sins in his own blood hath made us priests unto God and his Father, to offer up spiritual sacrifices, acceptable unto God through him;" in Reverend H.D.M. Spence, D.D. and Reverend Joseph S. Exell, M.A., The Pulpit Commentary: St. Matthew (Volume 2; London: Kegan Paul, Trench, Trubner, & Co., 1894), 612 7 Spence and Exell, The Pulpit Commentary: St. Matthew, 612. While commentary on the other items in the mosaic would only add further enlightenment, it is beyond the scope of this study to do so. 8 W.R. Morfill and R.H. Charles, The Book of the Secrets of Enoch: Translated from the Slavonic (Oxford: Oxford Clarendon Press, 1896), Appendix, 90 (emphasis added); for dating of the text, see The Jewish Encyclopedia (12 Vols.; New York: Funk and Wagnalls Company, 1903), 5:182 9 Hebrews 6:20, Alma 13:14, Doctrine & Covenants 107:1-2 10 Hebrews 7:3 (JST) 11 Alma 13:1-9 (especially vs. 7); D&C 39:1 12 Euclid, The Elements of Euclid; VIZ: The First Six Books, Together with the Eleventh and Twelfth, ed. Robert Simson (London: S. Hamilton, 1816), 392; also see Richard Fitzpatrick, Euclid's Elements (self published, 2007), 4 13 Fitzpatrick, Euclid's Elements, 46, 4 (respectively) 14 I. Edward Clark, Royal Secret (Whitefish, MT: Kessinger Publishing, 1995), 93, 203-204; Charles Clyde Hunt, Masonic Symbolism (Whitefish, MT: Kessinger Publishing, 1942), 141-154; Joseph White Norwood, "Evolution of Masonic Sybmols VIII," in The American Tyler-Keystone 26/1 (July 5, 1911):280 15 Hunt, Masonic Symbolism, 142 16 Norwood, "Evolution of Masonic Symbols VIII," 280 17 Fitzpatrick, Euclid's Elements, 4 18 Henry Pelham Holmes Bromwell, Restorations of Masonic Geometry and Symbolry Being a Dissertation on the Lost Knowlege of the Lodges (Denver, CO: H.P.H. Bromwell Masonic Publishing Company, 1905), 170 19 Albert G. Mackey, An Encyclopaedia of Freemasonry and its Kindred Sciences (Philadelphia, PA: Moss and Company, 1874), 496, 6 (respectively) 20 Joseph Smith, Jr., Teachings of the Prophet Joseph Smith, ed. Joseph Fielding Smith, Jr. (Salt Lake City: Deseret News Press, 1965), 237 21 Smith, Teachings of the Prophet Joseph Smith, 308
Scientists are trying to melt a thin layer of ice that is increasingly clouding the vision of the "dark universe detective" space telescope Euclid, the European Space Agency said on Tuesday.
Mathematicians are often overlooked for their contributions to history.We've curated the 20 mathematicians who changed the world.
Includes, with special title pages: Notes, critical and geometrical (p. [297]-362); Euclid's Data (p. [363]-477); The elements of plane and spherical...
His most innovative educational work was a version of 'Euclid's Elements' which used coloured graphic explanations of each geometric principle. It was...
Науковці отримали перші повноколірні знімки з телескопа Euclid, на яких зафіксовані різні куточки Всесвіту з безліччю деталей.
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Mathematical Chronology Age of Geometry – Euclid (325-365 BC) is the Father of Geometry Age of Algebra – Al-Khwarizmi (780-850 AD) is the Father of Algebra Age of Analytic Geometry …
Euclid, the most prominent mathematician of Greco-Roman antiquity, best known for his geometry book, the Elements. It is sometimes said that, other than the Bible, the Elements is the most translated, published, and studied of all the books produced in the Western world.
His most innovative educational work was a version of 'Euclid's Elements' which used coloured graphic explanations of each geometric principle. It was...
Art.com | We Are Art We exist so you can have the art you love. Art.com gives you easy access to incredible art images and top-notch craftsmanship. High-Quality Framed Art Prints Our high-end framed wall art is printed on premium paper using non-toxic, archival inks that protect against UV light to resist fading. Experience unmatched quality and style as you choose from a wide range of designs to enhance your room décor. Professionally Crafted Framed Wall Art Attention to detail is at the heart of our process, as we exclusively use 100% solid wood frames that include 4-ply white core matboard and durable, frame-grade clear acrylic for clarity, long-lasting protection of the artwork and unrivaled quality. With a thoughtfully selected frame and mat combination, this piece is designed to complement your art and create a visually appealing display. Easy-to-Hang & Ready-to-Display Artwork Each framed art piece comes with hanging hardware affixed to the back of the frame, allowing for easy and convenient installation. Ready to display right out of the box. Handcrafted in the USA. Figurative Art Think reality delights? You bet your walls do too. So, why not introduce them to our collection of figurative art. Make acquaintance with inspiring muses of famous masters or get a glimpse of pop culture icons caught on camera. Any masterpieces you choose will give your space a unique story to share in our handcrafted frames. This genre of art involves a realistic depiction of living as well as inanimate objects. Artists like Jean Michel Basquiat, Norman Rockwell, and Banksy are renowned for giving a platform to cultural commentary and human experiences through their art. The Print This art print displays sharp, vivid images with a high degree of color accuracy. A member of the versatile family of art prints, this high-quality reproduction represents the best of both worlds: quality and affordability. Art prints are created using a digital or offset lithography press. Paper Type: Art Print Finished Size: 12" x 18" Arrives by Fri, Apr 26 Product ID: 55571051106A
His most innovative educational work was a version of 'Euclid's Elements' which used coloured graphic explanations of each geometric principle. It was...
Euclid, the most prominent mathematician of Greco-Roman antiquity, best known for his geometry book, the Elements. It is sometimes said that, other than the Bible, the Elements is the most translated, published, and studied of all the books produced in the Western world.
Released in December 2017 in five weights. Italics followed in July 2018. Type Designers: Emmanuel Rey, Swiss Typefaces. Foundry: Swiss Typefaces
About The Artwork Euclid´uncertainties, abstract, expressionism, oil on canvas. Original Created: 2015 Subjects: Fantasy Materials: Canvas Styles: Abstract Expressionism Conceptual Mediums: Oil Details & Dimensions Painting: Oil on Canvas Original: One-of-a-kind Artwork Size: 9.8 W x 12.6 H x 0.1 D in Frame: Not Framed Ready to Hang: Not applicable Packaging: Ships Rolled in a Tube
Images and Interactives for Euclid (Greek mathematician)
