Book on the Measurement of Plane and Spherical Figures information
Mathematical treatise by the Banū Mūsā
The Book on the Measurement of Plane and Spherical Figures (Arabic: كتاب معرفة مساحة الأشكال البسيطة والكريّة, Kitāb maʿrifah masāḥat al-ashkāl al-basīṭah wa-al-kuriyyah)[note 1] was the most important of the works produced by the Banū Mūsā.[2] A Latin translation by the 12th century Italian astrologer Gerard of Cremona was made, entitled Liber trium fratrum de geometria and Verba filiorum Moysi filii Sekir. The original work in Arabic was edited by the Persian polymath Naṣīr al‐Dīn al‐Ṭūsī in the 13th century.[3] The original work in Arabic is not extant, but its contents are known from later translations.[4]
The treatise, which is about geometry, was similar to two books by Archimedes, On the measurement of the circle and On the sphere and the cylinder.[3] It was used extensively in the Middle Ages, and was quoted by authors such as Thābit ibn Qurra, Ibn al‐Haytham, Leonardo Fibonacci (in his Practica geometriae), Jordanus de Nemore, and Roger Bacon.[5] It deals with the geometrical concepts of area and volume, angle trisection, construction, and conic sections.[6] It includes theorems not known to the Greeks.[7]
The book was re-published in Latin with an English translation by the American historian Marshall Clagett, who has also summarized how the work influenced mathematicians during the Middle Ages.[8]
^ abO'Connor, J.J.; Robertson, E.F. (1999). "Banu Musa brothers". MacTutor. University of St Andrews. Retrieved 18 March 2023.
^Pascual 2015, p. 117.
^Casulleras 2007.
^Papadopoulos 2016, p. 5.
^al-Dabbagh 1970, p. 445.
^Pingree 1988.
Cite error: There are <ref group=note> tags on this page, but the references will not show without a {{reflist|group=note}} template (see the help page).
and 26 Related for: Book on the Measurement of Plane and Spherical Figures information
used to specify the position of a point, but they may also be used to specify the position of more complex figures such as lines, planes, circles or spheres...
The parallel postulate of Euclidean geometry is replaced with: For any given line R and point P not on R, in theplane containing both line R and point...
There are 13 books in the Elements: Books I–IV and VI discuss plane geometry. Many results about planefigures are proved, for example, "In any triangle,...
. Here two cases of non-Euclidean geometry are considered—spherical geometry and hyperbolic plane geometry; in each case, as in the Euclidean case for...
base unit ofmeasurement for a base quantity (and dimension) of "plane angle". Quincey's review of proposals outlines two classes of proposal. The first option...
latitude of a point is the angle formed between the vector perpendicular (or normal) to the ellipsoidal surface from the point, andtheplaneofthe equator...
metabolism and animal behavior. The study andmeasurementof solar irradiance have several important applications, including the prediction of energy generation...
known as spherical astrolabe, armilla, or armil) is a model of objects in the sky (onthe celestial sphere), consisting of a spherical framework of rings...
Catoptrics concerns the mathematical theory of mirrors, particularly the images formed in planeandspherical concave mirrors, though the attribution is sometimes...
spherical (and actually orbits the Sun, influenced by the heliocentric theory of Aristarchus of Samos). A parallel later ancient measurementofthe size...
al-Tūsī. In his Onthe Sector Figure, he stated the law of sines for planeandspherical triangles and provided proofs for this law. In the 9th century,...
measurement'; from γῆ (gê) 'earth, land', and μέτρον (métron) 'a measure') is a branch of mathematics concerned with properties of space such as the distance...
context, the shape is sometimes called a spherical triangle, which should not be confused with spherical triangle meaning a triangle onthe surface of a sphere...
Geometry (from the Ancient Greek: γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships. Geometry...
instrument involving the stereographic projection: "Hipparchus long ago hinted at the unfolding of a spherical surface [on a plane], so as to keep a proper...
long distances and very sensitive measurements, their finite speed has noticeable effects. Any starlight viewed on Earth is from the distant past, allowing...
spherical trigonometry by resolving the polar measurements directly into their Cartesian components. Following the conception ofthe torquetum, the device...
Palimpsest include: On the Equilibrium ofPlanesOn Spirals Measurementof a Circle Onthe Sphere and Cylinder On Floating Bodies The Method of Mechanical Theorems...
cylindrical color model is the early-20th-century Munsell color system. Albert Munsell began with a spherical arrangement in his 1905 book A Color Notation, but...
consisting of all points in a plane that are at a given distance from a given point, the centre. The distance between any point ofthe circle andthe centre...
measurable figures. I also realized: that in the system in which they find themselves bound, they must be restricted primarily to a plane, because they...
meet), and other linear subspaces, which exhibit the principle of duality. The simplest illustration of duality is in the projective plane, where the statements...
techniques. Depending onthe application, measurement microphones must be tested periodically (every year or several months, typically) and after any potentially...