Who is the 1st century BC Roman architect who wrote that the figure of a man can be inscribed both in a circle and a square in his best known work De architectura?
"Vitruvius Marcus Vitruvius Pollio (; c. 80–70 BC – after c. 15 BC), commonly known as Vitruvius, was a Roman author, architect, civil engineer and military engineer during the 1st century BC, known for his multi-volume work entitled ""De architectura"". His discussion of perfect proportion in architecture and the human body led to the famous Renaissance drawing by Leonardo da Vinci of ""Vitruvian Man"". By his own description Vitruvius served as an artilleryman, the third class of arms in the military offices. He probably served as a senior officer of artillery in charge of ""doctores ballistarum"" (artillery experts) and ""libratores"""
"Vinci: the human body inscribed in the circle and the square (the fundamental geometric patterns of the cosmic order). In this book series, Vitruvius, also wrote about climate in relation to housing architecture and how to choose locations for cities. Vitruvius is sometimes loosely referred to as the first architect, but it is more accurate to describe him as the first Roman architect to have written surviving records of his field. He himself cites older but less complete works. He was less an original thinker or creative intellect than a codifier of existing architectural practice. It should also be noted"
"of the arts, the Italian techniques became part of the training of artists across Europe, and later other parts of the world. The culmination of these Renaissance traditions finds its ultimate synthesis in the research of the architect, geometer, and optician Girard Desargues on perspective, optics and projective geometry. The ""Vitruvian Man"" by Leonardo da Vinci(c. 1490) depicts a man in two superimposed positions with his arms and legs apart and inscribed in a circle and square. The drawing is based on the correlations of ideal human proportions with geometry described by the ancient Roman architect Vitruvius in Book III"
"century BCE. He was the most prominent architectural theorist in the Roman Empire known today, having written ""De architectura"" (known today as ""The Ten Books of Architecture""), a treatise written in Latin and Greek on architecture, dedicated to the emperor Augustus. Probably written between 27 and 23 BCE, it is the only major contemporary source on classical architecture to have survived. Divided into ten sections or ""books"", it covers almost every aspect of Roman architecture, from town planning, materials, decorations, temples, water supplies, etc. It rigorously defines the classical orders of architecture. It also proposes the three fundamental laws that"
"of these. In Book III, Chapter 1, Paragraph 3, Vitruvius writes about the proportions of man... It was upon these writings that Leonardo da Vinci based his Vitruvian Man. Vitruvius described the human figure as being the principal source of proportion. The drawing itself is often used as an implied symbol of the essential symmetry of the human body, and by extension, of the universe as a whole. In the introduction to book seven, Vitruvius goes to great lengths to present why he is qualified to write ""De Architectura"". This is the only location in the work where Vitruvius specifically"
"Vitruvian Man The Vitruvian Man (, which is translated to ""The proportions of the human body according to Vitruvius""), or simply L'Uomo Vitruviano (), is a drawing made by the Italian polymath Leonardo da Vinci around 1490. It is accompanied by notes based on the work of the architect Vitruvius. The drawing, which is in ink on paper, depicts a man in two superimposed positions with his arms and legs apart and inscribed in a circle and square. The drawing and text are sometimes called the ""Canon of Proportions"" or, less often, ""Proportions of Man"". It is kept in the"
"known as the golden ratio, which was studied by the ancient Greeks and has been considered the ideal architectural ratio for centuries. The circle and the square that are combined so dramatically in the atrium were considered to be the paradigmatic geometric units by the ancient Roman architect Vitruvius. He also noted that the human body is proportioned so that it can fit in both shapes, a concept that was famously expressed with a combined circle and square by Leonardo da Vinci in his drawing ""Vitruvian Man"". The specifications of the academy's building committee called for a large number of"
"of squaring the circle, he did not do so using ruler and compass alone, and so it was clear to the Greeks that his solution violated the foundational principles of their mathematics. Over 2,200 years later Ferdinand von Lindemann would prove that it is impossible to square a circle using straight edge and compass alone. Dinostratus Dinostratus (; c. 390 – c. 320 BCE) was a Greek mathematician and geometer, and the brother of Menaechmus. He is known for using the quadratrix to solve the problem of squaring the circle. Dinostratus' chief contribution to mathematics was his solution to the"
"of his friend Giacomo Andrea de Ferrara, a Renaissance architect and an expert on Vitruvius. Andrea's drawing features erasure marks indicating its unique creation. As with Leonardo's ""Vitruvian Man"", Andrea's circle is centered on the naval, but only one pose is included. Leonardo's design includes two sets of arms and legs to touch both the circle and the square. The text is in two parts, above and below the image. The upper part paraphrases Vitruvius: The lower section of text gives these proportions: The points determining these proportions are marked with lines on the drawing. Below the drawing is a"
"the diagonal of a square. His authority was so great that architects and other artists continued using this proportion, even when ignorant of its source, as late as the Middle Ages. Another early idea — one that was to be espoused by many illustrious writers and artists of various periods — found perfection in the circle and the sphere. Aristotle wrote in the ""Physica"" that the circle was ""the perfect, first, most beautiful form."" Cicero wrote in ""De Natura Deorum"" (On the Nature of the Gods): ""Two forms are the most distinctive: of solids, the sphere... and of plane figures,"
"accompanying text, written in mirror writing, it was made as a study of the proportions of the (male) human body as described in Vitruvius' ""De architectura"" 3.1.2–3, which reads: Leonardo's drawing combines a careful reading of the ancient text with his own observation of actual human bodies. In drawing the circle and square he observes that the square cannot have the same centre as the circle, but is centered at the groin. This adjustment is the innovative part of Leonardo's drawing and what distinguishes it from earlier illustrations. He also departs from Vitruvius by drawing the arms raised to a"
"sculpture, is a familiar Hellenistic structure, characteristically sited along sacred ways or in open places in sanctuaries, such as at Delos or Epidaurus. Some Hellenistic exedras were built in relation to a city's agora, as in Priene. Monument architects have also used this free-standing style in modern times. The exedra achieved particular popularity in Roman architecture during the Roman Empire. In the 1st century AD, Nero's architects incorporated exedrae throughout the planning of his ""Domus Aurea"", enriching the volumes of the party rooms, a part of what made Nero's palace so breathtakingly pretentious to traditional Romans, for no one had"
"of Hadrian. While all that is fictional, the book follows the known facts of Apollodorus' life (and accepts the account of his death at Hadrian's hands). Apollodorus of Damascus Apollodorus of Damascus () was a Syrian-Greek engineer, architect, designer and sculptor from Damascus, Roman Syria, who flourished during the 2nd century AD. Apollodorus was a favourite of Trajan, for whom he constructed Trajan's Bridge over the Danube, for the 105–106 campaign in Dacia. He also designed Trajan's Forum, the Temple of Trajan, and Trajan's Column within the city of Rome, beside several smaller projects. Apollodorus also designed the triumphal arches"
"Vitruvius, a Roman author and engineer, wrote the oldest extant design manual in 27 BC. ""De architectura libri decem"" (""Ten Books on Architecture"") addressed design theory, landscape architecture, engineering, water supply, and public projects, such as parks and squares. Vitruvius asserted that ""firmitas"" (firmness, durability, strength), ""utilitas"" (commodity, convenience, utility) and ""venustas"" (delight, loveliness, beauty) were the primary objectives of design. Some still consider these elements essential to quality design of landscape. After the emergence of the first civilizations, wealthy persons began to create gardens for purely aesthetic purposes. Egyptian tomb paintings of the 16th century BC are some of"
"given to Marin Mersenne. Beginning with the work of Moritz Cantor and Siegmund Günther, scholars now assign priority to French mathematician Charles de Bovelles based on his description of the cycloid in his ""Introductio in geometriam"", published in 1503. In this work, Bovelles mistakes the arch traced by a rolling wheel as part of a larger circle with a radius 120% larger than the smaller wheel. Galileo originated the term ""cycloid"" and was the first to make a serious study of the curve. According to his student Evangelista Torricelli, in 1599 Galileo attempted the quadrature of the cycloid (constructing a"
"New World. He also looks at its place in the history of map-making from the days of the second-century Greek-Egyptian geographer Ptolemy and his treatise on geography. His second book, ""Da Vinci's Ghost"" (2011), tells the story of the ""Vitruvian Man"", Leonardo da Vinci's well-known drawing of a man inside a circle and a square. He explains how, in the first century BC, Vitruvius based his understanding of architecture on the principle that it should conform to the ""members of a well-shaped man"" and that it depended on squares and circles. Lester explores the relationships between Vitruvius' emperor Augustus and"
"Adriaan van den Spiegel Adriaan van den Spiegel (or Spieghel), name sometimes written as Adrianus Spigelius, (1578 – 7 April 1625) was a Flemish anatomist born in Brussels. For much of his career he practiced medicine in Padua, and is considered one of the great physicians associated with the city. At Padua he studied anatomy under Girolamo Fabrici. His best written work on anatomy is ""De humani corporis fabrica libri X tabulis aere icisis exornati"", published posthumously in 1627. He borrowed the title from ""De humani corporis fabrica"", written by his fellow countryman, Vesalius, who had also studied in Padua."
"a point on the quadratrix. The quadratrix is mentioned in the works of Proclus (412–485), Pappus of Alexandria (3rd and 4th centuries) and Iamblichus (c. 240 – c. 325). Proclus names Hippias as the inventor of a curve called quadratrix and describes somewhere else how Hippias has applied the curve on the trisection problem. Pappus only mentions how a curve named quadratrix was used by Dinostratus, Nicomedes and others to square the circle. He neither mentions Hippias nor attributes the invention of the quadratrix to a particular person. Iamblichus just writes in a single line, that a curve called a"
"Isidore of Miletus Isidore of Miletus (; ; ) was one of the two main Byzantine Greek architects (Anthemius of Tralles was the other) that Emperor Justinian I commissioned to design the cathedral Hagia Sophia in Constantinople from 532 to 537. The creation of an important compilation of Archimedes' works has been attributed to him. The spurious Book XV from Euclid's Elements has been partly attributed to Isidore of Miletus. Isidore of Miletus was a renowned scientist and mathematician before Emperor Justinian I hired him. Isidorus taught stereometry and physics at the universities, first of Alexandria then of Constantinople, and"
"and centers of gravity of various geometric figures including triangles, paraboloids, and hemispheres. Archimedes's work on this and his work on calculus and geometry, together with Euclidean geometry, underpin much of the mathematics and understanding of structures in modern structural engineering. The ancient Romans made great bounds in structural engineering, pioneering large structures in masonry and concrete, many of which are still standing today. They include aqueducts, thermae, columns, lighthouses, defensive walls and harbours. Their methods are recorded by Vitruvius in his De Architectura written in 25 BC, a manual of civil and structural engineering with extensive sections on materials"
"curve was alluded to by Proclus in his commentary on Euclid and attributed to Diocles by Geminus as early as the beginning of the 1st century. Fragments of a work by Diocles entitled ""On burning mirrors"" were preserved by Eutocius in his commentary of Archimedes' ""On the Sphere and the Cylinder"". Historically, ""On burning mirrors"" had a large influence on Arabic mathematicians, particularly on al-Haytham, the 11th-century polymath of Cairo whom Europeans knew as ""Alhazen"". The treatise contains sixteen propositions that are proved by conic sections. One of the fragments contains propositions seven and eight, which is a solution to"
"that contains all information about this science. He is also noted as the inventor of a sundial suitable for any specific region, as noted by Vitruvius, a Roman architect, engineer and author most famous for treatise On Architecture [1] . While there are no details of Theodosius every creating a sundial, there is little information discrediting what Vitruvius stated. Theodosius’ contributions consist of three works that make up the Sphaerics. The book contains to trigonometry and it was written to aid Euclid’s Elements in making up for the lack of results on the geometry if the sphere [2]. The works"
"it became the first printed book on architecture in 1485. It was partly based on Vitruvius's ""De architectura"" and, via Nicomachus, Pythagorean arithmetic. Alberti starts with a cube, and derives ratios from it. Thus the diagonal of a face gives the ratio 1:, while the diameter of the sphere which circumscribes the cube gives 1:. Alberti also documented Filippo Brunelleschi's discovery of linear perspective, developed to enable the design of buildings which would look beautifully proportioned when viewed from a convenient distance. The next major text was Sebastiano Serlio's ""Regole generali d'architettura"" (General Rules of Architecture); the first volume appeared"
"Bernward of Hildesheim, and St. Thomas Aquinas. In 1244 the Dominican friar Vincent of Beauvais made a large number of references to ""De architectura"" in his compendium of all the knowledge of the Middle Ages """"Speculum maius"""". Many copies of ""De architectura"", dating from the 8th to the 15th centuries, did exist in manuscript form during the Middle Ages and 92 are still available in public collections, but they appear to have received little attention, possibly due to the obsolescence of many specialized Latin terms used by Vitruvius and the loss of most of the original 10 illustrations thought by"
"an apse and four rounded corners of a vast rectangular interior. This was interpreted by mediaeval architects as representing the mundane below (the square base) and the divine heavens above (the soaring spherical dome). The emperor Justinian used two geometers, Isidore of Miletus and Anthemius of Tralles as architects; Isidore compiled the works of Archimedes on solid geometry, and was influenced by him. The importance of water baptism in Christianity was reflected in the scale of baptistry architecture. The oldest, the Lateran Baptistry in Rome, built in 440, set a trend for octagonal baptistries; the baptismal font inside these buildings"
"Apollodorus of Damascus Apollodorus of Damascus () was a Syrian-Greek engineer, architect, designer and sculptor from Damascus, Roman Syria, who flourished during the 2nd century AD. Apollodorus was a favourite of Trajan, for whom he constructed Trajan's Bridge over the Danube, for the 105–106 campaign in Dacia. He also designed Trajan's Forum, the Temple of Trajan, and Trajan's Column within the city of Rome, beside several smaller projects. Apollodorus also designed the triumphal arches of Trajan at Beneventum and others at Ancona. He is widely credited as the architect of the third iteration of the Pantheon, and cited as the"
"Den Danske Vitruvius Den Danske Vitruvius I-II (English: ""The Danish Vitruvius I-II"") is a richly illustrated 18th-century architectural work on Danish monumental buildings of the period, written by the Danish Baroque architect Lauritz de Thurah. It was commissioned by Christian V in 1735 and published in two volumes between 1746 and 1749. The title refers to the Roman architect and engineer Vitruvius, who published ""De architectura"" in the 1st century AD, an authoritative treatise on the architecture of the time. The direct inspiration for de Thurah's ""Den Danske Vitruvius"" was Colen Campbell's ""Vitruvius Britannicus"". With its numerous illustrations, ""Den Danske"
"though Varro granted that Numa could not have been a Pythagorean since he lived before Pythagoras himself. Antiquitates rerum humanarum et divinarum Antiquitates rerum humanarum et divinarum was one of the chief works of Marcus Terentius Varro (1st century BC). The work has been lost, but having been substantially quoted by Augustine in his ""De Civitate Dei"" (published AD 426) its contents can be reconstructed in parts. To a lesser extent, quotes from the work have also been transmitted by other authors, including (among others) Pliny (1st c.), Gellius (2nd c.), Censorinus (3rd c.), Servius (4th/5th c.), Nonius (4th/5th c.),"
"Cesare Cesariano Cesare di Lorenzo Cesariano (1475–1543) was an Italian painter, architect and architectural theorist. He authored the first Italian-language version of Vitruvius' ""De architectura"". Cesariano was born in Milan. Information about his life is scarce. In 1496 he lived for a period at Reggio Emilia; in the early 1500s he worked at Parma, where he painted the sacristy of San Giovanni Evangelista. In 1507 he was in Rome, where he met Perugino, Pinturicchio and Luca Signorelli. However, most of his activity was in Milan, where he returned in 1512-1513 as military engineer at Maximilian Sforza's court. He worked at"
"refine and implement their work. The oldest surviving book on architecture, ""De architectura"" by the Roman architect Vitruvius describes the design and construction of towns, buildings, clocks, and machines, but provides no information about the organization of the architect's assistants. It is generally accepted that throughout most of human history, most architects were wealthy individuals who derived their primary income from activities other than design and who practiced design as a part-time pursuit, employing assistants on a project-by-project basis. It was only in the 19th century that architecture began to be practiced as a full-time profession, when specific training and"
"of circles. The earliest known copy of the text is in Arabic. The scholars T.L. Heath and Marshall Clagett argued that it cannot have been written by Archimedes in its current form, since it quotes Archimedes, suggesting modification by another author. The ""Lemmas"" may be based on an earlier work by Archimedes that is now lost. It has also been claimed that Heron's formula for calculating the area of a triangle from the length of its sides was known to Archimedes. However, the first reliable reference to the formula is given by Heron of Alexandria in the 1st century AD."
"into the Vitruvian Man drawing by Leonardo da Vinci. The latter drawing was itself based on the much older writings of the Roman architect Vitruvius. Islamic geometric patterns are well known too, which are used in the Qu'ran, Mosques and even in the caligraphies of personal names. The Agamas are a collection of Sanskrit, Tamil, and Grantha scriptures chiefly constituting the methods of temple construction and creation of idols, worship means of deities, philosophical doctrines, meditative practices, attainment of sixfold desires, and four kinds of yoga. Elaborate rules are laid out in the Agamas for Shilpa (the art of sculpture)"
"Leon Battista Alberti, whose many talents truly epitomised the Renaissance Man, wrote the ""Descriptio urbis Romae"", where he proposed a system for a geometric arrangement of the city centered on the Capitol. He later became the architectural advisor to Pope Nicholas V, and was involved in a number of projects at the Vatican. Shortly after they arrived in town Beato Angelico and French Jean Fouquet began a series of frescoes in St. Peter's, which testifies to the presence of the nascent interest in Flemish painting and the Nordic generally. Although the duration of the pontificate of Eugene IV did not"